
Refining and extending my prior work on symmetric bargaining and coordination games, I propose to study the impact of rescaling, payoff perturbations, preplay communication, and other information conditions. Rescaling introduces into the discussion of coordination failures a well established body of experimental results on the costs of decision making. The proposed study promises three results: First, to increase our understanding of important modelling issues that afflict the use of evolutionary models in experimental economics. Second, to increase our understanding of strategic uncertainty, i.e., the dispersion of (initial) beliefs and strategies. Third, to clarify the relation of the eductive and evolutive approaches to equilibrium selection which are often seen as conflicting paradigms.
EDUCATION PLAN
I propose that game theory and experimental economics be made an integral part of the liberal arts curriculum. These fascinating developments of economic theory have been slow to find their way into the liberal arts colleges which supply more than their share of graduate students in economics. The slow adaptation of game theory and experimental economics is a deplorable fact as game theory and experimental economics signify a veritable paradigm shift in "the dismal science". Equally important, game theory and experimental economics seem ideally suited to address the welldocumented "chilly" classroom climate and to make female and minority students more welcome.
Table Of Contents
PROJECT SUMMARY
PRIOR NSF SUPPORT: None.
CAREER DEVELOPMENT PLAN
1.a. Summary of prior research
1.a.1. Symmetric bargaining games
Eductive analysis
Evolutive analysis
Experimental and computational results
1.a.2. Coordination games.
Eductive analysis
Evolutive analysis
Experimental results
1.a.3. Experimental design and other results
1.b. Relation of prior and proposed research to other research
1.c. General Plan of Work
Hypotheses to be tested
Refinement of prior work
Extensions of prior work
Applications of proposed work
1.d. Objectives and significance of proposed research.
2. EDUCATION PLAN
2.a. Discussion of prior education activities
2.b. Summary of teaching and other education accomplishments
2.c. Outline of future education activities
Refinement of existing offerings
Extensions of the current offerings:
Programming experiments as independent study.
An interdisciplinary major in organization science
2.d. Objectives and significance of the proposed
education activities in relation to the goals of the institution
2.e. Objectives and significance of the proposed education activities in relation to career goals.
BIBLIOGRAPHY
BIOGRAPHICAL SKETCH
PROPOSED BUDGET: DETAILS
PROPOSED BUDGET
PROPOSED BUDGET: NOTES
CURRENT AND PENDING SUPPORT: None
FACILITIES, EQUIPMENT, AND OTHER RESOURCES
SPECIAL INFORMATION AND SUPPLEMENTARY DOCUMENTATION
RESEARCH PLAN
1.a. Summary of prior research
One finds in the literature a growing number of papers that report experimental results for games with multiple equilibria where two key selection criteria, risk dominance and payoff dominance, are in conflict ([CDFR90,92b], [VHBB90,91,93], [VHB+fc], [RVHB94], [Fri 1994], [CF94]; see also [Cra91,93], [CB94], [Kim94], [Kim92a,92b] for discussions of the results reported in [VHBB90,91,93], [CF94] for additional experimental results, and [CJ88] for numerous examples of the important phenomena represented by such games.)
Interest in these games has been spawned by experimental evidence for important classes of games that often contradicts the wellknown HarsanyiSelten axiomatization which ranks the payoff dominance criterion over the risk dominance criterion ([HS88]). The experimental evidence seems to argue for the evolutive approach to equilibrium selection instead of the eductive (note 1). Possibly motivated by these results Kandori et al. [KRM93] and Young [You93] have proposed models in which, in the ultralong run, the risk dominant outcome is always selected. Binmore et al. [BSV93] discuss these models and demonstrate that models can be found where the payoff dominant rather than the risk dominant equilibrium is selected. Carlsson & Van Damme argue that in global games, i.e. games with welldefined payoff perturbations, "rational players are forced to pick the risk dominant equilibrium even when the other equilibrium is Paretopreferred." [CVD93]
Much of my prior research has focused on symmetric bargaining games and the particular class of coordination games known as stag hunt games. For certain parameterizations, both staghunt games and symmetric bargaining games feature multiple equilibria and the tension between risk dominance and payoff dominance. Through my prior research I addressed modelling issues regarding the use of evolutionary models in experimental economics. Closely related, I explored the impact of re scaling, the role of the secure strategy (which tends to undermine the salience of the payoff dominant outcome(s)), payoff perturbations, and other information conditions. Let me first explain why I have chosen these classes of games and the results I (and collaborators) have come up with.
1.a.1. Symmetric bargaining games.
Description. Symmetric bargaining games are, subject to positive monotone transformation, based on variants of the following payoff matrix:
 x,x x,0 y,z
 B = 0,x e,e 0,0
 z,y 0,0 0,0
where y > e > z > x, and y + z = e + e = 1. In my prior research with collegues at Texas A&M University [VHB+fc], I have used x = 3, y = 6, z = 4, and e = 5 where numerals denote dimes. Thus parameterized, the symmetric bargaining game can be thought of as a divideadollar bargaining game that features three feasible outcomes on the reverse diagonal plus a secure strategy (x,x,y). It is this strategy that tends to undermine the salience of the payoff dominant outcome(s)).
