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FACULTY WORKING PAPER NO. 89-1609
Communication Structures, Incentive Systems and Coordinated Decision Making
William N. Dilla Marya L. Leatherwood Richard J. Boland
College of Commerce and Business Administration Bureau of Economic and Business Research University of Illinois Urbana-Champaign
BEBR
FACULTY WORKING PAPER NO. 89-1609
College of Commerce and Business Administration
University of Illinois at Urb ana -Champaign
October 1989
Communication Structures, Incentive Systems and Coordinated Decision Making
William N. Dilla
Assistant Professor of Accountancy
University of Illinois at Urbana- Champaign
Marya L. Leatherwood
Assistant Professor of Business Administration
University of Illinois at Urbana- Champaign
Richard J. Boland
Professor of Management Information Systems
Case Western Reserve University
Please do not quote without permission
We would like to acknowledge the assistance of John Chandler, Karen Gaddis , and the Office for Information Management research programming staff. We would also like to acknowledge Steve Silvis' sessions. Financial and programming assistance was provided by the Office for Information Management in the College of Commerce, University of Illinois at Urbana- Champaign.
COMMUNICATION STRUCTURES, INCENTIVE SYSTEMS AND COORDINATED DECISION MAKING
ABSTRACT
Organizations are increasingly using information technologies as a means for coordinating the independent decision making activities of individual agents. Two important factors which facilitate such coordination are organizational communication pattern and the nature of incentives provided to individual agents.
In this paper, we investigate the effects on organizational performance of different communication structures, under both conflicting and nonconf licting incentive schemes. We report the results of a laboratory experiment designed to test hypotheses based on prescriptive design viewpoints espoused by Ackoff (1967) and Rappaport (1968) against hypotheses based on game-theoretic and decision-theoretic models. Student participants were paired into dyads and assigned the role of either a purchasing or merchandising manager. Participant teams were compensated based on one of two incentive schemes (conflicting and nonconf licting) and given one of three types of communication structures (no communication, unidirectional communication, and bidirectional communication) .
The results show that teams with communication performed significantly better than those with no access, regardless of incentives structure. For conflicting incentives, this is consistent with the predictions of a game-theoretic model. For nonconf licting incentives, this is inconsistent with the assumption of perfect_rationality, but consistent with alternative views on communication .
The analyses indicated no significant differences in performance between a simple, unidirectional communication structure, and a bidirectional structure, where a series of messages was sent between agents. Thus, for tasks such as the one examined in this study, a rudimentary communication system may achieve effective coordination of decision making. Also, learning effects are stronger and more consistent under nonconf licting incentives than under conflicting, indicating more effective coordination may be possible with nonconf licting than with conflicting incentives.
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http://www.archive.org/details/communicationstr1609dill
COMMUNICATION STRUCTURES, INCENTIVE SYSTEMS AND COORDINATED DECISION MAKING
In today's organizational environments, decision issues are increasingly modularized and distributed among individual managers who must interact with each other to coordinate their independent decision making. In many cases, these managers are located at widely dispersed sites. Therefore, organizations are turning to information technologies as a medium for coordinating their activities in a distributed decision making environment. The emergence of organizational environments with modularized tasks has stimulated research on new principles of organization design to facilitate the interaction of individual agents (Huber, 1984; Huber and McDaniel, 1986; Malone 1987; Malone and Smith, 1988) .
In this research, a number of factors which expedite effective coordination have been identified. Among these, the organizational communication pattern is considered to be particularly important. The structure of linkages between agents (e.g., Malone 1987; Malone and Smith, 1988), as well as the manner in which messages are distributed (Huber, 1982) are both posited to have significant effects on organizational performance. A second factor, which has received somewhat less emphasis, is the nature of incentives provided to agents within the organization. Huber and McDaniel (1986) indicate that decision units should be rewarded for the quality of their decisions, but give only very general guidance as to the types of reward systems that should be implemented.
The prescriptive management information systems literature also has addressed communication and incentives issues relevant to the design of systems which are compatible with the structures and processes of user organizations. A classic article by Ackoff (19 67) gives advice on whether or not to allow communications between decision makers, as well as on other design factors. In particular, Ackoff indicates that restrictions should be placed on communication between agents in order to enhance corporate
performance outcomes when agents are assigned to maximize divergent goals. In a response to Ackoff, Rappaport (1967) cautions that the degree of information access afforded agents may not be the crux of the problem. Instead, Rappaport suggests that organizational incentives need to be considered when designing information systems, as well. He argues that full communication between agents may be in the interest of an organization, if corporate incentive schemes are "appropriate" and "nonconf licting" .
In this study, we investigate the effects on organizational performance of allowing communication access between agents, under both conflicting and nonconf licting incentives schemes. For conflicting incentives, we develop and test a set of hypotheses which posit that communication may be a beneficial coordination mechanism, contrary to the viewpoint espoused by Ackoff (1967) . The hypotheses are based on the assumption that individual agents act strategically. That is, agents consider the results of both their own actions and those of others in their environment when making decisions. This viewpoint is consistent with the assumptions of game-theoretic models, which have been applied to a variety of problems in business, economics, and public policy (e.g., Schotter and Schwodiauer, 1980; Ponssard, 1981; Shubik, 1982) .
For nonconf licting incentives, we test Rappaport â– s viewpoint that communication will facilitate coordination of agents' activities when they have "appropriate" measures of performance. We also test a competing hypothesis which assumes that agents will approach the nonconflicting incentives scenario as a joint expected value maximization problem, where communication is not necessary to achieve an optimal solution.
In addition, we investigate the effects on performance of different types of communication structures, both under conflicting and nonconflicting incentives. This is done by comparing a simple communication structure, where a single message
between agents is allowed, to a more complex one where multiple messages are allowed prior to agents' making a decision. We tested the propositions regarding communication in a simulated retailing environment similar to the one described by Ackoff (1967) , in which participants assumed the role of merchandising or purchasing managers.
THEORETICAL DEVELOPMENT AND HYPOTHESES
Conflicting Incentives: The Ackoff Scenario
In his article, "Management Misinformation Systems", Ackoff (1967) described a retailing organization in which an information system provided full access to data and complete communication between two managers (merchandising and purchasing) . The merchandising manager was evaluated based on gross sales; the purchasing manager was evaluated based on inventory turnover. Merchandising set the firm's selling prices, while purchasing determined order quantities. Merchandising made selling price decisions and order quantity requests based on optimistic estimates of sales demand. On the other hand, purchasing would consistently order less than merchandising had requested, not wanting to be penalized for poor inventory turnover. Upon learning of purchasing's actions, merchandising then would raise its selling price, after which purchasing would again lower its order quantity. According to Ackoff, this cycle of actions would continue if left unchecked, resulting in progressively deteriorating performance for the organization as a whole. His proposed solution is to stop all communication between the two managers and force them to "guess what the other was doing." His specific example is reproduced in Appendix A.
Conflicting Incentives: A Strategic Viewpoint
A fundamental problem with the Ackoff scenario is that the managers apparently ignore the effects their own actions would have on subsequent actions of the other manager. This is inconsistent with a strategic, or game -theoretic view of the
world. We show here that the managers in Ackoff's scenario should be better off with communication than without, if they act in a strategic fashion.
First, consider the case where the managers must "guess what the other is doing", as Ackoff recommends. Figure 1 represents this case as a game in extensive form. The diagram is drawn as if merchandising first makes a price decision, purchasing makes a quantity decision, then a random market outcome occurs. However, the oval around the purchasing manager's nodes on the game tree indicates that purchasing's information set at the time he makes an order quantity decision does not include the selling price set by merchandising. Therefore, the game operates as if both managers were making their decisions simultaneously. The problem facing the managers is to determine a pair of actions such that neither individual, assuming the other is committed to their choice, can increase their payoff by unilaterally changing strategies. This pair of actions yields an equilibrium point (e.g., Shubik, 1982, p. 240).
