ten little treasures of game theory and ten intuitive contradictions this paper reports laboratory data for games that are played only once these games span the standard categories static and dynamic games with complete and incomplete information for each game the treasure is a treatment in which behavior conforms nicely to predictions of the nash equilibrium or relevant refinement in each case however a change in the payoff structure produces a large inconsistency between theoretical predictions and observed behavior these contradictions are generally consistent with simple intuition based on the interaction of payoff asymmetries and noisy introspection about others decisions

dynamic limit pricing i study a multiperiod model of limit pricing under one sided incomplete information i characterize pooling and separating equilibria and their existence and determine when these involve limit pricing for some parameter constellations the unique equilibrium surviving a d1 type refinement involves immediate separation on monopoly prices for others there are limit price equilibria surviving the refinement in which different types may initially pool and then possibly separate separation involves setting prices such that the inefficient incumbent s profits from mimicking are negative as the horizon increases or as firms become more patient limit pricing becomes increasingly difficult to sustain in equilibrium

boundedly rational nash equilibrium a probabilistic choice approach we propose an equilibrium for n person finite games based on bounded rationality using the legit model of discrete choice theory at equilibrium each player uses appropriate choice probabilities given those used by the others rationality is parameterized on a continuum from complete rationality to uniform random choice results on the existence of equilibrium and on convergence to nash as rationality becomes perfect are similar to results due to mckelvey and palfrey we identify conditions such that for a given rationality parameter range the path of choices over time when the players use fictitious play converges to equilibrium c 1997 academic press

a theoretical analysis of altruism and decision error in public goods games abstract we formalize an equilibrium model in which altruism and decision error parameters determine the distribution of contributions for linear and quadratic public goods games the equilibrium density is exponential for linear games and normal for quadratic games our model implies i contributions increase with the marginal value of the public good ii total contributions increase with the number of participants iii mean contributions lie between the nash prediction and half the endowment these predictions which are not implied by a nash analysis are consistent with laboratory data maximum likelihood estimates of altruism and error parameters are significant and plausible

borrowing constraints and credit demand in a developing economy summary this paper investigates the determinants of credit demand in the presence of borrowing constraints in a developing economy we model the determinants of observed debt for chilean households while accounting for selection bias and the endogeneity of their income and specific household assets using a novel chilean dataset we estimate the relationship between household characteristics and consumer and mortgage debt we find substantial differences in the nature of these relationships across the types of debt for example we find that the income elasticity for consumer debt is greater than 1 whereas for mortgage debt it is not the results suggest the increased availability of credit combined with the aging of the chilean population is likely to drastically change the distribution and level of chilean debt these findings are particularly relevant for other developing economies currently experiencing rapid income and debt growth copyright 2015 john wiley sons ltd

rent seeking with bounded rationality an analysis of the all pay auction the winner take all nature of all pay auctions makes the outcome sensitive to decision errors which we introduce with a logit formulation the equilibrium bid distribution is a fixed point the belief distributions that determine expected payoffs equal the choice distributions determined by expected payoffs we prove existence uniqueness and symmetry properties in contrast to the nash equilibrium the comparative statics of the logit equilibrium are intuitive rent dissipation increases with the number of players and the bid cost overdissipation of rents is impossible under full rationality but is observed in laboratory experiments our model predicts this property

games with unique mixed strategy equilibria an experimental study abstract the results of an experiment studying the choices of subjects playing mixed extensions of three variants of simple 2 2 non constant sum strictly competitive games of the same form matching pennies are presented subjects exhibited a variety of behavioral adaptive learning strategies this heterogeneity of individual behavior produced aggregate dynamics whose estimated steady states are quite different from those predicted by the nash equilibria of those stage games with asymmetrical payoff functions the observed aggregative dynamics are well accounted for both by a quantal equilibrium model of mckelvey and palfrey and by a learning model of roth and erev journal of economic literature classification number c72