Eductive analysis. (note 2) The feasible outcomes on the reverse diagonal are the three pure strategy Nash equilibria (note 3). Two mixed strategy Nash equilibria are located at (6/7,0,1/7) and (2/5,3/5,0). The intuition underlying the first mixed strategy (which is of major interest) is instructive. Assume that one has reason to expect that the other player will play the first action, then one has an incentive to play the third action.
The eductive approach per se does not help to identify a unique equilibrium for the symmetric bargaining game(note 4). Fortunately, a number of general equilibrium selection theories are available, notably Harsanyi and Selten's [HS88]. Building on the eductive approach, their axiomatization postulates and ranks desirable properties like symmetry, efficiency (payoff dominance), risk dominance (security), etc. For the parameterization of the symmetric bargaining game utilized in [VHB+fc], neither symmetry (which selects the equal division outcome and the two mixed strategy Nash equilibria) nor payoff dominance (which selects the three pure strategy Nash equilibria) by themselves help to select a unique equilibrium. However, if we combine both criteria the equal division equilibrium (e,e) gets selected.
Evolutive analysis. The evolutive approach to equilibrium selection predicts the outcome of a game by tracking the distribution of actions in repeated (anonymous) encounter games given an initial distribution of actions. The basic idea is that "fitter" actions will displace those that are less fit. (See [Fri91,94], [Har81], [KO93], [RE93] for examples.) This process of gradual displacement of actions can be modelled by means of systems of differential and difference equations  often labeled dynamical systems  which are derived from the payoff matrix of the game being played (note 5). Dynamical systems allow for analysis of stable and/or unstable fixed points and basins of attraction, i.e., regions of the state space whose points are attracted to particular equilibria. Remarkable results are available in the literature regarding the relationship between static, quasidynamic, and dynamic steady state equilibria (note 6). The problem is that an infinite number of dynamical systems can easily be generated allowing for successful model mining. (See [KO93].)
If for instance we employ the continuous replicator dynamical system, then the state space for the symmetric bargaining (and the onepopulation experiments) is partitioned into two basins of attraction, one associated with the unique equilibrium predicted by the eductive analysis, the other associated with the mixed strategy equilibrium (6/7,0,1/7). (See figure 1 which is taken from [KO93].) Given this partition, equilibrium selection depends on the initial distribution of actions.
Results of my prior research. In the onepopulation random anonymous encounter experiments reported in [VHB+fc], the initial distributions of subjects' choices of actions were all located in the basin of attraction associated with the mixedstrategy equilibrium (6/7,0,1/7), leading the particular dynamical system employed, the continuous replicator dynamics, to predict correctly the outcome of the experimental sessions. (See [VHB+fc].) (Clearly, that is not the prediction of the eductive analysis.)
But why the continuous replicator dynamical system? Why not another model function, for instance a rate of change function? (For scores of other functions, see [Fri91], [KO93], [KMR93], [You93], [LS94].) And why a continuous model function? (note 7) Experiments, by their very nature, are discrete after all. Also, the typically small number of experimental subjects seems to suggest that stochastic dynamics may be the most appropriate.
Drawing on the results of the onepopulation experiments reported in [VHB+fc], Knapp & Ortmann [KO93] study, analytically and numerically, two model functions (replicator and rate of change) and their associated dynamics (continuous or discrete, deterministic or stochastic) for their robustness. We show, among other things, that the basins of attraction as well as trajectories are very sensitive to both the particular model function and their dynamics. Our discrete and stochastic dynamics incorporate important experimental design parameters like step size and population size. Specifically, we tied discreteness to step size and proposed to operationalize step size in experiments through rescaling which we defined as the simultaneous multiplication of payoffs by a positive rational number m (note 8). Without loss of generality, the restriction defines 'rescaling' as 'rescaling down.'
Rescaling is motivated by the following observations and empirical regularities. Symmetric bargaining games (and coordination games as well) confront players with the choice between a secure action and risky actions, with the risk dominant outcome being associated with the secure action and the payoff dominant outcome being associated with a risky action. Thus, a wellestablished body of experimental results on individual decision making becomes relevant for the discussion of equilibrium selection principles ([BKJ90], [TK92], [MRS88]; see also [Har92], [SW93a,b], [Abb94], and [SB94]. Experimental results and theoretical considerations suggest roughly that, as expected payoffs per round are reduced, a subject is more and more likely to choose the risky action. The intuition is clear and important. As expected payoffs per period are reduced, the opportunity cost of employing the risky action decreases (note 9).
In sum, I conjecture that subjects would be more willing (initially) to employ the risky strategy if payoffs would be rescaled; specifically, I conjecture that through rescaling I would be able to systematically shift the initial distribution of actions of subjects toward the basin of attraction of the risky equal division outcome (note10). (Recall that 'rescaling' is defined as 'rescaling down.')