A version of the Ackoff scenario with communication is shown in Figure 2. Here, the merchandising manager first chooses a price, which is communicated to purchasing. Then, purchasing chooses an order quantity, after which a random state of nature is realized. Merchandising knows that for a given selling price, purchasing will choose the order quantity that yields the highest expected value of inventory turnover. Therefore, merchandising must choose the selling price that yields the highest expected value of gross sales, in anticipation of purchasing's actions. This pair of actions is an equilibrium point for the scenario with communication. Even if one allows the managers to communicate price and quantity information back and forth several times before a state realization occurs, as occurs in Ackoff's example, it is still only the final price and quantity decisions that affect the payoffs to the two managers. Therefore, the complete Ackoff
scenario can be modelled using a game tree such as that in Figure 2 .
Insert Figures 1 and 2 about here.
Appendix B gives a numeric example for the Ackoff scenario which shows that the expected payoffs to both managers are greater when communication is allowed than when it is suppressed. Also, Appendix B uses a game theory result by Dubey and Shubik (1981) to show how in most cases, both managers will be better off with communication than without.
Another case to consider is what occurs when the Ackoff scenario is played out over a series of repeated trials. The game-theoretic analysis outlined here thus far presumes a single- period setting. However, players in a repeated noncooperative game may achieve outcomes which are Pareto improvements over single-period equilibrium outcomes through cooperation. They may play as if they were playing a cooperative, or bargaining game, since if one player "defects" from a cooperative solution, the other can "punish" him by changing strategies on the next round (Luce and Raiffa, 1957; Friedman, 1977) . Therefore, it is possible that even pairs of managers with limited communication may achieve Pareto-optimal outcomes by coordinating their actions over time. However, it is still likely that pairs with communication will be better off than those without since the noncooperative "starting point" with communication yields higher expected payoffs for both managers than without.
Conflicting Incentives: Hypotheses
Based on the above discussion, there are two divergent hypotheses concerning performance under conflicting incentives when communication is and is not allowed.
Hia (Ackoff) : With conflicting incentives, performance
outcomes will be less for dyads with communication than without .
Hib (Strategic) : With conflicting incentives, performance outcomes will be greater for dyads with communication than without .
Nonconflicting Incentives
As stated in the introduction, Rappaport (1968) suggests that communication between agents may be beneficial, if corporate incentive schemes are "appropriate" and "nonconflicting". However, he does not specify the "nonconflicting" incentives he had in mind. For purposes of this study, we operationalize a "nonconflicting" incentives scheme as an equal division of gross margin less inventory holding costs. The nonconflicting scheme is described more fully in Appendix C.
As shown in Appendix C, compensation for the two agents has a unique maximum. From a decision-theoretic viewpoint, communica- tion should not be necessary for the agents to jointly select the price and quantity that will yield maximum compensation, if both are expected value maximizers (i.e., are risk-neutral) . Even if one or both of the agents is not risk-neutral, outcome feedback from each trial conveys information about preferences. Therefore, they should be able to infer each others' risk preferences after a series of trials.
On the other hand, there may be limits to agents' abilities to infer each others' preferences. Not only is this a difficult problem to begin with, but it may be further complicated by individual preferences which are not stable across time. It seems reasonable to expect that allowing communication between agents under nonconflicting incentives may provide additional information that will assist them in overcoming their cognitive limitations. Indeed, March and Simon (1958, Ch. 6) indicate that communication between agents is one means by which organizations serve to mitigate the effects of individual agents' bounded rationality.
Rappaport (1968) does not explicitly mention this idea, but his assertions regarding communication as an aid to the decision maker are consistent with March and Simon's ideas.
Hypotheses concerning the effects of communication on performance under nonconflicting incentives are as follows.
H2A (Rappaport) : With nonconflicting incentives,
performance outcomes will be greater for dyads with communication than without.
H2B (Joint EV Maximization) : With nonconflicting
incentives, there will be no difference in performance outcomes for dyads with and without communication.
Degree of Communication
The prescriptive literature discussed above does not specify the form or amount of communication afforded agents within an information system. Ackoff describes a fairly rich communication structure, with multiple messages between agents. On the other hand, Rappaport ' s discussion of a nonconflicting incentives setting indicates communication may be beneficial, without indicating a precise communication structure.
The strategic analysis in this paper is quite specific about communication structure under conflicting incentives. It shows that a significant improvement in performance outcomes can be achieved by allowing a single message to be sent from the merchandising to the purchasing manager. Other messages could be sent prior to the final price and quantity decisions, but the predicted outcomes for such settings should be identical to the game diagrammed in Figure 2. This is because outcomes for the two managers depend only on the final price and quantity decisions. As far as final outcomes are concerned, messages sent before the final decisions are irrelevant.
There is a possibility, however, that allowing more than a single message between agents may affect performance outcomes . This argument follows from bounded rationality considerations similar to those discussed above. Specifically, the analysis in
Appendix B presumes risk-neutral agents. Like the nonconf licting incentives case, if one or both of the agents are not risk- neutral, they must infer each others1 risk preferences over a series of trials. On the other hand, allowing agents to communicate their intended moves previous to taking final actions conveys additional information about their preferences beyond that contained in the outcome feedback from each trial of the game. In particular, this communication structure gives both agents information about each others' preferences during the course of each trial, while the communication structure diagrammed in Figure 2 only gives the purchasing manager information about the merchandising manager's preferences. In the rest of the paper, we will refer to a communication structure which allows multiple messages between agents as bidirectionalf to distinguish it from the unidirectional structure diagrammed in Figure 2.
H3 : With conflicting incentives, performance outcomes will be greater for dyads with bidirectional communication than with unidirectional communication.
Likewise, we can make a similar set of arguments about the effects of bi- versus unidirectional communication with nonconf licting incentives, as well.
H4 : With nonconf licting incentives, performance outcomes will be greater for dyads with bidirectional communication than with unidirectional communication.
METHOD
Experimental Task and Design
To test the above hypotheses, we conducted an experiment in which student participants were randomly paired into dyads and assigned the role of either a merchandising or purchasing manager. Participants' incentive schemes were either conflicting, as in the Ackoff example, or nonconf licting, as suggested by Rappaport . Under the conflicting scheme, merchandising managers were compensated for the gross margin earned during each period of the experiment. Compensation for purchasing managers was based on
inventory turnover. The conflicting compensation scheme was operationalized using the parameters described in Appendix B. The nonconflicting incentive scheme was an equal division of gross margin less inventory holding costs. The nonconflicting scheme is described more fully in Appendix C.
There were three types of communication structures within each incentives condition: no, unidirectional, and bidirectional communication. With no communication, the managers made their decisions simultaneously. (See Figure 3.) Participants did, however, learn the other manager's decision after the state outcome for each period was realized. With unidirectional communication, merchandising managers made a price decision and transmitted it to the purchasing manager. The purchasing manager then made a quantity decision. With bidirectional communication, merchandising managers made initial price (PI) and quantity (Ql) decisions and transmitted Ql to the purchasing manager. The purchasing manager then made an initial quantity (Q2) decision, and transmitted this figure to the merchandising manager. The merchandising manager made a revised price (P2) decision, which was revealed to the purchasing manager, who then made a final quantity (Q3) decision. In both partial and full access, the merchandising manager received feedback on the final quantity decision, once the outcomes for the period were realized.
Insert Figure 3 about here.
