reputation in dynamic games abstract we analyze reputation in a game between a large player and a continuum of long lived small players in which state variables affect players payoffs the large player s type is private information we give conditions under which in every nash equilibrium a very patient large player will get almost the largest payoff consistent with the small players choosing a best response in a large finite truncation of the game while our results apply to the time inconsistency problem of optimal government policy we show that for the durable goods monopoly reputation may fail to improve the monopolist s payoff journal of economic literatureclassification numbers c72 c73

when is reputation bad abstract in traditional reputation models the ability to build a reputation is good for the long run player in ely j valimaki j 2003 bad reputation naj econ 4 2 http www najecon org v4 htm quart j econ 118 2003 785 814 ely and valimaki give an example in which reputation is unambiguously bad this paper characterizes a class of games in which that insight holds the key to bad reputation is that participation is optional for the short run players and that every action of the long run player that makes the short run players want to participate has a chance of being interpreted as a signal that the long run player is bad we allow a broad set of commitment types allowing many types including the stackelberg type used to prove positive results on reputation although reputation need not be bad if the probability of the stackelberg type is too high the relative probability of the stackelberg type can be high when all commitment types are unlikely

reputation and experimentation in repeated games with two long run players this paper considers reputation effects in a repeated game between two long run players one of whom is relatively patient and may be committed to a fixed strategy which punishes the opponent for increasingly long periods whenever inappropriate actions are taken by following this commitment strategy the more patient player can induce a sufficiently patient opponent to experiment to see whether the commitment strategy is also being followed off the equilibrium path this can guarantee the more patient player in any nash equilibrium a payoff close to the highest feasible payoff consistent with the individual rationality of the other player for an arbitrary degree of patience of the less patient player a weaker result is established the more patient player is guaranteed an average equilibrium payoff close to the static stackelberg payoff this latter result generalizes that of schmidt 1993 who established the same result for the restricted class of games of conflicting interests

reputation and dynamic stackelberg leadership in infinitely repeated games abstract the paper studies a repeated game in which a long run player without discounting faces another long run player with strict discounting the game is perturbed so that there is uncertainty in the patient player s strategy choice she may be a rational player but she may also be one of many irrational types who are committed to various repeated game strategies the rational patient player s equilibrium payoff in this perturbed game is analyzed in particular it is shown that the lower bound on her payoff in the set of extensive form trembling hand perfect equilibria is given by her stackelberg payoff in a dynamics sense journal of economic literature classification numbers c72 d82

reputation in repeated games with no discounting abstract i study two player infinitely repeated games with no discounting i examine how perturbations afford players opportunities to establish reputations and i determine how potential reputations lead to outcome selection in both equilibrium and non equilibrium settings the main result is the following assume that players have beliefs of countable support players only adopt forgiving strategies and players best respond to their beliefs a forgiving strategy does not punish an opponent forever then if the game is perturbed each player expects to fare at least as well as if she selected any of her perturbation strategies and the opponent played a best response journal of economic literature classification numbers c72 c73

reputation and perfection in repeated common interest games abstract we consider a wide class of repeated common interest games perturbed with one sided incomplete information one player the informed player might be a commitment type playing the pareto dominant action as discounting which is assumed to be symmetric and the prior probability of the commitment type go to zero it is shown that the informed player can be held close to her minmax payoff even when perfection is imposed on the equilibrium journal of economic literature classification numbers c73 d83

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

impermanent types and permanent reputations we study the impact of unobservable stochastic replacements for the long run player in the classical reputation model with a long run player and a series of short run players we provide explicit lower bounds on the nash equilibrium payoffs of a long run player both ex ante and following any positive probability history under general conditions on the convergence rates of the discount factor to one and of the rate of replacement to zero both bounds converge to the stackelberg payoff if the type space is sufficiently rich these limiting conditions hold in particular if the game is played very frequently

maintaining a reputation against a long lived opponent we consider a game between a patient player 1 and a nonmyopic but less patient opponent player 2 as usual in reputation models we suppose that the patient player s type is private information and that he may be a commitment type who is locked into playing a particular strategy we investigate the extent to which an uncommitted or normal type of patient player can exploit his less patient opponent s uncertainty to maintain a reputation for playing like a commitment type