In [Ort94b] I analyzed both the impact of rescaling and the prominence (salience) of the secure strategy (note11). (Recall that the secure strategy tends to undermine the salience of the payoffdominant outcomes.) Specifically, I conducted four experimental sessions in which I rescaled the payoffs of the onepopulation symmetric bargaining experiments by a factor of 0.2, while simultaneously increasing the number of periods by a factor of 5. While the rescaling seems to have moved the initial distribution toward the basin of attraction for the equal division outcome  the number of data points is too small to draw firmer conclusions at this point  , all initial distributions were located in the same basin of attraction as before and the trajectories converged roughly to the stable fixed point (6/7,0,1/7). In essence, the secure strategy in the original symmetric bargaining game was too salient.
In four additional experimental sessions I made the secure strategy less salient by setting x = 2 (dimes) (in two of the sessions) and x = 2.5 (dimes) (in the other two sessions.) (note12) For x = 2, the initial distribution of choices was located in the basin of attraction associated with the equal division outcome (and indeed, that was the outcome). For x = 2.5, the initial distribution of choices was located in the basin of attraction associated with the stable fixed point (and, too, that was the outcome). In additional sessions I then rescaled the latter parameterization as before. The results of this treatment suggest that, first, rescaling affects the initial distribution of choices of participants in a predictable manner (toward the payoff dominant outcome), and, second, that rescaling affects the noisiness of trajectories. Further investigation seems warranted.
1.a.2. Staghunt games.
The symmetric bargaining game is relatively complex and puts fairly high cognitive demands on experimental subjects, notwithstanding the fact that the instructions are very simple. I therefore decided to investigate the impact of rescaling, the role of the secure strategy, and the consequences of payoff perturbations as well as changes in information conditions in a less complex setting (note 13). For certain parameterizations, coordination games of the staghunt variety are the simplest class of games with multiple equilibria that are Paretoranked and feature the conflict between risk dominance and payoff dominance. (They reduce the pure action space and the number of possible outcomes.) They are thus an ideal point of departure for the study of these treatments. Also, for staghunt coordination games both analytical and empirical results and thus benchmarks for systematic replication and comparison are readily available. (See [CVD91,93], [VD94], [Kim92a,b] for the former; see [CDFR92b] for the latter.)
Coordination games are, subject to positive monotone transformations, based on variants of the following payoff matrix:
x,x y,0
 C =
 0,z 1,1
where y and z are less than or equal to x and x, y and z are numbers in the open unit interval. Note that there are two pure strategy Nash equilibria at (x,x) and (1,1) which are Paretoranked. (There is also a mixed strategy Nash equilibrium.) For y = z, this game is known as a staghunt game (note 14). The staghunt game I studied is a 2x2 game of the following general form (note 15):
"alpha"2 "beta"2
"alpha"1 x,x x,0
g(x) =
"beta"1 0,x 4,4
Eductive analysis. The game has three Nash equilibria as long as x is an element of (0,4);two are pure strategy Nash equilibria (("alpha"1, "alpha"2),("beta"1, "beta"2)), one is mixed. For all values of x is an element of (0,4), g(x) is a game of common interest.
The notion of risk dominance is based on the Nash product of deviation losses, here given by x^2 for "alpha" = ("alpha"1, "alpha"2) and (4x)^2 for "beta" = ("beta"1, "beta"2). "alpha" risk dominates "beta" if its Nash product of deviation losses is greater, and vice versa. For example, for g(3), x^2 > (4x)^2, while for g(1) the opposite inequality holds. Note that for g(3) the risk dominant outcome, "alpha", does not coincide with the payoff dominant outcome, "beta". On the other hand, for g(1) the two outcomes coincide. The dividing line is represented by g(2). For x is an element of (0, 2), risk dominant outcome and payoff dominant outcome coincide; while for x is an element of (2,4) they do not (note 16).
Evolutive approach. As for symmetric bargaining games, the state space can be partitioned into basins of attraction, one associated with "alpha" and the other with "beta". (For details see [Ort94a].) ]
Experimental Results. [Ort94a] summarizes the results of ten experimental sessions that were conducted in the fall of 1993 and 1994; it includes those reported in [Ort93]. Eight of the sessions (1  3, 6  10) were conducted without, and two were conducted with payoff perturbations (4, 5) (note 17). Session 1 was an implementation of stage game g(2), sessions 2, 4, 5, and 6  8 were implementations of stage game g(3), and session 3 of g(3.5) (note 18). Sessions 9 and 10 were rescaled versions of g(3), with a rescaling factor of .2 and five times the number of announced rounds.
In sessions 1  5 (fall 1993) subjects' choices of actions converged to the payoff dominant outcome. These results differ significantly from experimental results in the literature, all of which seem to favor risk dominance instead of payoff dominance (note 19). In sessions 6  8 (fall 1994), subjects' choices of actions converged to the riskdominant outcome (note 20). Given the new results, sessions 9 and 10 were conducted to analyze whether rescaling would have an impact. The data show convergence to the riskdominant outcome in session 9 and convergence to the payoffdominant outcome in session 10. It is interesting to note that initially in session 10, none of the subjects played the second action. Yet, the subjects in that session manage to converge to the payoffdominant outcome.