Experimental Procedure
The participants were students at a large midwestern university. They were recruited from senior and graduate (MBA and Ph.D.) level business classes. Participants were assigned to experimental groups so that the proportion of each type of student was approximately equal in each group. There were ten dyads in each of the six experimental groups, for a total of 60 dyads or
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120 participants. All participants completing a given session were in the same experimental group. "Points" earned during the experiment (the compensation measures described in Appendices B & C) were converted into cash at the end of the experiment at the rate of 10,000 points = 1 cash dollar. In addition, participants were also paid a flat fee of $3.00 for completing a post- experimental questionnaire. The incentives were designed so that the average compensation for a two hour experimental session would be approximately $15.00.
Participants completed the task on networked microcomputers, using specialized software developed for the experiment. They simulated 18 periods of operations, indicating pricing or purchasing decisions for each period. Market demand levels were generated at random by the computer. These were displayed to the participants at the end of each period along with the actions taken by their partners and themselves, as well as other pertinent data.
Experiment Software
The experiment software incorporates a display which allowed participants to view data relevant to their decisions. Participants used a mouse to access data. During each period of an experiment, participants viewed one of four types of screens: (1) analysis, (2) decision, (3) results, or (4) history.
The analysis screen allows access to data necessary to make decisions in each period. At the beginning of the period, all data on the screen is hidden from view. To access data, a participant must select a display mode, an order quantity, and a row or column from the display matrix by clicking the appropriate boxes with the mouse (Figure 4) .
Participants use the decision screens to enter prices and order quantities (Figure 5) . These screens are also entirely mouse-driven. The results screen appears at the end of every
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period (Figure 6) . This is a "passive" screen in that all data are displayed; one need not use the mouse to view items on this screen. After the first period, participants may use the history screen to review the results of previous periods (Figure 7) . As with the analysis screen, one must use the mouse to view data, which is displayed either by period or by data type.
Insert Figures 4, 5, 6, and 7 about here.
RESULTS
Dependent Variables
In order to assess the affects of communication structure on performance outcomes in the conflicting condition, we analyzed three dependent variables: gross margin, inventory turnover, and efficiency. Gross margin and inventory turnover are measures of each individual agent's welfare under the various types of communication access. They are calculated as discussed in Appendix B. Efficiency (EFc) is a measure of the overall quality of decision outcomes for each conflicting condition dyad. It is defined as follows:
E (PERFC) EFc " E(OPTc)
where :
E(PERFc) = EV of (gross margin + (inventory turnover * 1000)) for actions actually taken during a period
E (OPTc) = Highest possible EV of (gross margin + (inventory turnover * 1000) ) .1
In the nonconf licting condition, we analyzed two dependent variables: net compensation (e.g., gross margin less holding costs, as defined in Appendix C) and efficiency. Both of these are measures of the overall quality of decision outcomes for each
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nonconflicting condition dyad. Efficiency in the nonconflicting condition (EFnc) is defined as follows:
. E (PERFNc) EFnc E(OPTNc)
where :
E(PERFnc) = EV of (gross margin - inventory holding costs) for actions actually taken during a period
E (OPTNc) = Highest possible EV of (gross margin - inventory holding costs)
Tables 1 and 2 show the mean values of the dependent variables for the nonconflicting and conflicting conditions.
Insert Tables 1 and 2 about here.
Tests of Hypotheses
No communication versus communication allowed:
Hia and Hib were tested by comparing the dependent variable means for dyads with no communication to the average of the means for dyads with unidirectional and bidirectional communication, within the conflicting incentives condition. The multivariate test of this contrast is highly significant (Wilks A, = 0.56;
F(3,25) = 6.67; p = 0.002). Univariate contrasts are statistically significant for all three dependent variables (See Table 3) .2 For all three variables, the means with communciation are greater than without, consistent with Hib/ i.e., with the predictions of the game-theoretic model.
Insert Table 3 about here
The multivariate test of H2a and H2b (no communication vs. communication with nonconflicting incentives) is also highly significant (Wilks X = 0.44; F(2,26) = 16.56; p < 0.001), as are
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the univariate tests of both nonconflicting condition dependent variables (See Table 4) . Again, the partial and full communication access means are greater than the no access means for both dependent variables, consistent with H2a-
Insert Table 4 about here.
Comparisons of communication levels:
H3 and H4 were tested by comparing unidirectional and bidirectional communication means within conflicting and nonconflicting incentives. Neither of these contrasts were statistically significant (conflicting: Wilks X = 0.93; F(3,25) = 0.63; p = 0.600; nonconflicting: Wilks X = 0.94; F(2,26) = 0.77; p = 0.466) .
Within-Subjects Analyses
The means of the dependent variables were computed across blocks of trials to test for learning effects and the interaction these effects might have with tests of individual hypotheses. The overall main effect for trials is statistically significant in the conflicting incentives condition (Wilks X = 0.46; F(6,22) = 4.34;
p = 0.005).3 While the individual variables in the conflicting condition tended to increase across time, tests of statistical significance show varying results. Gross margin showed neither a significant linear (F(l,27) = 2.78; p = 0.107) nor nonlinear (F(l,27) = 2.92; p = 0.099) trend across time. Inventory turnover showed a marginally significant increasing linear trend (F(l,27) = 3.89; p = 0.059) and a highly significant nonlinear trend (F(l,27) = 7.04; p = 0.013). Analysis of the nonlinear trend for inventory turnover shows a fairly large increase in mean inventory turnover per period from the first to the second block of trials, with a slight decrease from the second to the third block. Efficiency showed a highly significant increasing linear trend (F(l,27) =
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22.83; p = 0.000), but the nonlinear trend was not significant (F(l,27) = 3.11; p = 0.089) .
The overall main effect for trials is also statistically significant in the nonconf licting incentives condition (Wilks A, =
0.43; F(4,24) = 8.07; p < 0.001). Here, tests for increasing linear trends are highly significant for both net compensation (F(l,27) = 30.78; p < 0.001) and efficiency (F(l,27) = 29.59; p < 0.001). Tests for nonlinear trends are not significant for either of these variables (net compensation: F(l,27) = 1.11; p = 0.302; efficiency: F(l,27) = 0.45; p = 0.509).
The only within-subjects interaction test which approaches statistical significance is the test for the interaction between trials and the test of H2A and H2B (Wilks X = 0.73; F(4,24) = 2.27;
p = 0.092) . The linear components of the interaction were not significant, but the nonlinear components were significant (F(l,27) = 6.51; p = 0.017 for gross margin, F(l,27) = 6.24; p = 0.019 for efficiency). Figure 8 is a diagram of this effect for efficiency. Inspection of the diagram shows that only a slight increase in performance occurred under full and partial access and that most of the increase occurred from the first to the second block of trials. On the other hand, the increase in performance under no access was somewhat larger, but it did not occur until after the third block of trials.
Insert Figure 8 about here.
Efficiency Data
The analysis of results thus far has shown that communication had a significant positive effect on performance, regardless of incentives. Given that these effects exist, another issue for investigation is how performance under the various communication conditions compares to normative efficiency benchmarks. The nonconf licting incentives problem has a unique
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maximum, so the benchmark in this condition is 1.0, regardless of communication structure. With conflicting incentives, we define the benchmarks as efficiency at the single-period equilibrium point. The efficiency benchmarks are 0.681 for no communication and 0.875 for unidirectional and bidirectional communication.4
Insert Table 5 about here
95% confidence intervals were computed for the efficiency measures for each level of communication access within each communication condition. (See Table 5.) Within the nonconf lict- ing incentives condition, efficiency measures which are significantly less than 1.0 indicate actions inconsistent with coordination of actions for expected payoff maximization. None of the confidence intervals for mean efficiency across all trials of the experiment in the nonconf licting incentives condition include the benchmark of 1.0. However, both the upper and lower confidence limits for the last 6 trials are close to 1.0 with unidirectional (0.963 - 0.994) and bidirectional (0.970 - 0.997) communication. The confidence limit for no communication (0.804 - 0.970), however, is somewhat further away from 1.0. Consistent with the within-sub jects tests, learning appears to have occurred in all nonconf licting incentives conditions, but the dyads allowed communication achieve near optimal performance, while those with no communication do not.