appropriation and concern for resource scarcity in the commons an experimental study abstract we use an experimental linear design and a logit probabilistic choice function to model and estimate agents concern for resource scarcity although full appropriation is the dominant strategy of the basic game whatever the resource size we expect that if agents exploiting a common pool resource feel any concern for resource scarcity they would be more likely to alter their appropriation strategy the scarcer the resource stock our results show that this expectation holds and appropriation is restrained when resources are scarce further as this result could be attributed to both agents concern for resource scarcity and calculation errors in the determination of the appropriation strategies we estimate the relevance of both

why do people give testing pure and impure altruism abstract researchers measure crowd out around one level of charity output to identify whether giving is motivated by altruism and or warm glow however crowd out depends on output implying first that the power to reject pure altruism varies and second that a single measurement of incomplete crowd out can be rationalized by many different preferences by instead measuring crowd out at different output levels we allow both for identification and for a novel and direct test of impure altruism using a new experimental design we present the first empirical evidence that consistent with impure altruism crowd out decreases with output jel d64 l31

the effect of exit on entry deterrence strategies abstract recent analyses of entry deterrence strategies have required an incumbent s post entry output or pricing strategy to be profit maximizing however most papers have continued to assume that either an incumbent can commit not to exit after entry or that exit is never optimal when there are avoidable fixed costs of operating in any period however exit can be the optimal strategy in this situation entry deterrence strategies operate very differently than when exit is never optimal in fact the possibility of exit can make some previously effective strategies completely ineffective while improving the effectiveness of others

crowding out voluntary contributions to public goods we test the null hypothesis that involuntary transfers for the provision of a public good will completely crowd out voluntary transfers against the warm glow hypothesis that crowding out will be incomplete because individuals care about giving our design differs from the related design used by andreoni in considering two levels of the involuntary transfer and a wider range of contribution possibilities and in mixing groups every period instead of every four periods we analyse the data with careful attention to boundary effects we retain the null hypothesis of complete crowding out in two of three pairwise comparisions but reject it in favour of incomplete crowding out in the comparison most closely akin to andreoni s design thus we confirm the existence of incomplete crowding out in some environments but suggest that the warm glow hypothesis is inadequate in explaining it

progress in behavioral game theory i s game theory meant to describe actual choices by people and institutions or not it is remarkable how much game theory has been done while largely ignoring this question the seminal book by von neumann and morgenstern the theory of games and economic behavior was clearly about how rational players would play against others they knew were rational in more recent work game theorists are not always explicit about what they aim to describe or advise at one extreme highly mathematical analyses have proposed rationality requirements that people and firms are probably not smart enough to satisfy in everyday decisions at the other extreme adaptive and evolutionary approaches use very simple modelsmostly developed to describe nonhuman animals in which players may not realize they are playing a game at all when game theory does aim to describe behavior it often proceeds with a disturbingly low ratio of careful observation to theorizing this paper describes an approach called behavioral game theory which aims to describe actual behavior is driven by empirical observation mostly experiments and charts a middle course between over rational equilibrium analyses and under rational adaptive analyses the recipe for behavioral game theory i will describe has three steps start with a game or naturally occurring situation in which standard game theory makes a bold prediction based on one or two crucial principles if behavior differs from interested readers familiar with game theory should read crawford 1997 whose approach is more eclectic than mine he concludes p 236 that most strategic behavior can be understood via a synthesis that combines elements from each of the leading theoretical frameworks traditional game theory evolutionary game theory and adaptive learning with a modicum of empirical information about behavior behavioral game theory adds psychological interpretations to this synthesis

reputation and imperfect information abstract a common observation in the informal literature of economics and elsewhere is that is multistage games players may seek early in the game to acquire a reputation for being tough or benevolent or something else but this phenomenon is not observed in some formal game theoretic analyses of finite games such as selten s finitely repeated chain store game or in the finitely repeated prisoners dilemma we reexamine selten s model adding to it a small amount of imperfect or incomplete information about players payoffs and we find that this addition is sufficient to give rise to the reputation effect that one intuitively expects