At first sight, the results of these experimental sessions may seem inconclusive. It turns out that the first impression is misleading. A preliminary analysis suggests strongly that the results are driven by the inherent randomness of the matching protocol [Ort94a] (note 21). On the other hand, given the randomness of the matching protocol, subjects react in fairly systematic ways to the positive or negative reinforcements that they are handed. Simple "learning direction models" ([MN93], [Nag93,94], [SB94], [TFF94], [Har81], [RE93]) appear to organize the data surprisingly well, incidentally, confirming recent results regarding the levels of reasoning typically employed. (See [CJRS93], [Nag93], [Sta92],[StaW92].) The stability of choice behavior seems to warrant further investigation, too (note 22).
The stability of choice behavior notwithstanding, the data document heterogeneity across subjects and variation across experiments. A special aspect of that, differential ability to reason, I have started to investigate in [OT94], where we explore the induced value approach to the modeling of differential ability proposed by [Sobl91]. I currently work on the extension of [OT94] to nonconstantsum games, especially coordination games.
1.a.3. Experimental design, facilities, pilot experiments.
All experiments summarized above used a random anonymous encounter protocol and, with the exception of those reported in [OT94], were conducted in a computerized environment. (Please see facilities statement.)
In addition to the experiments summarized above, several other programs are ready to be run. The most intriguing of those are replications of the coordination game experiments used in [VHBB90], with two additional twists. First, motivated by the definition of the replicator model function, students consult a history screen which summarizes the distribution of actions over time. If the only pilot session conducted so far is any indication, this change in information has a dramatic impact on outcomes. (The pilot session used a rescaled version of the coordination game experiment in [VHBB90].) The identical information treatment has been programmed for both symmetric bargaining games and coordination games. Second, motivated by the impact of information treatments in general, and that of preplay communciation in particular, students are prompted for their intended play before every round of actual play, with the results being communicated. (See [BDKS94] and [BKS93] for rationale.) This latter investigation is joint work with Andreas Blume from the University of Iowa.
1.b. Relation of prior and proposed research to other research
As regards evolutive models, in addition to the payoff matrix, aspects of the matching protocol ([Fri94], [CF94], [VHB+fc]), information conditions ([Fri94], [CF94]), and population size (([Fri94], [CF94]) are generally considered relevant for a description of the strategic environment. Crawford [Cra93] also addresses the importance of population size and the rules that govern the interaction of agents as point of departure for his unified explanation of how agents learn in the wellknown coordination game experiments by Van Huyck, Battalio, and Beil [VHBB90], [VHBB91]. More specifically, he proposes an evolutionary explanation of how the interaction between strategic uncertainty (which finds its expression in the dispersion of (initial) beliefs and strategy choices) and learning induce the observed outcomes. Along the same lines, Crawford and Broseta [CB94] propose evolutionary explanations of [VHBB93] who use an auction as a (successful) coordination device for the coordination game underlying [VHBB91]. The intriguing work by Crawford and Broseta is built on the premise that fully endogenizing differences in subjects' beliefs is impossible since subjects' relevant information or characteristics are unobservable. It follows that "even a normative theory of coordination must have an empirical component" ([Cra93]); hence, Crawford characterizes subjects' beliefs statistically.
While accepting that reasoning, my prior work is informed by the conjecture that rescaling, the salience of the secure strategy, payoff perturbations and other information conditions are all parameters that can help us understand better the empirical content that we ultimately will have to rely on. The evidence accumulated so far suggests that this is indeed so. Further investigation seems warranted.
1.c. Outline of general plan of work
Detailling the experiments I intend to run is difficult because the research questions to be answered are path dependent. What experiment to do next is often dictated by the results of earlier experiments. Thus, I shall enumerate here the key hypotheses that underlie my prior and future research. (All hypotheses assume games like the ones discussed earlier, i.e., games where risk dominance and payoff dominance are in conflict.)
Hypotheses to be tested
H1.: Rescaling is an important treatment parameter that affects in a systematic manner, initial conditions and noisiness of trajectories (and hence selection of outcomes.)
(Recall that 'rescaling' is defined throughout as 'rescaling down.')
H1.1.: Rescaling increases the likelihood of payoff dominant outcomes (by shifting the initial distribution of actions toward them and making trajectories noisier, thereby increasing the likelihood of trajectories crossing from one basin of attraction to another.) H1.2.: Rescaling reduces strategic uncertainty (by reducing the dispersion of initial beliefs and choices of subjects.)
H2.1.: Giving information about the distribution of actions in previous rounds increases the likelihood of payoff dominant outcomes. H2.2.: Preplay communication in the form of messages increases the likelihood of payoff dominant outcomes. H2.3.: Payoff perturbations increase the likelihood of payoff dominant outcomes.