In the conflicting incentives condition, efficiency measures which are significantly greater than those associated with single- period equilibria indicate that dyads may be achieving increased performance through cooperation across time. Efficiency measures which are significantly lower than those expected for single- period equilibria indicate that dyad members are not acting in a strategic fashion, as defined within the game-theoretic framework outlined in Appendix B.
The lower limit of the 95% confidence interval for mean efficiency across all trials of the experiment in the conflicting incentives / no communication condition is greater than the benchmark of 0.681 for all trials (0.692) and for the last six trials (0.695). On the other hand, the benchmark of 0.875 for the unidirectional communication condition is just barely inside the upper limit of the confidence interval (0.876) for all trials. However, the benchmark is well within the confidence interval for the last six trials (0.838 - 0.907). With bidirectional communication, the benchmark is well within the confidence limit for all trials (0.825 - 0.898) and the last six trials (0.812 - 0.909) .
Indications of Cooperative Behavior
The efficiency data for the conflicting incentives condition indicate that cooperative behavior occurred in the no access condition, but not in the full and partial access conditions. However, efficiency measures which are greater than those expected at single-period equilibrium points do not by themselves indicate the presence of cooperation. This is because a 'cooperative' outcome is by definition a Pareto-improvement over a single-period equilibrium point. However, there are outcomes which represent efficiency improvements over single-period (noncooperative) equilibrium points, but do not represent Pareto-improvements over these points.5 Therefore, analyses of gross margin and inventory turnover similar to the one for efficiency were performed in order to assess whether payoffs to both types of agents under conflicting incentives were consistent with those predicted by the single-period game-theoretic analysis. (See Table 6.)
Insert Table 6 about here.
The mean gross margin for no communication across all trials (13408) is greater than the expected single-period equilibrium
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outcome of 12596, but the lower bound of the 95% confidence interval (12581) is slightly less than the expected outcome. In the last six periods, the mean gross margin is 13506 and the lower bound of the 95% confidence interval is 12398. For mean inventory turnover, the lower bounds of the 95% confidence interval are greater than the noncooperative equilibrium expected outcome of 3.769 for all trials (4.002) and the last six trials (3.830) . Therefore, while the efficiency data indicate cooperation took place in the no communication condition, only purchasing managers achieved significant gains from cooperation, on average.
In the unidirectional and bidirectional communication conditions, the mean gross margin for all trials (14267 and 14211, respectively) is slightly greater than the predicted single period equilibrium outcome of 14000, but the predicted outcome is above the lower bounds of the 95% confidence intervals (1370 6 and 13728) . For the last six periods, the predicted equilbrium outcome is still greater than the lower bounds for both unidirectional (13739) and bidirectional (13308) access. The mean inventory turnover values for unidirectional communication are less than the single period equilibrium value of 7.000 for all trials (6.019) and for the last six trials (6.404). Only for the last six trials does the the 95% confidence interval (5.513 - 7.295) include the equilibrium value. With bidirectional communication, the mean inventory turnover values are also less than the noncooperative equilibrium value for all trials (6.403) and the last six trials (6.206) . The predicted equilibrium value of inventory turnover is within the 95% confidence interval for all trials (5.706 - 7.100) and but is slightly outside the confidence interval for the last six trials (5.438 - 6.974).
To summarize, merchandising managers in the conditions with communication had performance outcomes on average that were as high as would be expected by dyads choosing the single-period (i.e., noncooperative) equilibrium point. On the other hand, the mean compensation to purchasing managers with communication was
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less than expected at the single-period equilibrium point. Therefore, the results for the communication conditions are not entirely consistent with the predictions of the game-theoretic model. Even so, the average payoffs to both types of managers with communication were significantly greater than without.
Selling Price and Order Quantity Data
Thus far, the presentation of results has focused on outcome data. The Ackoff scenario, however, also makes certain predictions about the prices and quantities chosen by the managers. If Ackoff s predictions are true, we should see higher selling prices and lower order quantities with communication than without, at least with conflicting incentives. Also, selling prices should increase and order quantities should decrease over time .
Table 7 shows mean selling price and order quantity data for blocks of trials and for the entire experiment. Multivariate tests on selling price and order quantity indicate significant differences between dyads with no and some communication, in both the conflicting (Wilks ' X = 0.76; F(2,26) = 4.20; p = 0.026) and nonconflicting (Wilks' X = 0.59; F(2,26) = 8.97; p = 0.001) incentives conditions. Univariate tests showed that dyads with communication set significantly lower selling prices than those without, in both the conflicting and nonconflicting incentives conditions. (See Table 8.) Inventory order quantities were significantly larger with communication than without, again for both types of incentives. All these results are contrary to Ackoff 's predictions. Multivariate tests showed no significant differences between unidirectional and bidirectional communication dyads, again in both the conflicting (Wilks' X = 0.92; F(2,26) = 1.14; p = 0.336) and nonconflicting (Wilks' X = 0.99; F(2,26) = 0.07; p = 0.937) incentives conditions.
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Insert Tables 7 & 8 about here.
Within-sub jects tests also show results contrary to Ackoff s
predictions. The overall effect for trials only approaches significance in the conflicting incentives condition (Wilks' X =
0.74; F(4,24) = 2.15; p = 0.106). Univariate tests do show a significant downward linear trend across trials for selling price (F(l,27) = 7.61; p = 0.010) and an upward linear trend for order quantity (F(l,27) = 5.78; p = 0.023). The overall effect for trials is highly significant in the nonconflicting incentives condition (Wilks' X = 0.49; F(4,24) = 6.15; p = 0.001).
Univariate tests in nonconflicting incentives also show a significant downward linear trend across trials for selling price (F(l,27) = 15.96; p < 0.001) and an upward linear trend for order quantity (F(l,27) = 16.86; p < 0.001).
SUMMARY AND CONCLUSIONS
This paper began by discussing contrasting views regarding the effects of communication on agents ' performance in a distributed decision making environment. For environments where agents are assigned to maximize conflicting incentives, the contrasting viewpoints were: (1) Ackoff s (1967) view that communication between agents may be detrimental, and (2) a game- theoretic analysis, which showed that in many cases, communication is beneficial for pairs of managers with conflicting incentives. For environments with nonconflicting incentives, we discussed: (1) Rappaport's (1968) view that communication could be beneficial in such a setting, and (2) a decision-theoretic analysis, which indicated that communication access should not be necessary to find the optimal solution to the nonconflicting incentives problem. We also proposed hypotheses which indicate that not only the existence of communication, but the type of communication pattern may have an effect on performance outcomes.
The results of the experiment showed that dyads with communication performed significantly better than those with no communication, regardless of incentives. On the other hand, varying the type of communication structure had no significant effects on performance in either incentives condition. The results with conflicting incentives are contrary to Ackoff's views, but are consistent with the game-theoretic model. The results with nonconflicting incentives support Rappaport's viewpoint, that is, communication enhances performance with nonconflicting incentives. This is contrary to the assumption of perfectly rational agents who should be able to maximize their joint outcomes without communication.
Comparison of efficiency measures against normative benchmarks under conflicting incentives revealed that dyads with no communication performed significantly better than predicted by a noncooperative equilibrium model, but dyads with communication on average only performed at least as well as predicted by the model. Even so, both types of agents with communication still earned significantly higher payoffs than their counterparts without communication.