regulatory schemes and self protective environmental risk control a comparison of insurance liability and deposit refund systems abstract there has been an increasing interest in considering non traditional regulatory instruments for control of environmental risks traditional regulation has relied on liability in various forms after risky events have actually occurred there is concern that traditional instruments do not provide adequate signals to firms regarding social costs of risks this paper considers two important alternatives to traditional liability instruments insurance and deposit refund systems the purpose of the paper is to determine whether there is any theoretical superiority of these non traditional instruments in controlling environmental risk and safety a relatively simple model designed to capture the essential features of liability insurance and deposit refund instruments is developed and used to compare the resulting control levels under pure risk and pure uncertainty the paper shows how risk aversion limited liability afforded through bankruptcy and differences between social and private discount rates can affect the ranking of control levels under each of the three primary instruments the paper shows that under reasonable assumptions deposit refund systems such as input or discharge deposits or performance bonds will result in higher levels of controls than the other instruments results also suggest that it may be necessary to tailor regulatory instruments to specific firm situations such as requiring deposits from small firms in competitive industries

on reputation refinements with heterogeneous beliefs consider a repeated game with incomplete information in which a patient long run player whose type is unknown faces a sequence of short run opponents as in fudenberg and levine 1989 the standard reputation result is that the patient long run player can obtain an average long payoff almost equal to the stackelberg payoff of the stage game by consistently playing as a stackelberg leader in the analysis one generally takes as fundamental an assumption that the players have common prior beliefs on the states of the world and that behavior is consistent with the concept of bayesian nash equilibrium however these related suppositions have been called into question as unrealistic and too stringent cf gul 1991 in many games of incomplete information a player s prior probabilities on types or states of the world are best regarded as purely subjective psychological parameters unknown to the modeler and to this player s opponents therefore it is important to understand whether the standard reputation results among others are implied by weaker assumptions on the knowledge and behavior of the players in fact as watson 1993 demonstrates the reputation result does not require equilibrium it is implied by a weak notion of rationalizability with some restrictions on the beliefs of the players here we qualify watson s 1993 study and extend the line of inquiry of watson 1993 and battigalli 1994 concerning settings in which reputations are effective as watson shows two main conditions on the beliefs of the players along with weak rationalizability imply the reputation result first there must be a strictly positive and uniform lower bound on the subjective probability that players assign to the stackelberg type second the conditional beliefs of the short run players must not be too dispersed watson 1993 does not explicitly indicate on what the updated beliefs of the short run players are conditioned we make this explicit and show that it is necessary to assume that the conditional beliefs of the short run players satisfy a stochastic independence property cf battigalli 1996 we also comment on the dispensability of equilibrium regarding the reputation result in games with two long run players

disequilibrium institutional factors in aggregate money demand evidence from three economies abstract this paper investigates the disequilibrium effects of a number of institutional factors on the aggregate money demand behaviour of three asian economies japan korea and singapore it identifies these institutional factors with strong government interventions through monetary or fiscal policies the investigation is carried out through progressive model search following the equilibrium correction modelling ecm approach the findings confirm to the arguments that undesirable empirical results from the ecm procedure such as residual unconditional or conditional heteroscedasticity or coefficient non constancy are most probably symptoms of the missing variable problem in the underlying theoretical model and that extension of the theoretical model accordingly to include certain institutional factors pertaining to the particular economies under investigation can enhance the significance of the empirical studies in a substantial way

nonzero sum two person repeated games with incomplete information and known own payoffs this paper deals with repeated games with incomplete information where the uninformed player has complete knowledge of his own payoffs this is a specific case of hart s model we provide a characterization of the set of equilibrium payoffs which is simpler than that of the general case and prove the existence of an equilibrium in addition we show by example how arbitrarily small doubts about the payoff matrices can radically alter the set of equilibrium payoffs in particular we partially characterize how a player can increase his minimum equilibrium payoff by sowing doubt about his payoffs journal of economic literature classification number c72