H3: Rescaling interacts in important (and predictable) ways with other aspects of the experimental design, namely information about the distribution of actions in previous rounds, preplay communication in the form of messages, and payoff perturbations. Specifically, rescaling in all three cases increases the likelihood of payoff dominant outcomes.
H4: Rescaling, information about previous distribution of actions, pre play communication in the form of messages, and payoff perturbations all interact with the other relevant parameters, namely population size.
Refinement and extension of prior work
Using symmetric bargaining games, staghunt games, and the [VHBB] coordination games I shall first run those experiments which are already programmed and that were described in 1.a.3.. (To proceed in this order is suggested by the prospect of getting early results.) I expect to see the selection of different equilibria than the ones reported in the literature in several of the treatments. In those cases, formal statistical tests seem less important. That said, I will study the impact of the treatments suggested by the hypotheses on belief parameter estimates [Cra93],[CB94], quantal response parameters [MP93], and the discount parameters of the RothErev dynamics ([RE93]).
Application of proposed work
The research which I have documented so far is not the only line of research I pursue. Of particular interest in this context is research that I did after the College asked me and a colleague to study whether an expansion of the College would be feasible. The resulting study brought up a number of issues that traditional I.O. theory does not address. I have since then written several papers that use game theory (in its eductive incarnation) to understand the organization of nonprofit organizations in general and educational organizations in particular. (See the biographical sketch.) Specifically, by modelling educational institutions as cascades of principal agent games, I have identified the sources of influence and laid the groundwork for my current investigation of the cognitive aspects of sensemaking [GTCC94], an inherently evolutive process. It turns out that this latter work benefits immensely from my experimental research. For example, one of the papers I am working on frames a famous "story" in organization/management science, the "Abilene paradox", as a coordination game.
1.d. Objectives and significance of proposed research.
Through my prior research I addressed modelling issues regarding the use of evolutionary models in experimental economics and, closely related, the impact of rescaling, the role of the secure strategy (which tends to undermine the salience of the payoff dominant outcome(s)), the consequences of payoff perturbations, and other information conditions. This research plan proposes to refine and extend my prior research. In doing so, I incorporate a wellestablished body of experimental results on individual decision making into the discussion of equilibrium selection principles. At the same time, I increase our understanding of how these treatments affect strategic uncertainty i.e., dispersion of beliefs and strategies as the game proceeds, and in the first round. The importance of the first round data has been stressed by many studies recently [BH93],[CGK93,94],[RE93], [VHBB91,93],[Cra93],[CB94]. Given the situation, while ideally we would like to be able to rely on a theory of initial beliefs, the best we can hope for is a better understanding of the relevant factors that affect the initial distribution of actions in games where risk dominance and payoff dominance are in conflict. Such an understanding will allow us to define the empirical content that we have to evaluate on a casebycase basis.
Finally, in incorporating the treatments suggested in the hypotheses, and to the extent that they allow us to shift the initial distribution of subjects' choices toward payoffdominance outcomes, it might become clearer that the eductive and evolutive approaches are not necessarily conflicting paradigms. The evidence of my prior research strongly suggests so.
2. EDUCATION PLAN
2.a. Discussion of prior education activities
The state of the economics major has been of concern to economists for quite a while. (See [SBH+91a,b], and [SS94] for recent statements.) Siegfried et al. identify two deficiencies of introductory courses: "Introductory courses tend to be encyclopedic, and all too often oriented toward formalism of theory at the expense of application." ([SBH+91a]) The underlying report ([SBH+91b]) blames a "chilly" classroom climate on content and methodology as well as the incongruity of student learning and faculty teaching styles. Others ([Cat91], [Sha92]) have pointed out that these factors erect barriers to entry for female and minority students. In addition, principles courses are only now starting to catch up with recent fascinating developments in economic theory, namely the innovations introduced by game theory and experimental economics.
Over the last three years I have endeavored to incorporate both game theory and experimental economics into the curriculum of the principles courses as well as other courses (namely, "Modern Industrial Organization", "Financial Markets", and "The History of Economic Thought" (all intermediate courses)) and "Theory and Practice of Games and Decisions" (an upper level course).
In my principles class, I have incorporated a variety of experiential learning strategies, use of inclass experimental demonstrations being one of them. I have detailled the rationale for such an approach in "The Ordinary Business of Students' Lives, or Business As Usual? A plea for the incorporation of game theory, experiments, and experiential learning into the principles course," (w/ Akiba Scroggins, in Aslanbeigui & Naples (eds), Rethinking Economic Principles: Critical Essays on Introductory Textbooks, Homewood: Irwin, forthcoming.) We argue that the introduction of game theory and classroom experiments, will address the concerns enumerated at the beginning of this section. Namely, the introduction of classroom experiments creates all by itself a less chilly classroom climate. (A number of classroom experiments that I use routinely in my classes can be found in [OC95a,b].) Equally important, the introduction of game theoretic concepts allows most micro concepts to be built from a relatively small number of key principles and games (two sided and onesided prisoner's dilemma games), which themselves are often the basis for classroom experiments.
