reciprocity and cooperation in repeated coordination games the principled player approach abstract two long lived players play a repeated coordination game i show the restrictions on players beliefs which imply that cooperation is optimal play journal of economic literature classification number d83

on the complexity of strategy switching dynamics abstract a new approach has been proposed to analyze the strategy switching dynamics in a discrete model or a non cooperative game with the following characteristics i the agents are motivated by absolute payoffs rather than relative ones ii the payoffs vary as the composition of the population changes iii the agents are boundedly rational in the sense that they can only predict the outcomes of their own actions rich dynamic phenomena are exhibited for such discrete dynamic models or games the approach is then applied to explore the relative profitability of price taking behavior in a quantity competing heterogeneous oligopoly

strategy subsets closed under rational behavior a set of strategy profiles is here said to be closed under rational behavior curb of it contains all its best replies each curb set contains the support of at least one nash equilibrium in mixed

learning in games by random sampling abstract we study repeated interactions among a fixed set of low rationality players who have status quo actions randomly sample other actions and change their status quo if the sampled action yields a higher payoff this behavior generates a random process the better reply dynamics long run behavior leads to nash equilibrium in games with the weak finite improvement property including finite supermodular games and generic continuous two player quasi concave games if players make mistakes and if several players can sample at the same time the resulting better reply dynamics with simultaneous sampling converges to the pareto optimal nash equilibrium in common interest games journal of economic literature classification numbers c70 c72 c73

evolution rationality and equilibrium in games abstract evolutionary game theory studies the robustness of strategy profiles and sets of strategy profiles with respect to evolutionary forces in games played repeatedly in large populations of boundedly rational agents the approach is macro oriented in the sense of focusing on the strategy distribution in the interacting population s some of the main features of this approach are here outlined and connections with learning models and standard notions of game theoretic rationality and equilibrium are discussed some desiderata and results for robust long run predictions are considered

rationalizable strategic behavior the notion of equilibrium proposed by nash 19 has come to play a dominant role in economic applications of noncooperative games while analyses of nash equilibria have unquestionably contributed to our understanding of economic behavior it would be unreasonably optimistic to maintain that nash solved the problem of noncooperative strategic choice there is a small literature beginning with ellsberg 6 and a much larger oral tradition which argues that nash behavior is neither a necessary consequence of rationality nor a reasonable empirical proposition in this paper i take the view that although there may be various reasons why an agent might select a nash strategy the notion of an equilibrium has little intrinsic appeal within a strategic context when an agent reaches a decision in ignorance of the strategies adopted by other players rationality consists of making a choice which is justifiable by an internally consistent system of beliefs rather than one which is optimal post hoc this point of view is not original indeed most serious justifications of the nash hypothesis embrace such an approach arguing that agents will expect the game to yield a nash outcome and consequently will choose their equilibrium strategies nevertheless when we think in terms of maximizing utility subject to expectations rather than realizations it becomes clear that the nash hypothesis far from being a consequence of rationality arises from certain restrictions on agents expectations which may or may not be plausible depending upon the game being played we are then quite naturally led to ask are there any restrictions of individuals expectations and hence choices which are required by rationality alone rather than by subjective plausibility this paper is concerned with defining justifying characterizing and refining a criterion for rational strategic choice which i label rationalizability

multifaceted aid for low income students and college outcomes evidence from north carolina we study the evolution of a campus based aid program for low income students that began with grant heavy financial aid and later added a suite of nonfinancial supports we find little to no evidence that program eligibility during the early years 2004 2006 in which students received additional institutional grant aid and few nonfinancial supports improved postsecondary progress performance or completion in contrast program eligible students in more recent cohorts 2007 2010 when the program supplemented grant heavy aid with an array of nonfinancial supports were more likely to meet credit accumulation benchmarks toward timely graduation and earned higher grade point averages than their barely ineligible counterparts jel i21 i23 i24 j08