the role of cooperation and reciprocity in structuring carbon sequestration contracts in developing countries the reduction of emissions from deforestation and forest degradation redd presents a key opportunity for developing countries to mitigate global warming and to help meet long term global climate objectives however the success of a redd strategy in a post kyoto protocol regime depends primarily on the design and implementation of a financial mechanism that is feasible and effective in providing the right incentives to land holders to manage forests in a sustainable manner that contributes to climate goals optimal redd contracts must not only properly reward agents who reduce emissions from deforestation and degradation dd but also account for technical issues such as permanence and additionality of carbon offsets in many countries national authorities may not have the institutional capacity and the proper technology for measuring the delivery of carbon offsets furthermore contract enforcement becomes complex because the effort and outcomes described in such contracts are difficult for a third party to monitor and verify therefore contracts need to provide sufficient incentives to all parties to participate and perform in the long term i e to be self enforcing however the structure of the contracts may vary depending on the presence of selfish and altruistic agents this paper studies the role of cooperation and reciprocity on the structure of carbon sequestration contracts in the context of developing countries where legal enforcement may be impractical we examine if the optimal structure of self enforcing contracts differs if the paula cordero salas is a ph d candidate and brian roe is the mccormick professor of agricultural marketing and policy aede department the ohio state university this project was supported by the world bank s development research group energy and environment team under the contract a mechanism for reducing emissions from deforestation and degradation redd a framework to design cost effective contracts

altruism and charitable giving in a fully replicated economy abstract in this paper an economy is analyzed where one group of agents the altruists cares about the well being of another group of agents the recipients it is asked how changes in the size of these groups affect the altruists charitable giving in the nash equilibrium i show that a pure group size effect i e a proportional expansion of both subgroups can lead to less free riding and to a lower degree of underprovision relative to the efficient level of charitable giving

the logit equilibrium a perspective on intuitive behavioural anomalies costs associated with deviations from the nash equilibrium these payoff asymmetry effects are incorporated in an approach that introduces noisy behavior via a logit probabilistic choice function in the resulting logit equilibrium behavior is characterized by a probability distribution that satisfies a rational expectations consistency condition the beliefs that determine players expected payoffs match the decision distributions that arise from applying the logit rule to those expected payoffs we prove existence of a unique symmetric logit equilibrium and derive comparative statics results the paper provides a unified perspective on many recent laboratory studies of games in which nash equilibrium predictions are inconsistent with both intuition and experimental evidence

simultaneous decision making in competitive and cooperative environments we experimentally investigate simultaneous decision making in two contrasting environments a competitive environment a contest and a cooperative environment a voluntary contribution mechanism we find that the cooperative nature of the voluntary contribution mechanism spills over to the contest decreasing sub optimal overbidding in the contest however contributions to the public good are not affected by simultaneous participation in the contest there is a significant negative correlation between decisions made in competitive and cooperative environments i e more cooperative subjects tend to be less competitive and vice versa this correlation can be rationalized by heterogeneous social preferences towards inequality but not by bounded rationality theory

economic science an experimental approach for teaching and research economics experiments have been used to study theories and policies that are often difficult to evaluate with data from naturally occurring markets this paper is a selective summary of my work in the main areas of experimental economics markets individual decisions games and public choice the discussion pertains both to scientific discoveries and teaching innovations

efficiency of nonpoint source pollution instruments an experimental study in nonpoint source pollution problems the regulator does not observe each polluter s individual emission which prevents him from using the conventional policy instruments therefore new instruments have been designed to regulate this type of pollution in an experiment we compare the efficiency of some of these instruments an input based tax an ambient tax subsidy an ambient tax and a group fine we assume that polluters themselves are affected by environmental damages a control session without any regulation is also carried out in order to study the status quo situation our experimental data show that the input tax and the ambient tax are very efficient and reliable and the group fine is fairly efficient and reliable these instruments improve social welfare with respect to the status quo on the contrary the ambient tax subsidy decreases social welfare with respect to the status quo and its effect is very unreliable