As it is, I have already designed and implemented a principles class that is radically different from the way principles classes are typically taught. Likewise, in the intermediate classes I have used game theory (for instance, [OM95]) and experimental economics wherever possible. (Most of the experiments in [OC95a] can be used in intermediate classes.)
Of most immediate relevance to the Research Plan laid out earlier is my upper level class, "The Theory and Practice of Games and Decisions." This class is based on Binmore's Fun and Games [Bin92] (A rather rigorous text, its title not withstanding!) and articles from journals and recent working papers. I have taught the course twice (Spring 1992, 1994). Last Spring, as an alternative to writing a theory paper, I offered students the opportunity to design and implement pilot experiments that I suggested. Half the class took me up on the offer and I received some intriguing term papers. Based on one of the term papers, I conducted additional experiments and the resulting paper (with the student as coauthor) has been submitted for publication; two other papers are likely to follow the same path. My overall experience has been that students are fascinated by both game theory and experimental economics. Because of their interest in the material, they have surprisingly little difficulty dealing with often rather technical and subtle constructs. Many of the students also find that the course is rather practical. To quote from a student journal: "I had an interview with a senior manager ... He asked me what sort of classes I was taking. When I mentioned Games and Decisions, he reacted positively. He said he often uses the Prisoner's Dilemma with his clients to explain his recommendations. ... I was pleased that at least one class I have taken was immediately applicable to my postgraduate life."
Student evaluations (very positive), enrollments (all courses I mentioned above are viable and enrollments are increasing), and enrollment patterns (comparatively high percentage of female students especially in principles classes), indicate that my attempts to incorporate experimental economics and game theory into the classroom successfully address the concerns enumerated above. Further evidence is supplied by the fact that four of the students who took my intermediate or upper level classes have applied and been awarded Surdna undergraduate research fellowships. These fellowships pay a generous stipend and are hence quite competitive. Their explicit purpose is to encourage serious research by undergraduates of a topic in which a faculty member is independently interested. One of the collaborations has resulted in a coauthored publication ([OM95]) and a revised and resubmitted manuscript ([MO95]); I'm confident others will follow. It is noteworthy that of the four students who were awarded Surdna undergraduate research fellowships two were female, one of the two in addition a minority student who attended the AEA program at Stanford University this past summer (Akiba Scroggins.) As of the writing of this proposal I am preparing two more applications, both prospective applicants are female. Finally, a number of my students have either already entered or are seriously considering entering graduate school; among them are all past, current, and prospective Surdna fellows.
Looking at the examples that the CAREER guidelines supply on page 3 to guide applicants' summary discussion of planned education activities, it appears that I engage already in many of the activities listed.
2.b. Summary of teaching and other education accomplishments
I'd like to relate my tenured colleagues' assessment in the second year review (Spring 1993, the only review before the tenure decision) in lieu of the required summary.
"Andreas is a dedicated and tireless teacher who places heavy demands on his students. His teaching style is highly interactive, involving student journals, classroom simulations and experiments, group projects, dialectic exchanges with and between students, continual feedback and extensive office hours. This pedagogy, as well as the structure of assignments and the nature of exam questions, stresses the application of economic principles to the student's everyday decisions. It challenges students to discover and synthesize on their own. We praise these objectives and this approach.
The student evaluations indicate effective teaching, improvement, and some notable successes. Some students found the presentation, and the response to questions, in Andreas' first version of introductory economics to be unclear. Some of the students felt threatened by the aggressive teaching style. Neither issue resurfaces in Andreas' second version of this course, which earns high praise from students. ... In Andreas' other courses, especially economic thought and game theory, the student evaluations were most positive. Here, some students felt that the novelty of the material and the intellectual freedom of the classes made these courses unique at Bowdoin. ...
We also note that Andreas has guided five students in independent study during his first two years. He has attracted several of our best students to undertake creative projects, several of which may result in coauthored publications. ... This propensity to attract and motivate our best students indicates Andreas' special abilities as an instructor."
Much as I am tempted to take credit, I am convinced that the nature of the subject matter and the use of (classroom) experiments deserve a significant portion of it.
2.c. Outline of future education activities.
Refinement of existing offerings. It is likely that I will teach the same set of classes I taught between 1991  1994 during the 1995  1998 academic years. Specifically, I will teach Principles, Industrial Organization, Financial Markets, and Theory and Practice of Games and Decisions in academic years 1995/1996 and 1997/1998, and Principles, Financial Markets, and either Mathematics for Modern Economics or History of Economic Thought in 1996/1997. My simple game plan is to refine my current course offerings, incorporating even more game theory and experimental economics into the curriculum.
As regards the principles course, I shall continue to re design it (using the article I wrote with Akiba as a point of departure.) I intend to document the resulting curriculum in lecture notes. In Theory and Practice of Games and Decisions I shall make design and implementation of an experiment a mandatory assignment. All the while I shall continue the kind of joint research projects (independent studies, Surdnas) that I have been heavily involved with in the past.