experimental evidence on the evolution of the meaning of messages in sender receiver games an experiment this paper experimentally investigates the evolution of message meanings when talk is cheap we consider communication between a privately informed sender and a receiver when the sender s message does not affect payoffs directly sender receiver games introduced by jerry green and nancy stokey 1980 and vincent p crawford and joel sobel 1982 provide the simplest stylized environment in which communication is essential communication is the only way to link the receiver s action to the sender s private information in addition sender receiver games have been widely used to study communication in accounting economics finance and political science intuition strongly suggests that effective communication will evolve when the players interests are closely aligned however there is always a nash equilibrium in which the sender randomizes uniformly across all messages such babbling equilibria are proper roger b myerson 1978 blume 1994 and even strategic stability elon kohlberg and jeanfrancois mertens 1986 does not rule out uninformative equilibria in general in response a literature developed that formulates equilibrium selection criteria by appealing to the existence of a commonly understood language matthew rabin 1990 steven a matthews et al 1991 joseph farrell 1993 that can be used to formulate credible deviations from equilibrium unfortunately the selection criteria from this literature are frequently strong enough to remove all equilibria from consideration in addition these arguments are vulnerable to stiglitz s observation in koo cho and david m kreps 1987 that successful deviations from equilibrium may induce further deviations which in turn may undermine the credibility of the original deviations both problems can be avoided by a dynamic approach as in rabin and sobel 1996 we also adopt a dynamic perspective but do not require messages to have a priori meanings instead distinct meanings may emerge endogenously this is important for communication across cultures and for language change 2 we are guided by recent results of blume department of economics university of iowa iowa city ia 52242 dejong department of accounting university of iowa iowa city ia 52242 kim department of economics sung kyun kwan university seoul 110 745 korea sprinkle department of accounting university of wisconsin madison wi 53706 we thank joyce berg vince crawford robert forsythe joel horowitz deirdre mccloskey forrest nelson larry samuelson gene savin joel sobel and especially two anonymous referees for their advice and suggestions we benefitted from comments and discussions resulting from presentations at the 1994 summer meetings of the econometric society the 1996 social learning workshop at suny stony brook the io me gt workshop at the university of iowa the university of bonn the university of bielefeld the center for economic research at tilburg university ohio state university seoul national university and texas a m university we are grateful for financial support from the college of business administration at the university of iowa the ira b mcgladrey institute and the national science foundation

rationalizable strategic behavior and the problem of perfection this paper explores the fundamental problem of what can be inferred about the outcome of a noncooperative game from the rationality of the players and from the information they possess the answer is summarized in a solution concept called rationalizability strategy profiles that are rationalizable are not always nash equilibria conversely the information in an extensive form game often allows certain unreasonable nash equilibria to be excluded from the set of rationalizable profiles a stronger form of rationalizability is appropriate if players are known to be not merely rational but also cautious what constitutes rational behavior in a noncooperative strategic situation this paper explores the issue in the context of a wide class of finite noncooperative games in extensive form the traditional answer relies heavily upon the idea of nash equilibrium nash 17 the position developed here however is that as a criterion for judging a profile of strategies to be reasonable choices for players in a game the nash equilibrium property is neither necessary nor sufficient some nash equilibria are intuitively unreasonable and not all reasonable strategy profiles are nash equilibria the fact that a nash equilibrium can be intuitively unattractive is well known the equilibrium may be imperfect introduced into the literature by selten 20 the idea of imperfect equilibria has prompted game theorists to search for a narrower definition of equilibrium while this research some of which will be discussed here has been extremely instructive it remains inconclusive theorists often agree about what should happen in particular games but to capture this intuition in a general solution concept has proved to be very difficult if this paper is successful it should make some progress in that direction the other side of the coin has received less scrutiny can all non nash profiles really be excluded on logical grounds i believe not the standard justifications for considering only nash profiles are circular in nature or make gratuitous assumptions about players decision criteria or beliefs the following discussion of these points is extremely brief due to space constraints more detailed arguments may be found in pearce 18

tenable strategy blocks and settled equilibria when people interact in familiar settings social conventions usually develop so that people tend to disregard alternatives outside the convention for rational players to usually restrict attention to a block of conventional strategies no player should prefer to deviate from the block when others are likely to act conventionally and rationally inside the block we explore two set valued concepts coarsely and finely tenable blocks that formalize this notion for finite normal form games we then identify settled equilibria which are nash equilibria with support in minimal tenable blocks for a generic class of normal form games our coarse and fine concepts are equivalent and yet they differ from standard solution concepts on open sets of games we demonstrate the nature and power of the solutions by way of examples settled equilibria are closely related to persistent equilibria but are strictly more selective on an open set of games with fine tenability we obtain invariance under the insertion of a subgame with a unique totally mixed payoff equivalent equilibrium a property that other related concepts have not satisfied

admissibility in games suppose that each player in a game is rational each player thinks the other players are rational and so on also suppose that rationality is taken to incorporate an admissibility requirement that is the avoidance of weakly dominated strategies which strategies can be played we provide an epistemic framework in which to address this question specifically we formulate conditions of rationality and mth order assumption of rationality rmar and rationality and common assumption of rationality rcar we show that i rcar is characterized by a solution concept we call a self admissible set ii in a complete type structure rmar is characterized by the set of strategies that survive m 1 rounds of elimination of inadmissible strategies iii under certain conditions rcar is impossible in a complete structure

evolutionary game theory game theory has been developed as a theory of rational behavior in interpersonal conflict situations with economics and the other social sciences being the intended fields of application since the theory is based on an idealized picture of human rationality it is by no means obvious that it can be applied to situations in which the players cannot be attributed any intellectual capabilities however in their seminal paper the logic of animal conflict maynard smith and price showed that animal contests can be modeled as games and that game theory can be applied successfully in biology the objective of this chapter is to review some of the developments in this biological branch of game theory and to point out the distinctions and similarities with the classical branch also see parker and hammerstein 1985 the main emphasis will be on the mathematics involved lack of space prevents an extensive discussion of the underlying biological assumptions as well as an analysis of specific examples for these the reader is referred to the very stimulating book evolution and the theory of games by john maynard smith

