VOL 89 NO 4 CO0PER ET AL: GAMING AGAINST MANAGERS IN INCENTIVE SYSTEMS neither type of F can gain by deviating from 2 IL. Experimental Treatments, Research The pure strategy pooling equilibria at outp Hypotheses, and Procedures levels I and 3 are supported by similar strate gies and beliefs The motivation for our experimental treat- The set of equilibria can be narrowed down ments, as well as the predicted impact of these by using the equilibrium refinements which treatments, can be best summarized within the have been proposed for signalling games. Un- framework of a belief-based learning model fortunately, most of the standard refinements do such as the modified fictitious play model of not yield a unique outcome. For example, the Cooper et al. (1997a, b). Play in this model intuitive criterion (In-Koo Cho and David M. consists of two distinct stages. Prior to any Kreps, 1987) leaves both pooling at I and 2. actual play, agents must form initial beliefs Only perfect sequential equilibrium(Sanford J. about the likely actions of their opponents. As Grossman and Motty Perry, 1986), an ex- play takes place, players modify their initial tremely strong refinement, is able to make a beliefs in response to the observed play of ot unique prediction, pooling at 2 ers and choose actions to maximize their pay ere is considerable experimental research offs subject to their updated beliefs, We propose indicating that none of the standard equilibrium that incentives, expertise, and context can affect refinements adequately organizes data from sig- agents initial beliefs and/or the evolution of nalling games(see Brandts and Holt, 1992; Par- these beliefs over time in the following ways tow and Schotter, 1993; Cooper et al., 1997a) As an alternative, we ran simulations using the A. Incentives simple adaptive learning model developed in Cooper et al. (1997b). This is essentially a mul Subjects who put themselves into the other tiplayer version of fictitious play with initial players'shoes in forming initial beliefs have a beliefs fitted from the data. Cooper et al. substantial advantage over players who simply (997a, b) demonstrate that this model does a assume a distribution(such as a uniform distri good job of characterizing play in signaling bution over all strategies). However, such de- game experiments similar to the ratchet effect ductive reasoning involves some effort on game. For our game, simulations of the adaptive players part which, ceteris paribus, they prefer learning model overwhelmingly converge to the to avoid. Thus, the amount of effort players pooling equilibrium at 2.(This result holds expend on reasoning about the game before whether initial beliefs are fitted from the data or forming initial beliefs should be sensitive to the flat priors are imposed. ) Convergence to this payoffs resulting from their actions. Since in pooling equilibrium follows a typical pattern of creased deductive reasoning should lead to play: simulated players early beliefs fail to more strategic play, increasing the payoffs adequately account for the relationship between should, if anything, increase the initial levels of Fs'choices and CPs' responses, so that Fs' strategic play. initial choices are clustered around their full While there are strong theoretical reasons to information output levels(2 for FLs and 5 for expect increased incentives to yield more stra- FHs). These initial choices induce CPs to give tegic play, past experiments reveal that incen yes do not typically play as strong a role contract for higher output levels. As FHs learn behavior as anticipated. There are numerous that the likelihood of an easy contract is much reports of experimental phenomena that are higher at 2 than at higher output levels, play essentially unaffected by incentives(see the converges on a pooling equilibrium at 2. many examples cited in Colin Camerer, 1995) Further, when incentives have impacted on behavior, they typically reduce the variance of This has no pure strategy separating equilibria. There do exist mixed strategy equilibria; these equilibr nalogous to the standard require all FHs to act strategically, choosing lower output analysis of the allocation of time between work and leisure than their full information output Gary S. Becker, 1965)
THE AMERICAN ECONOMIC REVIEW SEPTEMBER 999 outcomes around the mean, with little or no 1981). Novices tended to classify problems on impact on mean performance(see Vernon L. the basis of superficial details(problems with Smith and James M. Walker [1993b] for a re- balls or problems with springs) while experts view of the literature). In cases where mean concentrated on the physical principles in- erformance is altered, the observed changes volved(Newton's Second Law or conservation can usually be attributed to risk aversion(for of momentum) example, Yoram Kroll et aL., 1988; Steven J xpertise is narrowly defined and Kachelmeier and Mohamed Shehata, 1992; only likely to be transferred when situations are Smith and Walker, 1993a) perceived to be quite similar(Gick and Holy- Thus, we did not originally expect to find an oak, 1980; Perkins and Solomon, 1988; So- incentive effect which could not be explained lomon and Perkins, 1989). For example, several by reduced variance in outcomes or increased studies have examined the ability of students tion Il, subsection B, such an effect did logical problems(Roy D. Pea and D. M.Kur emerge. We discuss why the ratchet effect game land, 1984; Kurland et al., 1986; Perkins et al is particularly likely to be responsive to incen- 1988). Even though these problems drew up tives following documentation of these effects. skills used in computer programming, such planning ahead or breaking up problems into B. Expertise and Context manageable pieces, little transfer was found, except when generalizability was stressed in the There are strong reasons to presume an inter- training (David Klahr and Sharon