Extension of the current offerings: Progamming experiments as independent study. Making a virtue of necessity, this coming Spring semester I supervise (in conjunction with a colleague in the computer science department) an independent study whose explicit purpose is the programming of key pricing institutions (auction, posted prices.) While this project will clearly help me, the project will also give the student (who previously took my Industrial Organization class and who is a biology/computer science major) a chance to test his programming skills on more than a toy project. This independent study is by everyone involved understood to be a pilot project. As it is a rare Paretoimproving move for everyone involved  the College, the student, me  I expect such collaborations to become a fixture.
Extension of the current offerings: An interdisciplinary major in organization science. As mentioned in the research plan, I have studied whether the expansion of the College will pay off. Since that study was finished I have written several papers that explore issues of organization design using game theory as well as mathematical theory of complementarities ([MR90].) Experimental economics and game theory (both the eductive and evolutive incarnations) have been extremely helpful in conceptualizing issues of influence and sensemaking in organizations ([GTCC94]). My interest in organization science has led to numerous conversations with colleagues in other departments. Together with a colleague in Bowdoin's psychology department  Dr. Paul Schaffner  I have started to explore a new interdisciplinary major that is anchored in both economics (Principles of Microeconomics and Intermediate Microeconomics, Industrial Organization, Games and Decisions) and psychology (Introduction, Personality Theory or Social Psychology, Organizational Behavior, Cognition), but will also include the statistics and mathematics components as well as selected courses from the offerings of anthropology/sociology and government. Obviously, everything I said before about the merits of making experimental economics and game theory an integral part of the curriculum, applies.
Evaluation. Fels's important point regarding curricular innovations is well taken [Fels93]. I intend to rely on the evaluations utilized currently (student evaluations, departmental evaluation). Bowdoin's institutional commitment to evaluate, whether indeed the approach sketched in this education plan leads to results in accordance with the CAREER guidelines, is most welcome.
2.d. Objectives and significance of the proposed education activities in relation to the goals of the institution.
While experimental economics has firmly established itself in about two dozen universities, it has yet to reach the liberal arts college. (Classroom experiments are being used at several colleges, but to the best of my knowledge courses like my Theory and Practice of Games and Decisions are rather unusual.) If my reading of ESA meetings is correct, I am at this point the only person who conducts research experiments in the liberal arts college environment. To the extent that designing and implementing real experiments is qualitatively a different experience than the participation in a class room experiment, that fact reflects a deplorable state of affairs in light of the dramatic paradigm shift initiated by both experimental economics and game theory, and given that liberal arts colleges, while accounting for only two percent of the college graduates in the country, produce a high percentage of those who go on to graduate school. (David W. Breneman (1994), Liberal Arts Colleges: Thriving, Surviving, or Endangered ?, The Brookings Institution, chapter 1) (Bowdoin is one of twelve case studies presented in Breneman's book.)
The logistics of experimental economics, especially if they include both research and teaching (which I see as complementary), can be a quite a challenge per se (i.e., when one can rely on colleagues and graduate students.) They are even more so in a liberal arts college setting (where colleagues with similar interests and/or graduate students do not exist and one often finds oneself in and with multiple roles and responsibilities.) Things get more complicated when the conditions for both experimental research and teaching have to be created from scratch.
It is, in short, an uphill battle to make experimental economics an integral part of the liberal arts curriculum. The difficulties I had at Bowdoin are probably typical. I spent inordinate amounts of time and effort to convince the College (faculty research committee, dean for academic affairs) and department to fund subjects payments and programming work for the experiments summarized above. In doing so, I had to explain, over and over, elementary tenets of experimental economics like salient subject payments. ("Should not participation in the experiment as such be enough of a reward?", "I find paying subjects morally wrong!") Relying on student programmers and, by way of the UNIX operating system, on a computing center which was in disarray for the last couple of years did not make things easier.
Much of that is history now. As the facilities statement, the research documented in the research plan, and the biographical sketch document, I have demonstrated that experimental research can be done successfully at liberal arts colleges and with relatively small budgets. However, no doubt that I could have been more productive if I would have had my own resources and if I would not have had to spend so much time on compatability problems, petty turf wars ("This is my computer lab!"), writing applications for College grants and otherwise having to convince the relevant people that experimental economics ought to be an integral part of the liberal arts college.) Taking the desirability of making experimental economics and game theory an integral part of the liberal arts college curriculum for granted, I have shown that it is feasible  thus enriching the liberal arts college and (according to the preliminary evidence) demonstrating one way to attract members from groups that traditionally have been underrepresented in economics.
2.e. Objectives and significance of the proposed education activities in relation to career goals.
My goal is, quite simply, an academic career that integrates research and education activities. I believe that I am well on my way toward that end. The funding of this career development proposal would undoubtedly speed the convergence.
3. DEPARTMENTAL ENDORSEMENT
I have read and endorse this Career Development Plan.
...............
Rachel Connelly
Associate Professor and Department Head
Brunswick, ME, .....