who is credit constrained in the u s economy an important assumption of the life cycle model of consumption is the postulate of perfect capital markets this hypothesis has recently been challenged by substantial empirical evidence hall and mishkin 1982 using the panel study of income dynamics estimate that 20 percent of united states families are liquidity constrained mariger 1986 derives a life cycle model with endogenous liquidity constraints and using a cross section estimates this fraction to be 19 4 percent hubbard and judd 1986 simulate a model with a constraint on net worth which shows that with reasonable assumptions about preferences 19 0 percent of united states consumers are liquidity constrained the emerging consensus points therefore to a fraction of approximately 20 percent of the population behaving in a manner that is inconsistent with the pure life cycle model in addition hayashi 1985 and zeldes 1989 investigate the correlation among consumption wealth and income for various population groups and infer that liquidity constraints are more important for younger families with low levels of wealth and saving the main limitation of these studies is that in their data sets constrained consumers are not observable and have to be identified via indirect evidence thus there is as yet little firm evidence about the characteristics of the consumers who are likely to be credit constrained this paper adopts an approach that differs from previous tests for liquidity constraints because it makes use of data where constrained consumers are observable and explicitly links their existence to credit market imperfections and personal characteristics the data drawn from the 1983 survey of consumer finances scf and described in section ii provide information on individuals whose request for credit has been rejected by financial intermediaries in section iii a model is developed in which consumers and lenders behavior jointly determines the probability that a consumer is rationed in the credit market this probability is then

noisy directional learning and the logit equilibrium we specify a dynamic model in which agents adjust their decisions toward higher payoffs subject to normal error this process generates a probability distribution of players decisions that evolves over time according to the fokker planck equation the dynamic process is stable for all potential games a class of payoff structures that includes several widely studied games in equilibrium the distributions that determine expected payoffs correspond to the distributions that arise from the logit function applied to those expected payoffs this logit equilibrium forms a stochastic generalization of the nash equilibrium and provides a possible explanation of anomalous laboratory data

mandatory minimum contributions heterogeneous endowments and voluntary public good provision abstract in a public good experiment with heterogeneous endowments we investigate if and how the contribution level as well as the previously observed fair share rule of equal contributions relative to one s endowment hofmeyr et al 2007 keser et al 2014 are influenced by minimum contribution requirements we consider three different schedules fixmin requiring the same absolute contributions relmin requiring the same relative contributions and progmin requiring minimum contributions that progressively increase with the endowment we find that minimum contributions exert norm giving character and may lead to an increase in average group contributions this is especially true for the progressive schedule on the individual level this schedule leads to higher relative contributions by the wealthier players and thus violates the fair share norm on the group level it leads to the highest contribution level and the lowest inequality in total profits as measured by the gini index

promises and conventions an approach to pre play agreements abstract i analyze how informal agreements can be sustained by moral emotions with regard to a large class of two player games specifically i assume that people feel guilty if they breach an agreement and that the guilt increases according to the degree of the harm inflicted on the other a central insight is that it is easier to sustain efficient informal agreements if actions are strategic complements than if they are strategic substitutes i complement this general insight by studying two specific cases where negotiators face uncertainty about the breach of the agreement i show that while the optimal agreement in a game with strategic substitutes must compromise on surplus maximization and efficiency the optimal agreement in a game with sufficiently strong strategic complements tends to maximize both the surplus and the probability of compliance especially if the game is symmetric

oligopolistic entry deterrence under incomplete information recent work has investigated the effects of asymmetric information between an incumbent firm and a potential entrant this study extends the analysis to allow the initial market structure to be a noncooperative oligopoly we show that there is a bayesian nash equilibrium in which the incumbent firms although unable to collude strategically deter entry that would have occurred under complete information in contrast to the past limit pricing literature it is a high price that deters entry as it signals to the potential entrant that this is a high cost industry extending the model to allow for multiple potential entrants we find that increasing the degree of potential competition raises the preentry price and reduces the likelihood of entry