M. Carver, action effect between expertise(as reflected in 1988) managers past experience with the ratchet ef- Context plays an important role in fostering fect) and the context treatment. Psychologists transfer because of its impact on perceptions of have done extensive work analyzing differences similarity. Information and knowledge are in performance and cognitive processes be- learned within a specific context. Even when tween experts and novices(see Robert glaser context is not directly relevant to what is being [1990] and Colleen Zeitz and Glaser [1994] for learned, it can serve as a trigger for recall. In summaries of the many differences between one dramatic example, Duncan R Godden and experts and novices identified to date). Experts Alan D. Baddeley (1975) had divers learn lists ypically employ more sophisticated approaches of words either on dry land or under 20 feet of in solving problems and see larger patterns in ocean water. One day later, subjects were ran data than novices. For example, in classic ex- domly assigned to one of these two environ periments involving chess pieces arranged as ments and asked to recall the lists of words they might be in the course of an actual game, Subjects in the same environment where they experts recalled the position of many more had learned the list were able to recall 59 per pieces than novices (William G. Chase and cent of the words, while subjects in a different Herbert A. Simon, 1973; Adrianus D. DeGroot, environment only recalled 46 percent of the list 1978). This greater recall was not based on Turning to our experiment, we expect that greater memory capacity but rather on the abil- managers, based on their past experiences ity to organize groups of pieces into subpatterns would be expert in recognizing and dealing with which could then be recalled as a chunk(e. g,a the ratchet effect. However, this expertise can castled king, a chain of pawns). As a result only have an effect if managers recognize the when pieces were arranged on the board in similarity between our laboratory ga random positions, experts were no longer able their field experiences. Context can be expected to recall the positions with any greater accuracy to play an important role in triggering this con- than the novices. Experts also tend to approach nection, resulting in heightened levels of strate- problems in terms of basic principles, rather gic play to begin with and/or more rapid than focusing on surface details as novices tend adjustments towards equilibrium compared to to do. One classic example involves the ap- managers playing the generic version of the proach to simple physics problems(D P. Simon same game and Simon, 1978: Michelene t. Chi et al However. the existence of a context effect
VOL 89 NO 4 COOPER ET AL.: GAMING AGAINST MANAGERS IN INCENTTVE SYSTEMS requires two necessary conditions: (I)the exis- game. Although we made some effort to control tence of a ratchet effect in field settings, and (2) for these problems, the education effect clearly the ability of subjects to transfer knowledge makes it difficult to compare the absolute from field settings to a laboratory experiment. levels of strategic play between students and Neither of these points can be taken for granted. managers As noted previously, there exists no general consensus that CPs actually ratcheted up quotas C. Summary of Research Hypotheses (see footnote 1), and psychologists have found that transfer tends to be narrow in scope. As such, it cannot be assumed ex ante that a context To summarize, ex ante we had three general effect will exist for our manager subjects. Con- hypotheses to test: (1)Increased incentives lead sequently, if such an effect exists, it suggests to increased strategic play. Based on past ex- that the strategic situation in the field must be perimental outcomes, we anticipated at best a quite close to the model implemented in the lab. weak effect. (2)Context promotes heightened Unlike managers, students do not have levels of strategic play among managers com- levant field experience to become expert in pared to generic sessions. Necessary conditions the ratchet effect game. However, to the extent for this effect are the existence of the ratchet that central planning and the ratchet effect per- effect in field settings and similarity, actual and meate Chinese culture, there may exist a context perceived, between managers' field experiences effect within the student subject population. and our laboratory game. By the same token But we expect that any observed context effect context should have a much less pronounced (or will be larger for managers than for students nonexistent) effect for PRC students. (3) Field because of their greater experience in dealing experience with the ratchet effect results in with the problem heightened levels of strategic play for managers Along similar lines, our prior beliefs were compared to students, particularly in context that managers would exhibit at least as much(if sessions. Ex post, we discovered an education not more) strategic behavior than students, par- effect among older managers which weakens ticularly if we confined our attention to context our last prediction. Our experimental design sessions. What we did not anticipate was that tests these three predictions and attempts to recent experience as a student provides a sig- control for the education effect nificant advantage in our experiment for reasons Differing payoff levels were used to deter- not directly related to understanding the strate- mine the effect of incentives on strategic play. gic problem. The experiment involved figuring All sessions were conducted with payoffs in out a relatively complex payoff table and a fair an experimental currency called"francs. In amount of record keeping. Students are used to standard-pay PRC student sessions, francs were dealing with arcane computational tasks de- converted into yuan so