NOTES
1. As to the terminology, Binmore [Bin90] uses the words eductive and evolutive to denote what Van Huyck at al [VHB+fc] call deductive and inductive. Binmore explains, "There are two types of influence, not necessarily independent, which could well be relevant to an explanation of why homo economicus might be a useful approximation to homo sapiens in a given context. The first is the influence of education and the second is that of evolution." [Bin90, 15] "The word eductive will be used to describe a dynamic process by means of which equilibrium is achieved through careful reasoning on the part of the players. Such reasoning will usually require an attempt to simulate the reasoning process of other players. ... The word evolutive will be used to describe a dynamic process by means of which equilibrium is achieved through evolutionary mechanisms. ... adjustment takes place as a result of iterated play by myopic players." [Bin90, 155]
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2. The following analysis is concerned only with onepopulation experiments. See [VHB+fc], [KO93], and [Fri94] for the consequences of switching to twopopulation experiments, i.e. experiments where row and column players are distinguished.
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3. Note that, if one were to cross out the third action one would be left with a game of the coordination game variety. (To be explained presently.) If, on the other hand, one were to cross out the second action one would be left with a variant of the battle of the sexes game. In my prior research I have not explored the latter class of games for which interesting results exist [CDFR92b].
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4. Refinements do not produce unique solutions in games with multiple strict Nash equilibria.
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5. The terminology is not standardized. [KO93] define a dynamical system as being constituted by a model function (replicator, rate of change) and a dynamic (stochastic, discrete, continuous). Here I follow this convention.
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6. For instance, Friedman [Fri91] has shown that the stable fixed points of a large class of dynamical systems, among them the dynamics considered in Van Huyck et al. [VHB+fc], are Nash equilibria of the related static game. See also Mailath [Mai92].
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7. Knapp & Ortmann [KO93] suggest, for the onepopulation experiments reported in [VHB+fc], a rate of change model function as one that does a better job in explaining the results than the often used replicator model function. The replicator model function sets the growth rate of a strategy proportional to its relative fitness; the rate of change model function sets the rate of change of a given strategy proportional to the normalized fitness minus the percent of the population that previously played that strategy.
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8. We employed the word 'rescaling' to distinguish our procedure from 'scaling.' See for instance [Bin92].
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9. While the experiments we discussed are not experiments in individual decision making, the general principle remains the same.
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10. Note that rescaling does not affect the equilibria structure and associated basins of attraction for continuous replicator dynamics (or for that matter any other continuous model function.) It can dramatically affect those of discrete dynamics. See [KO93] for examples.
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11. See Mehta et al [MSS94] for a recent discussion and experimental investigation of salience.
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12. Technically, making the secure strategy less attractive contracts the basin of attraction associated with the stable fixed point, simultaneously it expands the basin of attraction associated with the equal division outcome. (See [Ort94b].) This is not the only effect though. I conjecture that it also affects the initial distribution of outcomes, systematically reducing strategic uncertainty.
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13. The impact of context and transference of experience in related environments is increasingly acknowledged as an important issue.
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14. The games underlying the experiments reported in [VHBB90,91,93] are of the same basic structure, but feature seven Paretoranked pure strategy Nash equilibria for a 7x7 game. [Cra91,93], [CB94] analyze those variants of the game where y = z
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15. This particular parametrization is the running example of Carlsson & Van Damme's analysis of global games [CVD93].
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16. The underlying rationale is intuitive. Assume, for example, that you have reason to believe that all other players will choose their actions randomly, and that the row player (you) is risk neutral. Then, the expected value of choosing the risky strategy is higher if x (0, 2), while the expected value of the secure strategy is greater if x (2, 4). Roughly, as x increases, the secure strategy becomes more and more attractive relative to the risky strategy.
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17. Payoff perturbations were induced by random draws in each period from the open interval (30  2.5, 30 + 2.5).
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18. The benchmark parameterization in [CDFR92b] is g(3.2).
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19. Friedman [Fri94] documents "Kantian behavior" for small groups of 2, 4, and 6 players. Rankin et al. [RVHB94] also document the dramatic impact of payoff perturbations. In light of the wellknown results on equilibria [Bin92] the payoff perturbations do not come totally surprising.
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20. It is noteworthy that the immediate environment (including laboratory, experimenter, and instructions) had not changed between the fall of 1993 and of 1994.
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21. Specifically, the small number of subjects employed (which was motivated by budget constraints and justified by Friedman's results regarding group size and "Kantian behavior" [Fri94]) and the random matching protocol can lead to rather erratic reinforcements. To illustrate, if four of eight players have decided to play the strategy associated with the payoff dominant outcome, then they can end up being paired with each other or the four players that have chosen the other strategy. In the first case, they get positive feedback; in the second, negative. The randomness of the matching protocol may create "runs" of postive or negative reinforcements prompting players to misread their situation.
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22. Learning direction theory is based on the empirical observation that subjects tend to change actions in response to last period's experience.
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Last updated: 3/26/1998