An analysis of performance across time showed that dyads with nonconflicting incentives and communication were able to achieve nearly optimal performance with experience. Even though nonconflicting incentives dyads with no communication exhibited stronger learning effects than those with partial or full access, their performance in the last block of trials was still significantly less than optimal. Also, most of the learning for no communication dyads did not take place until the last block of experimental trials. Learning effects also occurred with conflicting incentives, but were not as pronounced as those for nonconflicting incentives. Only inventory turnover and overall efficiency showed statistically significant increases across time.
21
From a prescriptive standpoint, it appears that . in an environment where decision issues are modularized and distributed among managers, communication is beneficial under both conflicting and nonconf licting incentives systems. However, the results for conflicting incentives are conditional on whether or not game- theoretic equilibrium outcomes are predicted to be greater when communication is allowed than when it is not. We did not make a direct performance comparison between incentives conditions was not made, since performance under different schemes is contingent on the precise incentives chosen. However, the differential learning effects observed under the two schemes suggest nonconf licting incentives schemes are superior, as far as coordination issues are concerned. Apparently, improvements in performance under conflicting incentives are limited to the degree individual agents are willing to cooperate. On the other hand, no such limitation exists for nonconf licting incentives.
The lack of a significant difference between partial and full access results indicates that only a fairly rudimentary communication system is necessary in tasks such as the one presented here. This result is particularly important in situations where communication is costly, such as when operating divisions are located in different areas around the world. However, this finding is conditional on two factors. First, the task used in the experiment was a fairly simple one, although similar tasks are often found in practice. More complex tasks may require the transmission of more extensive verbal and numeric data,, or even social cues such as vocal inflection or facial expression, to achieve optimal outcomes (Treviho, Lengel, and Daft, 1987; McGuire, Kiesler, and Siegel, 1987) . Second, substantial opportunities for learning existed in the experiment, since the task was carried out over a number of repeated trials. In a case where such learning opportunities do not exist, then communication beyond a rudimentary level may be necessary.
22 FOOTNOTES
inventory turnover is multiplied by 1,000 in these analyses to make the gross margin and inventory turnover scales compatible. For example, at the outcome p = 85 and q = 350 with conflicting incentives, expected gross margin is 12250 and inventory turnover is 7.000, making E (PERFC) = 12250 + 7000 = 19250. The highest possible outcome with conflicting incentives occurs at p = 75 and q = 550, where E (PERFC) = 13667 + 10333 = 24000. So, efficiency for the outcome p = 85 and q = 350 is 19250/24000, or 0.802.
2Since the efficiency data are proportions, a variance- stabilizing arcsin transformation was applied to them before analysis (Neter and Wasserman, 1974, p. 507) .
3A multivariate repeated measures approach was used, as described in Bock (1975, Ch. 7) .
Computations are as follows: no access — 16364/24000; partial and full access — 21000/24000.
5For example, the outcome (p = 100, q = 400) yields an efficiency measure of 0.72, which is greater than the no communication EP efficiency of 0.68. However, the expected payoff for the purchasing manager at this point is 2311, which is less than the EP expected payoff of 3769.
23
REFERENCES
Ackoff, R. L., "Management Misinformation Systems," Management Science Vol. 14, No. 4, (December, 1967), pp. B147-B156.
Bock, R.D., Multivariate Statistical Methods in Behavioral Research. New York: McGraw-Hill, 1975.
Dubey, P. and M. Shubik, "Information Conditions, Communication and General Equilibrium," Mathematics of Operations Research. Vol. 6, No. 2, (May 1981), pp. 186-189.
Friedman, J. W., Oligopoly and the Theory of Games. New York: North- Holland, 1977.
Huber, G. P., "Organizational Information Systems: Determinants of Their Performance and Behavior," Management Science. Vol. 28, No. 2, (Feb. 1982), pp. 138-155.
, "The Nature and Design of Post-Industrial Organizations, "
Management Science, Vol. 30, No. 8, (Aug. 1984), pp. 928-951. , and McDaniel, R. R., "The Decision Making Paradigm of
Organizational Design," Management Science. Vol. 32, No. 5, (May 1986) , pp. 572-589.
Luce, R. D., and H. Raiffa, Games and Decisions. (New York: John Wiley and Sons, 1957) .
Malone, T. W., "Modeling Coordination in Organizations and Markets,' Management Science Vol. 33, No. 10, (Oct. 1987), pp. 1317-1332
, and Smith, S. A., "Modeling the Performance of
Organizational Structures," Operations Research. (May-June, 1988), pp. 421-436.
March, J.G., and H.A. Simon, Organizations (Wiley, New York, 1958).
Mc Guire, T.W., S. Kiesler, and J. Siegel, "Group and Computer- Mediated Discussion Effects in Risky Decision Making, " Journal of Personality and Social Psychology, 1987, pp. 917-930.
Neter, J. and W. Wasserman, Applied Linear Statistical Models. Homewood, IL: Richard D. Irwin, 1974.
Rappaport, A., "Management Misinformation Systems - Another Perspective," 15, 1968, pp. B133-B136.
Schotter, A. and G. Schwodiauer, "Economics and the Theory of Games: A Survey." Journal of Economic Literature (June 1980): 479- 527.
Shubik, M., Game Theory in the Social Sciences (Cambridge, Mass., MIT Press, 1982) .
Ponssard, J. P., Competitive Strategies. (New York, North-Holland, 1981) .
24
Treviho, L.K., R.H. Lengel, and R.L. Daft, "Media Symbolism, Media Richness, and Media Choice in Organizations" Communication Research, 1987, pp. 553-574.