contributions in linear public goods experiments with stranger matching two motivations we investigated why subjects contribute to the public good in a linear public goods game with stranger matching in this experiment subjects were asked to determine their contributions to the publ

anomalous behavior in a traveler s dilemma the notion of a nash equilibrium has joined supply and demand as one of the two or three techniques that economists instinctively try to use first in the analysis of economic interactions moreover the nash equilibrium and closely related game theoretic concepts are being widely applied in other social sciences and even in biology where evolutionary stability often selects a subset of the nash equilibria many people are uneasy about the stark predictions of the nash equilibrium in some contexts where the extreme rationality assumptions seem implausible kaushik basu s 1994 traveler s dilemma is a particularly convincing example of a case where the unrelenting logic of game theory is at odds with intuitive notions about human behavior the story associated with the dilemma is that two travelers purchase identical antiques while on a tropical vacation their luggage is lost on the return trip and the airline asks them to make independent claims for compensation in anticipation of excessive claims the airline representative announces

reciprocity and wage undercutting it is well documented that employers refuse to hire workers who o er their services at less than the prevailing wage the received explanation is that workers are motivated by reciprocity they desire to reward kindness and punish hostility to refuse an outsider s underbid is viewed as a kind choice that is met with good e ort a low wage is viewed as an insult that is met with shirking we have developed a general theory of reciprocity which in this paper is applied to a wage setting game played by an employer and two workers we show that when workers are motivated by reciprocity equilibrium behaviour accords well with the aforementioned stylized facts 2000 elsevier science b v all rights reserved jel classixcation d63 e24 j41

predation reputation and entry deterrence abstract economists often argue that predatory practices are irrational since there exist cheaper or more certain means to gain or maintain a monopoly our gametheoretic equilibrium analysis suggests that if a firm is threatened by several potential entrants then predation may be rational against early entrants even if it is costly when viewed in isolation because it yields a reputation which deters other entrants asymmetric information plays a crucial role in our analysis since it provides the rationale for entrants to base their expectations of the firm s future behavior on its past actions the analysis also suggests methods to treat general reputational phenomena

pricing strategy quality signaling and entry deterrence abstract i investigate a pricing strategy that is aimed at deterring entry by applying a two period model of a durable goods monopolist there exists an incumbent that is of two types that is high and low quality types they differ in terms of their r d capabilities and the incumbent s type is assumed to be unknown to an entrant if the entrant decided to enter the market nash bertrand price competition ensues between the incumbent and the entrant i show that not only limit pricing but also prestige pricing signals the incumbent s quality type which serves to discourage entry in the prestige pricing the high quality type sells the products at an intentionally higher price i also show that although limit pricing is more desirable than prestige pricing from a social welfare viewpoint the incumbent can still choose prestige pricing

the voluntary provision of a pure public good with diminishing marginal returns in experiments investigating the voluntary provision of a pure public good participants consistently allocate resources to this good when the nash prediction is to allocate nothing this paper explores the robustness of this result when the nash prediction calls for a division of resources between the private and public goods we consider how a change in individual resource endowments and supplemental earnings information affect allocations to the public good results indicate that under both the high and low endowment conditions groups continue to allocate more resources than the nash prediction however providing participants with detailed instructions that describe the declining marginal benefit to the public good leads to a significant decrease in allocations to the public good

an explanation of anomalous behavior in models of political participation this paper characterizes behavior with noisy decision making for models of political interaction characterized by simultaneous binary decisions applications include voting participation games candidate entry the volunteer s dilemma and collective action problems with a contribution threshold a simple graphical device is used to derive comparative statics and other theoretical properties of a quantal response equilibrium and the resulting predictions are compared with nash equilibria that arise in the limiting case of no noise many anomalous data patterns in laboratory experiments based on these games can be explained in this manner