that, for the pooling signed by professors and did not seem bothered equilibrium at 2, the expected value of subject y these details. In contrast, many of the older earnings was 30 yuan(approximately $3.75 at managers were having so much trouble with the the official exchange rate). These earnings were even thinking about the actual game. On a more a good flow of recruits in Shanghai(whinh mure paperwork that it is hard to imagine they were thought to be the minimum necessary to ins mundane level, bifocals are rare in China. This high-wage area in China) and to be reasonably meant that many of our older managers had to consistent, in terms of purchasing power and use glasses to read the blackboard but removed outside income, to earnings in typical U.S.stu- their glasses to complete their record sheets. dent experiments. For high-pay PRC student They were so busy taking their glasses on and sessions, payoffs were scaled up by a factor of off that they scarcely had time to think about the five, giving an average payoff of 150 yuan for he poc dent in the prc this was a sizable amount of COntext may also improve performance as it can ai money. As points of comparison, the monthly omprehension by illustrating the meaning of otherwise wage was about 550 yuan for an instructor and 1, 200 yuan for an associate professor at China
THE AMERICAN ECONOMIC REVIEW SEPTEMBER 1999 Textile University during the time period our tegic play than the other subject groups and experiments were run, and the vast majority of never caught up. To compensate for this educa our manager sample earned less than 2, 000 tion effect, we simplified the procedures in two yuan per month ways. First, for each output level which was To test for the effects of expertise, we used actually selected by an F, the experimenter an- three subject populations: college students, nounced the Fs payoffs conditional on the CPs older managers, and younger managers. The responses and the payoffs of both CPs and Fs college students were from China Textile Uni- for these choices, so that subjects no longer had versity, which is considered a high-quality uni- to compute their own payoffs. Second, forms versity in China. (Less than 0.7 percent of for recording past play were eliminated, with Chinas population attend any university, and the entire history posted in several places (in China Textile University is considered a top 20 extremely large print), making it easier for sub university )Few of these students would have to see and think about the outcomes had any direct experience with the ratchet In addition, we recruited younger managers effect who were all university educated and under age Whenever possible all workers in China, in- 30. This group included graduate students at cluding foremen, are subject to product China Textile University who had spent at least plans. Therefore, all of the managers in our five years in factories before returning to the experiment should have had extensive field ex- university to obt a graduate (M. B A-type) perience with the strategic situation our ratchet degree and China Textile University alumni effect game was designed to capture. Older working in the area, with at least two years of manager sessions employed relatively high- experience. Thus, all of these subjects should ranking managers(some of whom partic- have had some experience as managers con- ipating in a two-year, part-time M. B A-style fronting the ratchet effect. Because all of these program at China Textile University), mid-level managers were relatively recent college gradu toies operating in Shanghai. About 25 percent the education effec bect them to be subject to managers, and senior foremen from textile fac- ates, we would not ex of the older managers had university degrees; To capture the interaction between expertise another 48 percent had some post-high-school and context, we ran approximately half of the education, typically a two- or three-year degree sessions as generic sessions and half as context imilar to community college or trade school in sessions. Generic sessions employed the same the United States. Among those who had post- payoffs as the context sessions. The only differ high-school training, most had not been stu- ence was in the instructions. The instructions dents any time recently as 40 percent were over for generic sessions used abstract language the age of 50 and another 40 percent were designed to minimize the similarity between the between 40-50 years old. Moreover, age is experiment and field settings. In context inversely correlated with quality of formal ed- ucation in China (even for the college ed cated). These factors probably all contributed to Under our original procedures, Fs' payoff table in- a substantial education effect. I cluded two additional output choices attached to either the riginal procedures, older PRC beginning or end of Table 1. These choices were designed managers started out with substantially less str shift the precise location of the equilibrium between ssions(to offset possible information leakage across rep- inated by one or more of the outputs in Table 1. so heoa ot alter the The conversion rate was 0.0026 yuan= 1 franc after choices were climinated in the modified trcatments subtracting 18,000 francs from total earnings. This total iversity degree holders in China can become fore- included subjects' show-up fee. All sessions were con- men after six months of training. After one or two years. 12 All of the PRC manager sessions employed the san be in charge of a department in the firm. Average earn- n rate as the high-pay student sessions. Given the ings for the young managers abstantially higher than es of the managers(as compared to students), for the older managers, as many worked in joint venture these sessions might best be viewed as standard-pay ses- enterprises involving some private capital and some state enterprise or government capital