TABLE 1
Dependent Variable Means per Period
Conflicting Condition
|
Trials |
||||
|
1-6 |
7-12 |
13-18 |
Mean |
|
|
Gross Marain |
||||
|
No Communication |
12858 |
13859 |
13507 |
13408 |
|
Unidirectional |
13803 |
14410 |
14588 |
14267 |
|
Bidirectional |
14312 |
14332 |
13988 |
14211 |
|
Mean |
13658 |
14200 |
14028 |
13962 |
|
Efficiency |
||||
|
No Communication |
0.71 |
0.77 |
0.76 |
0.75 |
|
Unidirectional |
0.81 |
0.85 |
0.87 |
0.84 |
|
Bidirectional |
0.85 |
0.87 |
0.86 |
0.86 |
|
Mean |
0.79 |
0.83 |
0.83 |
0.82 |
|
Inventory Turnover |
||||
|
No Communication |
4.292 |
5.239 |
4.788 |
4.773 |
|
Unidirectional |
5.256 |
6.398 |
6.404 |
6.019 |
|
Bidirectional |
6.463 |
6.539 |
6.206 |
6.403 |
|
Mean |
5.337 |
6.059 |
5.799 |
5.732 |
TABLE 2
Dependent Variable Means per Period
Nonconf licting Condition
|
Trials |
||||
|
1-6 |
7-12 |
13-18 |
Mear |
|
|
Net Compensation |
||||
|
No Communication |
6212 |
6316 |
7021 |
6516 |
|
Unidirectional |
7218 |
7910 |
7623 |
7583 |
|
Bidirectional |
7051 |
7620 |
7822 |
7498 |
|
Mean |
6828 |
7282 |
7489 |
7199 |
|
Efficiency |
||||
|
No Communication |
0.79 |
0.80 |
0.89 |
0.83 |
|
Unidirectional |
0.92 |
0.97 |
0.98 |
0.96 |
|
Bidirectional |
0.93 |
0.97 |
0.98 |
0.96 |
|
Mean |
0.88 |
0.92 |
0.95 |
0.92 |
TABLE 3
Univariate Hypothesis Tests
Conflicting Incentives Condition
No Communication vs (Unidirectional + Bidirectional) /2
Unidirectional vs. Bidirectional
Gross Margin Inv. Turnover Efficiency E 2 E £ E E
5.74 .024 16.78 .000 19.17 .000
0.01 .889
0.90 .352
0.65 .428
TABLE 4
Univariate Hypothesis Tests
Nonconf licting Incentives Condition
No Communication vs (Unidirectional + Bidirectional) /2
Unidirectional vs. Bidirectional
Compensation
-E E-
17.16
0.89
.000
.768
Efficiency F a
30.51
0.07
.000
.794
TABLE 5 Confidence Intervals for Efficiency Measures
|
All 18 Periods |
Mean |
Std. Dev. |
|
Conflicting Incentives |
||
|
No Communication |
0.747 |
0.078 |
|
Unidirectional |
0.841 |
0.048 |
|
Bidirectional |
0.862 |
0.051 |
|
Nonconflicting Incentives |
||
|
No Communication |
0.825 |
0.134 |
|
Unidirectional |
0.958 |
0.022 |
|
Bidirectional |
0.964 |
0.024 |
95% Conf. Interval
0.692 - 0.803 0.807 - 0.876 0.825 - 0.898
0.729 - 0.922 0.942 - 0.974 0.947 - 0.982
Periods 12-18
Conflicting Incentives
No Communication 0.765 0.097 0.695 - 0.834 Unidirectional 0.873 0.049 0.838 - 0.907 Bidirectional 0.860 0.068 0.812 - 0.909
Nonconflicting Incentives
No Communication 0.887 0.116 0.804 - 0.970
Unidirectional 0.978 0.021 0.963 - 0.994
Bidirectional 0.984 0.019 0.970 - 0.997
TABLE 6
Confidence Intervals for Gross Margin and Inventory
Turnover—Conflicting Condition
|
All 18 Periods |
Mean |
Std. Dev. |
|
Gross Margin |
||
|
No Communication |
13408 |
1156 |
|
Unidirectional |
14267 |
785 |
|
Bidirectional |
14211 |
675 |
|
Inventory Turnover |
||
|
No Communication |
4.723 |
1.077 |
|
Unidirectional |
6.019 |
0.595 |
|
Bidirectional |
6.403 |
0.975 |
|
Periods 12-18 |
||
|
Gross Margin |
||
|
No Communication |
13507 |
1550 |
|
Unidirectional |
14588 |
1186 |
|
Bidirectional |
13988 |
951 |
|
Inventory Turnover |
||
|
No Communication |
4.788 |
1.338 |
|
Unidirectional |
6.404 |
1.245 |
|
Bidirectional |
6.206 |
1.074 |
95% Conf. Interval
12581 - 14234 13706 - 14828 13728 - 14693
4.002 - 5.544 5.594 - 6.445 5.706 - 7.100
12398 - 14616 13739 - 15436 13308 - 14669
3.830 - 5.745 5.513 - 7.295 5.438 - 6.974
TABLE 7
Means for Sales Price and Order Quantity
Across Blocks of Six Trials
Sales Price
|
Trials |
||||
|
1-6 |
7-12 |
13-18 |
Mean |
|
|
Conflicting Incentives |
||||
|
No Communication |
97.6 |
96.8 |
97.1 |
97.2 |
|
Unidirectional |
96.1 |
93.0 |
91.6 |
93.6 |
|
Bidirectional |
92.6 |
91.1 |
91.1 |
91.6 |
|
Mean |
95.4 |
93.6 |
93.3 |
94.1 |
|
Nonconflicting Incentives |
||||
|
No Communication |
98.5 |
97.6 |
95.5 |
97.2 |
|
Unidirectional |
93.4 |
91.3 |
89.7 |
91.5 |
|
Bidirectional |
93.5 |
92.0 |
90.0 |
91.8 |
|
Mean |
95.1 |
93.6 |
91.7 |
93.5 |
|
Order Ouantity |
Trials |
|||
|
1-6 |
7-12 |
13-18 |
Mean |
|
|
Conflicting Incentives |
||||
|
No Communication |
309.9 |
329.1 |
321.7 |
320.2 |
|
Unidirectional |
336.7 |
360.8 |
372.6 |
356.7 |
|
Bidirectional |
353.4 |
368.3 |
363.4 |
361.7 |
|
Mean |
333.3 |
352.7 |
352.6 |
346.2 |
|
Nonconflicting Incentives |
||||
|
No Communication |
365.8 |
350.0 |
385.0 |
366.9 |
|
Unidirectional |
403.3 |
435.8 |
448.2 |
429.1 |
|
Bidirectional |
397.7 |
425.7 |
445.9 |
423.1 |
|
Mean |
388.9 |
403.8 |
426.4 |
406.4 |
TABLE 8 Univariate Tests — Selling Price and Order Quantity
Selling Order
Price Quantity
J2-
Conflictina Incentives No Communication vs.
(Unidirectional +
Bidirectional) /2 8.68 .007 6.51 .017
Unidirectional vs.
Bidirectional 1.20 .283 0.08 .779
Nonconflictina Incentives No Communication vs. (Unidirectional + Bidirectional) /2 13.32 .001 17.32 .000
Unidirectional vs.
Bidirectional 0.04 .836 0.13 .718
Merchandising Purchasing Nature Manager Manager
Figure 1
Extensive Form
AcJcoff Scenario without Communication
Merchandising Purchasing Manager Manager
Nature
Figure 2
Extensive Form
Ackoff Scenario with Communication
No Communication Condition Merchandising Purchasing
Review demand curve; make price decision (PI) .
V ~7
Review demand curve; make quantity decision {Ql) ,
Quantity and price sold revealed to both managers; performance measures calculated and revealed to both managers .
Unidirectional Communication Condition Merchandising Purchasing
Review demand curve; make price decision (PI) .
(P.
V ~7
Review demand curve; make quantity decision {Ql) ,
Quantity and price sold revealed to both managers; performance measures calculated and revealed to both managers .
Bidirectional Communication Condition Merchandising Purchasing
Review demand curve; make initial price (PI) and quantity (Ql) decisions.
Ql
Make initial decision on quantity to order (Q2) .
Q2
Make revised price decision (P2) .
^:
P2
Make final quantity decision (Q3)
"Z"
Quantity and price sold revealed to both managers; performance measures calculated and revealed to both managers .
FIGURE 3
analysis SCREEN: DISPLAY ACTIVATED
ANALYSIS
oca si on
HISTODY
anq
PG3I0D 10
01 SPLAT nOCE
DOIANQ UNITS
SALES UNITS
S30SS rtAC6IN
LOST SALES UNITS
ENDING INUENTOQY
INUENTOQY TUCN0UO1
QQOO QUANTITY CDHS1 CEDED
100 I SI
200
250
300
too
450 500 1 550
LOG. OF rWfifcFT QEmNO
|
POICE |
|riEDjvurt !â– :<-:! |
EXPTED |
||
|
SX2Q |
J98 â– |
|||
|
Q15 |
141 |
|||
|
S110 |
133 |
|||
|
ao5 |
246 |
|||
|
soo |
300 |
|||
|
SS5 |
356 |
|||
|
so |
413 |
|||
|
Off |
472 |
|||
|
no |
532 |
|||
|
S75 |
535 |
Status: dick the HISTOQY box to rovieu results o* previous periods. Click the DECISION box uhen ready to enter planned selling prica and order quantity request.
ANALYSIS
OCCISION
WSTOQY
anq ttanager
PERIOD 10
DISPLAY ttOCE
QEHftNQ units:
SALES UNITS
SQOSS 1AQ6IN
LOST SALES UNITS
EN0IH6 INUENTOQY
INUENTDDY TUBNTJUED
QQOED QUANTITY CONSIDERED
100 1150
200
250 300
350 400
1 500 i 550
LOJEL OF riAOKET QEmNO
POICE
S20
ni5
aio
SX05
SOO
LOU
417
S75
maun
472
HIGH
527
EXPTED
472
Status: diet the HISTODY box to review results of previous periods, dick the DECISION box uhen readg to enter planned selling price and order quantity request.