the spite dilemma spite or no spite is there a dilemma abstract contributions from five voluntary contribution public goods laboratory sessions do not converge to the conventional equilibrium at which the individually rational action for each subject coincides with the collectively rational action deviations are not explained by the value orientations of the participants

an experimental study of jury decision rules we present experimental results on groups facing a decision problem analogous to that faced by a jury we consider three treatment variables group size three or six number of votes needed for conviction majority or unanimity and pre vote deliberation we find evidence of strategic voting under the unanimity rule a large fraction of our subjects vote for a decision analogous to conviction even when their private information indicates a state analogous to innocence this is roughly consistent with the game theoretic predictions of feddersen and pesendorfer although individual behavior is explained well by the game theoretic model there are discrepancies at the level of the group decision contrary to feddersen and pesendorfer in our experiments there are fewer outcomes analogous to incorrect convictions under unanimity rule than under majority rule in the case of no deliberation we simultaneously account for the individual and group data using quantal response equilibrium

price and advertising signals of product quality we present a signaling model based on ideas of phillip nelson in which both the introductory price and the level of directly uninformative advertising or other dissipative marketing expenditures are choice variables and may be used as signals for the initially unobservable quality of a newly introduced experience good repeat purchases play a crucial role in our model a second focus of the paper is on illustrating an approach to refining the set of equilibria in signalling games with multiple potential signals

signalling strength limit pricing and predatory pricing this article merges two areas of strategic pricing theory a dynamic signalling game with two sided uncertainty is presented in which an incumbent is confronted with potential entry and chooses between limit pricing and predatory pricing as a means of achieving or maintaining monopoly profit initial distributions across player types are pivotal to this decision results show that when the incumbent is likely to be strong relative to the entrant predatory pricing is chosen when the incumbent is likely to be weak relative to the entrant limit pricing is chosen for intermediate cases a strong incumbent may choose a combination of these two signalling strategies

on the empirical content of quantal response equilibrium the quantal response equilibrium qre notion of mckelvey and palfrey 1995 has recently attracted considerable attention due largely to its widely documented ability to rationalize observed behavior in games played by experimental subjects we show that this ability to t the data as typically measured in this literature is uninformative without ap riori distributional assumptions a qre can match any distribution of behavior by each player in any normal form game we discuss approaches that might be taken to provide valid empirical evaluation of the qre and discuss its potential value as an approximating empirical structure

altruism spillovers are behaviors in context free experiments predictive of altruism toward a naturally occurring public good abstract this paper addresses the external validity of experiments investigating the characteristics of altruism in the voluntary provision of public goods we conduct two related experiments that allow us to examine whether individuals who act more altruistically in the context free environment are also more likely to act altruistically toward a naturally occurring public good we find that laboratory behavior can be predictive of contributions toward naturally occurring goods but not in a uniform way in fact parametric measures of altruism do a poor job of predicting which subjects are most likely to contribute to a naturally occurring public good

modelling cognitively bounded rationality an evaluative taxonomy abstract since its origins in the 1950s the notion of bounded rationality has been incorporated into economic theory using an array of methodological approaches this paper presents a taxonomy by which these approaches can be categorized and understood evaluating each approach against a range of important criteria at a time when the foundations of economic theory are being re examined this paper should be viewed as a first step towards an assessment of the appropriate role that this more realistic view of cognition should take in different areas of economic theory and also of the desirable characteristics of models that incorporate it

advertising and limit pricing we enrich milgrom and roberts 1982 limit pricing model to allow an incumbent to signal his costs with both price and advertisements our fundamental result is that a cost reducing distortion occurs in that the incumbent behaves as if there were complete information but his costs were lower than they are preentry price is therefore distorted downward and demand enhancing advertising is distorted upward as a consequence of signalling if advertising is a purely dissipative signal it is not used nor therefore distorted recent refinements of the sequential equilibrium concept are featured