building routines learning cooperation and the dynamics of incomplete relational contracts this paper studies how agents with conflicting interests learn to cooperate when the details of cooperation are not common knowledge it considers a repeated game in which one player has incomplete information about when and how her partner can provide benefits initially monitoring is imperfect and cooperation requires inefficient punishment as the players common his tory grows the uninformed player can learn to monitor her partner s actions which allows players to establish more efficient cooperative routines because revealing information is costly it may be optimal not to reveal all the existing information and efficient equilibria can be path dependent jel c73 d82 d83 d86 this paper studies how agents with conflicting interests go about developing a successful cooperative relationship when the details of cooperation are not common knowledge in cir cumstances where formal contracts are unavailable or inconvenient agents frequently rely on informal cooperative agreements or relational contracts to resolve incentive conflicts in fact whenever the interested parties have better information than do outside courts relational con tracts can outperform formal contracts by allowing agents to adapt their joint behavior to contin gencies that cannot be assessed by third parties 1 the starting point of this paper is to recognize that even when agents have better information than outside courts this does not mean that the details of how and when cooperation should occur are common knowledge between the parties for instance a new plant manager may not have a complete understanding of what her produc tion teams can and cannot do a firm s ceo may have only partial understanding of how research teams should operate and so on the question is then how do players go about building a com mon agreement or formulated in a slightly different way how do they go about specifying the contingencies of their relational contract the model developed in the paper considers two players engaged in an infinitely repeated game with asymmetric information in each period player 1 decides to stay and interact with player 2 or exit and skip interaction for one period staying is costly for player 1 and yields a benefit for player 2 if player 1 stays player 2 can reciprocate by taking some action from a set of available actions which is randomly drawn in each period from a countable superset player 2 can take actions of two types unproductive actions that are costless to player 2 but yield zero benefit to

disappearance of reputations in two sided incomplete information games abstract this paper examines the sustainability of reputations in a class of games with imperfect public monitoring and two long lived players both of whom have private information about their own type and uncertainty over the types of the other player this class namely reputation games with one sided moral hazard can capture economic interactions that may involve hidden information or hidden action extending the techniques of cripps et al 2004 it is found that neither player can sustain a reputation permanently for playing a noncredible behavior in these games and the reputations disappear uniformly across all nash equilibria

reputation and the flow of information in repeated games this paper derives payoff bounds from reputation effects akin to those of fudenberg and levine 1992 for repeated moral hazard games in which a long run player interacts frequently with a population of short run players and the monitoring technology varies with the length of the period of interaction the bounds depend on the monitoring technology through the flow of information a measure of signal informativeness per unit of time based on the relative entropy examples are shown where under complete informatione the set of equilibrium payoffs of the long run player converges as the period length tends to zero to the set of static equilibrium payoffs whereas when the game is perturbed by a small ex ante probability on commitment types reputation effects remain powerful in the frequent interaction limit

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

reputation and equilibrium characterization in repeated games with conflicting interests a two person game is of conflicting interests if the strategy to which player one would most like to commit herself holds player two down to his minimax payoff suppose there is a positive prior probability that player one is a commitme nt type who will always play this strategy then player one will get a t least her commitment payoff in any nash equilibrium of the repeated game if her discount factor approaches one this result is robust against further perturbations of the informational structure and in striking contrast to the message of the folk theorem for games with incomplete information copyright 1993 by the econometric society

self confirming equilibrium rium path of play thus if a self confirming equilibrium occurs repeatedly no player ever observes play that contradicts his beliefs even though beliefs about play at off path information sets need not be correct we characterize the ways in which self confirming equilibria and nash equilibria can differ and provide conditions under which self con firming equilibria correspond to standard solution concepts nash equilibrium and its refinements describe a situation in which i each player s strategy is a best response to his beliefs about the play of his opponents and ii each player s beliefs about the opponents play are exactly correct we propose a new equilibrium concept self confirming equilibrium that weakens condition ii by requiring only that players beliefs are correct along the equilibrium path of play thus each player may have incorrect beliefs about how his opponents would play in contingencies that do not arise when play follows the equilibrium and moreover the beliefs of different players may be wrong in different ways the concept of self confirming equilibrium is motivated by the idea that noncooperative equilibria should be interpreted as the outcome of a learning process in which players revise their beliefs using their observations of previous play suppose that each time the game is played the players observe the actions chosen by their opponents but that players do not observe the actions their opponents would have played at the information sets that were not reached along the path of play then if a self confirming equilibrium occurs repeatedly no player ever observes play that contradicts his beliefs so the equilibrium is self confirming in the weak sense of not being inconsistent with the evidence by analogy with the literature on the bandit problem e g rothschild 1974 one might expect that a non nash self confirming equilibrium can be the outcome of plausible learning processes this point was made by fudenberg and