FIGURE k
4
DECISIONS MODE
ANALYSIS
DECISION
Hi STOGY
Merchandising Manager PERIOD 1L
Diet belou to select a planned selling price (not tr
Med to purchasing):
|
75 |
80 |90 |
95 ice |
105 |
110 |
115 |
120 |
Click belou to select en order quantity request to be transmitted to purchasing:
|
100 |
150 |
200 |
250 |
300 350 |
400 | |5Q0 |
550 |
You have entered a planned order quantity ol 450. Click belau to coniirm your entries and transmit your order quantity request to purchasing or to cancel.
coNFinrt anc ™p*«SMir
CANCEL
An order quantity request oi 46ft confirmed. Quantity request has been transmitted to purchasing.
Status Decision node temporarily inactive, to view the analysis or history, Awaiting planned order quantity lr
You may continue purchasing.
ANALYSIS
DEC! SIGN
HIST0OY
Purchasing Manager
PCniDD 10
Click belou to select a planned order quantity to transmit to merchandising:
|
100 |
150 |
200 |
250 |
300 35ft | |450 |
500 |
550 |
You have entered a planned order quantity oi 40ft. diet belou to contirn and transmit your entry to merchandising or to cancel.
coNnnn and ujAMsmr
CANCEL
Planned order quantity ol 400 confirmed and transmitted to merchandising
St at us: Decision node temporarily inactive. You may continue to vieu the analysis or history nodes. Awaiting final selling price from merchandising.
FIGURE 5
RESULTS SCREEN
ANALYSIS
OETI SI ON
H
HI STOGY
Purchase nci Manager
I
PERIOD 10
QAKOGrl NUnBED QDMJN LEUEL OF HAQICET DCttANO
14
LOU
♦I
|
PUOCHASE QUAWITY |
450 |
|
PQICE |
was |
|
DEMAND UMTS |
417 L |
|
SALES UMgS |
417 |
|
6QOSS HAQ6IN |
11595 |
|
LOST SALES UMTS |
Q |
|
DCIH6 rwoiroov |
33 |
|
inuentoqy rwm,o |
5,024 |
|
youp cofmc*no» |
5024 |
|
rcoca cowciisAnw |
7239 |
St at us: Click the ANALYSIS or HISTOQY box to proceed to the next period.
FIGURE 6
J
HISTORY MODE
ANALYSIS
DECISION
HISTODY
Purchasing Manager
PERIOD 11
RESULTS QT COMPLETED PERIODS
|
EM |
* |
9 |
7 |
6 |
5 |
4 |
3 |
2 |
1 |
|
|
PURCHASE CUANnTY |
450 |
|||||||||
|
POICE |
S85 |
|||||||||
|
DEMAND UNITS |
417 L |
|||||||||
|
SALES UMTS |
417 |
|||||||||
|
6QOSS nAPBIN |
14535 |
|||||||||
|
LOST SALES UNITS |
0 |
|||||||||
|
ENDING INUCNTOQY |
33 |
« |
||||||||
|
INUENTOQY TUHNOUED |
5.02 |
|||||||||
|
YOUQ COMPENSATION |
5024 |
|||||||||
|
PERCH- COMPENSATION |
7298 |
Status: Click the ANALYSIS box to vieu current period data.
Auaiting order quantity request fr<
chandisinq.
ANALrSIS DECISION
HISTORY
Purchasing Manager
RESULTS Of COnPLETED PERIODS
PERIOD 11
|
10 |
9 |
8 |
7 |
6 |
5 |
4 |
3 |
2 |
1 |
|
|
PUQCHASE QUANnTY |
||||||||||
|
POICE |
||||||||||
|
DEMAND UNITS |
417 L |
411 H |
527 H |
532 n |
532 n |
650 H |
650 H |
4t3 n |
358 L472 PI |
|
|
SALES UMTS* |
'■• |
..•■|
||||||||
|
GROSS MARGIN |
||||||||||
|
LOST SALES UNITS |
||||||||||
|
EN0IN6 INUENTOOY |
||||||||||
|
INUENTOQY TURNOVER |
||||||||||
|
YQUQ COMPENSATION |
||||||||||
|
KERCH. COMPENSATION |
Status: Click the ANALYSIS box to vieu current period data.
Auaiting order quantity request Iroa Merchandising.
FIGURE 7
1.00 T
•♦• No Access •o- Partial Access ■" Full Access
Trials 1 -6
Trials 7-12
Trials 13-18
Figure 8
Effciency across Blocks of Trials:
Nonconflicting Incentives Condition
35
APPENDIX A
Excerpts from Ackoff, R. L.,
"Management Misinformation Systems,"
Management Science r (December 1967), pp. B147-156
...For example, consider the following very much simplified version of a situation I once ran into. The simplification of the case does not affect any of its essential characteristics.
A department store has two "line" operations: buying and selling. Each function is performed by a separate department. The Purchasing Department primarily controls one variable: how much of each item is bought. The Merchandising Department controls the price at which it is sold. Typically, the measure of performance applied to the Purchasing Department was the turnover rate of inventory. The measure applied to the Merchandising Department was gross sales; this department sought to maximize the number of items sold times their price.
Now by examining a single item let us consider what happens in this system. The merchandising manager, using his knowledge of competition and consumption, set a price which he judged would maximize gross sales. In doing so he utilized price-demand curves for each type of item. For each price the curves show the expected sales and values on an upper and lower confidence band as well. (See Figure Al . ) When instructing the Purchasing Department how many items to make available, the merchandising manager quite naturally used the value on the upper confidence curve. This minimized the chances of his running short which if it occurred, would hurt his performance. It also maximized the chances of being overstocked but this was not his concern, only purchasing manager's. Say, therefore, that the merchandising manager initially selected price PI and requested that amount Ql be made available by the Purchasing Department.
In this company the purchasing manager also had access to the price-demand curves. He knew the merchandising manager always ordered optimistically. Therefore, using the same curve he read
over from Ql to the upper limit and down to the expected value from which he obtained Q2, the quantity he actually intended to make available. He did not intend to pay for the merchandising manager's optimism. If merchandising ran out of stock, it was not his worry. Now the merchandising manager was informed about what the purchasing manager had done so he adjusted his price to P2 . The purchasing manager in turn was told that the merchandising manager had made this readjustment so he planned to make only Q3 available. If this process — made possible only by perfect communication between departments — had been allowed to continue, nothing would have been bought and nothing would have been sold. This outcome was avoided by prohibiting communication between the two departments and forcing each to guess what the other was doing.
Optimistic
Expected
Pessimistic
Fig Al Price-demand curve
37
APPENDIX B A Game-Theoretic Analysis of Ackoffs Scenario
Basic Parameters
Assume that sales demand (d) is jointly dependent on selling price (p) and on a random state of nature. Nature has three possible state realizations, which occur with equal probability. They represent high, medium, and low sales demand. The demand functions for each state are:
High demand: d = 2555 - 220 (p1/2)
Medium demand: d = 2500 - 220 (p1/2)
Low demand: d = 2445 - 220 (p1/2)
If demand is greater than the quantity ordered by purchasing (q) , the units sold for the period are equal to q, that is, no backorders are allowed. If demand is less than the quantity ordered by purchasing, the units sold for the period are equal to d. Remaining units are not carried over to the next period; it is assumed these are disposed of at cost. The cost for each item is 50, therefore, the gross margin for each period is:
(p - 50) x number of units sold
Merchandising ' s compensation for each period is one-half of gross margin. Purchasing's compensation is based on a modified version of the traditional inventory turnover ratio, specifically:
number of units sold . «___,
1000
ending inventory + 50
Merchandising may set a selling price anywhere from 75 to 120, in increments of 5. Purchasing may order from 100 to 550 units, in increments of 50." The expected values for each manager for each combination of selling price and order quantity are shown in Figure Bl .