a myopic adjustment process leading to best reply matching we analyze a myopic strategy adjustment process in strategic form games it is shown that the steady states of the continuous time limit which is constructed assuming frequent play and slow adjustment of strategies are exactly the best reply matching equilibria as discussed by droste kosfeld and voorneveld 2000 mimeo tilburg university in a best reply matching equilibrium every player matches the probability of playing a pure strategy to the probability that this pure strategy is a best reply to the pure strategy profile played by his opponents we derive stability results for the steady states of the continuous time limit in 2 2 bimatrix games and coordination games analyzing the asymptotic behavior of the stochastic adjustment process in discrete time shows convergence to minimal curb sets of the game moreover absorbing states of the process correspond to best reply matching equilibria of the game

clever agents in adaptive learning abstract saez marti and weibull j econom theory 86 1999 268 investigate the consequences of letting some agents play a myopic best reply to the myopic best reply in young s j econom theory 59 1993 145 bargaining model which is how they introduce cleverness of players i analyze such clever agents in general finite two player games and show young s individual strategy and social structure princeton university press princeton nj 1998 prediction to be robust adaptive learning with clever agents does select the same minimal curb set as in the absence of clever agents if their population share is less than one however the long run strategy distribution in such a curb set may vary with the share of clever agents

equilibrium selection in a merger game abstract a merger game is modeled as a non cooperative simultaneous moves exclusive membership game of coalition formation in the three player case in the equilibrium selected by refinements the merger is such that the participants prefer it to other mergers involving them

stochastic adaptation in finite games played by heterogeneous populations we analyze stochastic adaptation in finite n player games played by heterogeneous populations containing best repliers better repliers and imitators individuals select strategies by applying a

the impact of oligopsony and taxation on the haitian coffee economy abstract this paper assessed the impact of exporters oligopsony power and government taxation on coffee prices production consumption exports and income distribution in haiti calibration simulation analyses based on estimated supply and demand functions as well as economic surpluses are conducted for alternative oligopsony taxation scenarios and 1965 1984 data empirical results revealed that the market distortions caused by the government s export taxes have far outweighed those caused by the exporters oligopsony power

evolution in games with endogenous mistake probabilities abstract j bergin and b lipman econometrica 64 1996 943 956 show that the selection effect from the random mutations in the adaptive population dynamics in m kandori g mailath and r rob econometrica 61 1993 29 56 and p young econometrica 61 1993 57 84 is due to restrictions on how these mutation rates vary across population states we here model mutation rates as endogenously determined mistake probabilities by assuming that players with some effort can control the probability of implementing the intended strategy this is shown to corroborate the results in kandori mailath rob 1993 and under certain regularity conditions those in young 1993 journal of economic literature classification number c72

learning from schelling s strategy of conflict thomas schelling s strategy of confl ict is a masterpiece that should be recognized as one of the most important and infl uential books in social theory this paper reviews some of the important ideas in strategy of confl ict and considers some of the broader impact that this book has had on game theory economics and social theory by his emphasis on the critical importance of information and commitment in strate gic dynamics schelling played a vital role in stimulating the development of non cooperative game theory more broadly schelling s analysis of games with multiple equilibria has redefi ned the scope of economics and its place in the social sciences jel d74 f51 h56

individual learning and social rationality abstract classical game theory assumes that players have a coherent model of the game in which they are engaged that they make optimum plans assuming that everyone else makes optimum plans and that all of this is common knowledge evolutionary game theory postulates instead that players have limited understanding of their environment only modest reasoning ability and no common knowledge surprisingly a fair amount of classical solution theory survives with this change of perspective we show how high rationality solutions can emerge in low rationality environments provided the evolutionary process has sufficient time to unfold

online ascending auctions for gradually expiring items abstract we consider dynamic auction mechanisms for the allocation of multiple items items are identical but have different expiration times and each item must be allocated before it expires buyers are of dynamic nature and arrive and depart over time our goal is to design mechanisms that maximize the social welfare we begin by showing that dominant strategy incentive compatibility cannot be used in this case since any such auction cannot obtain any constant fraction of the optimal social welfare we then design two auctions that perform well under a wide class of semi myopic strategies for every combination of such strategies the auction is associated with a different algorithm or allocation rule and so we have a family of semi myopic algorithms we show that any algorithm in this family obtains at least 1 3 of the optimal social welfare we also provide some game theoretic justification for acting in a semi myopic way we suggest a new notion of set nash equilibrium where we cannot pinpoint a single best response strategy but rather only a set to which best response strategies belong we show that our auctions have a set nash equilibrium which is all semi myopic

a characterization of the class of rationalizable equilibria of oligopoly games abstract the set of rationalizable strategies of a firm in a quantity setting oligopoly is characterized it is shown that as the number of firms in the industry increases the rationalizable solution converges to the interval from zero to the monopoly output