traders vs relationship managers reputational conflicts in full service investment banks we present a model that explains why investment bankers struggle to manage conflicts of interest banks can build a type reputation for technical competence by performing complex deals that may not serve their clients interest on the other hand banks can sustain a behavioral reputation by refraining from doing so a behavioral reputation is a luxury reserved for banks that have proven their abilities the model sheds light on conflicts between the trading and advisory divisions of investment banks as well as the consequences of technological change for time variation in the relative strength of behavioral and type reputation concerns

merging reputation and repeated games with incomplete information we relate and unify several results that appeared in the following domains merging of probabilities perturbed games and reputation phenomena and repeated games with incomplete information journal of economic literature classification numbers c72 d83

reputation incomplete information and differences in patience in repeated games with multiple equilibria a game with multiple equilibria and incomplete information which allows for reputation building is repeated infinitely many times increasing differences in patience contribute to a greater likelihood of cooperation as one player becomes sufficiently more patient than the other player both players benefit and both players risk limits and the conflict between the players decrease

a reputation refinement without equilibrium the economic literature concerning agents reputations has grown steadily since the seminal work of kreps milgrom roberts and wilson 2 early work focused on how incomplete information leads to equilibria that are vastly different but more intuitive than those possible in the complete information game recently however game theorists have been studying how incomplete information might refine the set of equilibria 3 one important class of games is that in which a single long run agent plays a simultaneous move stage game with a sequence of opponents each of whom plays only once yet observes all previous play fudenberg and levine 1989 study the reputation of the long run player in this type of game they argue that the most reasonable equilibrium is the one which the long run player most prefers their intuition is sustained when one perturbs the game with the stackelberg strategy fudenberg and levine show that in the perturbed game the equilibrium payoffs of the long run player are bounded below by a number that converges to the stackelberg payoff

sequential common value auctions with asymmetrically informed bidders we study an in nitely repeated rst price auction with common values we focus on one sidedincomplete information in which one bidder learns the objects value which itself does not change overtime learning by the uninformed bidder occurs only through observation of the bids the proprietaryinformation is eventually revealed and the seller extracts essentially the entire rent for large discountfactors both players pay offs tend to 0 as the discount factor tends to 1 however the uninformed bidderdoes relatively better than the informed bidder we discuss the case of two sided incomplete informationand argue that under a markovian re nement the outcome is pooling as information is revealed onlyinsofar as it does not affect prices

reputation and equilibrium selection in games with a patient player a single long run player plays a simultaneous move stage game against a sequence of opponents who play only once but observe all previous play let the stackelberg strategy be the pure strategy to which the long run player would most like to commit himself if there is positive prior probability that the long run player will always play the stackelberg strategy then his payoff in any nash equilibrium exceeds a bound that converges to the stackelberg payoff as his discount factor approaches one when the stage game is not simultaneous move this result must be modified to account for the possibility that distinct strategies of the long run player are observationally equivalent

maintaining a reputation when strategies are imperfectly observed this paper studies reputation effects in games with a single long run player whose choice of stage game strategy is imperfectly observed by his opponents we obtain lower and upper bounds on the long run player s payoff in any nash equilibrium of the game if the long run player s stage game strategy is statistically identified by the observed outcomes then for generic payoffs the upper and lower bounds both converge as the discount factor tends to 1 to the long run player s stackelberg payoff which is the most he could obtain by publicly committing himself to any strategy

bayesian repeated games and reputation the folk theorem characterizes the subgame perfect nash equilibrium payoffs of an undiscounted or discounted infinitely repeated game with fully informed patient players as the feasible individually rational payoffs of the one shot game to which extent does the result still hold when every player privately knows his own payoffs under appropriate assumptions private values and uniform punishments the nash equilibria of the bayesian infinitely repeated game without discounting are payoff equivalent to tractable completely revealing equilibria and can be achieved as interim cooperative solutions of the initial bayesian game this characterization does not apply to discounted games with sufficiently patient players in a class of public good games the set of nash equilibrium payoffs of the undiscounted game can be empty while limit perfect bayesian nash equilibrium payoffs of the discounted game as players become infinitely patient do exist these equilibria share some features with the ones of multi sided reputation models