38
Game-Theoretic Analysis: No Communication Allowed
If one were to show the extensive form of this game, the diagram would look like Figure 1, except that it would have ten branches coming out of merchandising' s initial decision node and another ten branches coming off of these branches, at each of purchasing's decision nodes. Figure Bl shows the strategic form of the game. By successively eliminating dominated strategies (starting with p = 120, q = 100, and so forth), one can show that this game has a unique equilibrium point (EP) at p = 105, q = 250. The expected payoffs at this point are 62 98 to merchandising and 3769 to purchasing.
Game-Theoretic Analysis: Communication Allowed
In the case where communication from merchandising to purchasing is allowed, the game can be represented in extensive form by a diagram similar to Figure 2. The actions which yield the highest expected payoffs for merchandising in this game are p = 85 and p = 90. At p = 85, purchasing should choose q = 400, yielding expected payoffs of 7000 for merchandising and 8000 for purchasing. At p = 90, purchasing should choose q = 350, again yielding an expected payoff of 7000 for merchandising, but only 8000 for purchasing. Note that in either case, the expected payoffs to both managers are higher than without communication.
The predicted outcomes for the game with communication, however, are but two of many EPs. Also, note that the EP of the game without communication is one of the EPs of the game with communication. In fact, Dubey and Shubik (1981) have shown that for two games which are identical, except for the information sets of the players, the set of pure strategy EPs for the game with less information will be a subset of the set of pure strategy EPs of the game with more information.
In the Ackoff scenario, this means that the merchandising manager will be at least as well off with communication as without. His choice set of EPs with communication will always include the no
39
communication EP (s) , and in many cases, will also include an EP where the expected payoffs are greater than without communication. This does not by itself guarantee an increased expected payoff with communication for the purchasing manager. However, in cases where the payoff structure is similar to the one shown here, the action with the highest expected payoff for merchandising under communication is to set a lower selling price than without communication. Purchasing's best response to this is to order a higher quantity than without communication. This will yield a higher expected inventory turnover for purchasing than without communication and therefore, higher expected payoffs.
40
|
100 |
150 |
200 |
250 |
q 300 |
350 |
400 |
450 |
500 |
550 |
|
|
75 |
1250 |
1875 |
2500 |
3125 |
3750 |
4375 |
5000 |
5625 |
6250 |
6833 |
|
80 |
1500 |
2250 |
3000 |
3750 |
4500 |
5250 |
6000 |
6750 |
7385 |
7795 |
|
85 |
1750 |
2625 |
3500 |
4375 |
5250 |
6125 |
7000 |
7683 |
8103 |
8260 |
|
90 |
2000 |
3000 |
4000 |
5000 |
6000 |
7000 |
7720 |
8140 |
8260 |
8260 |
|
95 |
2250 |
3375 |
4500 |
5625 |
6750 |
7508 |
7928 |
8010 |
8010 |
8010 |
|
100 |
2500 |
3750 |
5000 |
6208 |
7042 |
7458 |
7500 |
7500 |
7500 |
7500 |
|
105 |
2750 |
4125 |
5418 |
6298 |
6756 |
6765 |
6765 |
6765 |
6765 |
6765 |
|
110 |
3000 |
4380 |
5310 |
5790 |
5790 |
5790 |
5790 |
5790 |
5790 |
5790 |
|
115 |
3098 |
4084 |
4583 |
4583 |
4583 |
4583 |
4583 |
4583 |
4583 |
4583 |
|
120 |
2625 |
3150 |
3150 |
3150 |
3150 |
3150 |
3150 |
3150 |
3150 |
3150 |
Expected Value of Payoffs for Merchandising Manager
(Gross Margin / 2)
|
100 |
150 |
200 |
250 |
q 300 |
350 |
400 |
450 |
500 |
550 |
|
|
75 |
2000 |
3000 |
4000 |
5000 |
6000 |
7000 |
8000 |
9000 |
10000 |
10333 |
|
80 |
2000 |
3000 |
4000 |
5000 |
6000 |
7000 |
8000 |
9000 |
8845 |
7567 |
|
85 |
2000 |
3000 |
4000 |
5000 |
6000 |
7000 |
8000 |
7675 |
6396 |
4395 |
|
90 |
2000 |
3000 |
4000 |
5000 |
6000 |
7000 |
6630 |
5423 |
3529 |
2411 |
|
95 |
2000 |
3000 |
4000 |
5000 |
6000 |
5680 |
4602 |
2868 |
2000 |
1547 |
|
p 100 |
2000 |
3000 |
4000 |
4818 |
4778 |
3860 |
2311 |
1636 |
1275 |
1046 |
|
105 |
2000 |
3000 |
3746 |
3769 |
3189 |
1851 |
1321 |
1033 |
850 |
723 |
|
110 |
2000 |
2742 |
2873 |
2475 |
1437 |
1030 |
807 |
665 |
566 |
492 |
|
115 |
1781 |
2048 |
1816 |
1058 |
758 |
593 |
488 |
415 |
361 |
320 |
|
120 |
1268 |
1222 |
702 |
499 |
388 |
318 |
270 |
234 |
207 |
186 |
Expected Value Payoffs for Purchasing Manager (Inventory Turnover * 1000)
Figure Bl Expected Values to Managers with Conflicting Incentives
41
APPENDIX C
* The Nonconflicting Incentives Condition
The demand functions and game rules used in the nonconflicting incentives condition are the same as with conflicting incentives, with the exception of how the payoffs to the managers are defined. Under nonconflicting incentives, each item remaining in ending inventory is assumed to have a holding cost of ten units. Payoffs are an equal division of gross margin less holding costs. Expected payoffs for each combination of selling price and order quantity are shown in Figure CI. By inspection, one can see that the highest expected payoff, 7925, occurs at p = 90, q = 450.
|
100 |
150 |
200 |
250 |
q 300 |
350 |
400 |
450 |
500 |
550 |
|
|
75 |
1250 |
1875 |
2500 |
3125 |
3750 |
4375 |
5000 |
5625 |
6250 |
6817 |
|
80 |
1500 |
2250 |
3000 |
3750 |
4500 |
5250 |
6000 |
6750 |
7347 |
7643 |
|
85 |
1750 |
2625 |
3500 |
4375 |
5250 |
6125 |
7000 |
7628 |
7918 |
7870 |
|
90 |
2000 |
3000 |
4000 |
5000 |
6000 |
7000 |
7650 |
7925 |
7825 |
7575 |
|
95 |
2250 |
3375 |
4500 |
5625 |
6750 |
7426 |
7689 |
7540 |
7290 |
7040 |
|
100 |
2500 |
3750 |
5000 |
6200 |
6950 |
7200 |
7000 |
6750 |
6500 |
6250 |
|
105 |
2750 |
4125 |
5403 |
6193 |
6484 |
6245 |
5995 |
5745 |
5495 |
5245 |
|
110 |
3000 |
4360 |
5195 |
5505 |
5255 |
5005 |
4755 |
4505 |
4255 |
4005 |
|
115 |
3075 |
3963 |
4288 |
4038 |
3788 |
3538 |
3288 |
3038 |
2788 |
2538 |
|
120 |
2500 |
2850 |
2600 |
2350 |
2100 |
1850 |
1600 |
1350 |
1100 |
850 |
Figure CI Expected Values: Nonconflciting Incentives
HECKMAN
BINDERY INC.
DEC 95
Bound -To-Pleas^ N.MANCHESTER, INDIANA 46962