minimum effort coordination games stochastic potential and logit equilibrium abstract this paper revisits the minimum effort coordination game with a continuum of pareto ranked nash equilibria noise is introduced via a logit probabilistic choice function the resulting logit equilibrium distribution of decisions is unique and maximizes a stochastic potential function in the limit as the noise vanishes the distribution converges to an outcome that is analogous to the risk dominant outcome for 2 2 games in accordance with experimental evidence logit equilibrium efforts decrease with increases in effort costs and the number of players even though these parameters do not affect the nash equilibria journal of economic literature classification numbers c72 c92

iterated regret minimization a new solution concept abstract for some well known games such as the traveler s dilemma or the centipede game traditional game theoretic solution concepts most notably nash equilibrium predict outcomes that are not consistent with empirical observations we introduce a new solution concept iterated regret minimization that exhibits the same qualitative behavior as that observed in experiments in many games of interest including traveler s dilemma the centipede game nash bargaining and bertrand competition as the name suggests iterated regret minimization involves the iterated deletion of strategies that do not minimize regret

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

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

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

information disclosure in auctions an experiment we report experimental results on the importance of information disclosure policy in first price sealed bid auctions interaction takes place in 10 periods according to a random matching protocol and we control the level of information feedback bidders receive after each period when bidders are informed about the losing bids in previous periods prices are higher than the theoretical prediction however when this information is not revealed the bidding becomes more competitive and the bids come close to the theoretical prediction we suggest that a signaling phenomenon may be important for explaining these results 2002 elsevier science b v all rights reserved

two little treasure games driven by unconditional regret for traveler s dilemma and minimal effort coordination games the unconditional regret matching urm procedure predicts outcomes close to the experimental ones this supports a claim that the urm procedure can be well suited to predict the behavior of experimental subjects in repeated games

group dynamics in experimental studies the bertrand paradox revisited abstract different information provision in experimental markets can drastically change subjects behavior considering the repeated bertrand duopoly game of dufwenberg and gneezy dufwenberg m gneezy s u 2000 price competition and market concentration an experimental study international journal of industrial organization 18 7 22 we find that population feedback about the prices in other markets outside a subjects own current market causes group dynamics that prevent prices from convergence to nash equilibrium limited information comprising only the decisions of a subject s own opponent in contrast leads to competitive behavior when we extend the number of periods from 10 to 25 in the full information treatment full we observe a very robust cyclical up and down movement of prices we can explain tacit coordination in our experiment with an extended learning direction model and leadership by example

simultaneous and sequential price competition in heterogeneous duopoly markets experimental evidence abstract we investigate simultaneous and sequential price competition in duoply markets with differentiated products and random matching of symmetric firms we find that second movers gain from the sequential structure in comparison to simultaneous move markets whereas first movers do not as predicted by the theory there is a significant first mover disadvantage in the sequential game finally we report the results of control treatments varying the matching scheme and the mode of eliciting choices strategy method vs standard sequential play

a quantitative easing experiment abstract we experimentally investigate the effect of a central bank buying bonds for cash in a quantitative easing qe operation in our experiment the bonds are perfect substitutes for cash and have a constant fundamental value which is not affected by qe in the rational expectations equilibrium we find that qe raises bond prices above those in the benchmark treatment without qe subjects in the benchmark treatment learned to trade the bonds at their fundamental value but those in treatments with qe became more convinced after repeated exposure to the same treatment that qe boosts bond prices this suggests the possibility of a behavioural channel for the observed effects of actual qe operations on bond yields

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

the effect of piracy on the market penetration of subscription software software piracy is not necessarily harmful to a software firm seeking to launch a new product when strategically managed through the use of price and protection measures piracy establishes the initial adopters of the software who in turn influence other users to buy the product we examine the role of piracy in affecting the adoption of subscription software products we present an individual level model in an adaptive population setting intended to determine the price protection mix that maximizes the discounted profit stream over the life of the software an extension for nonsubscription software is also discussed

homogeneity bias in models of discrete choice with bounded rationality abstract quantal response equilibrium captures bounded rationality in a strategic game by adopting a stochastic model of discrete choice along with the traditional rational expectation framework we examine the use of a single agent homogeneous parametric quantal response model e g logit response to describe the aggregate behavior of heterogeneous agents sharing the same parametric form for their quantal response functions but having individual rationality parameters in a symmetric population game for any parametric quantal response function arising from a unimodal distribution of exchangeable payoff disturbances we find that a mis specified homogeneous rationality parameter will have downward bias logit response is one such specification this result implies that empirical work that disregards heterogeneity underestimates subjects rationality

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

quantal response methods for equilibrium selection in 2 2 coordination games abstract the notion of quantal response equilibrium qre introduced by mckelvey and palfrey 1995 has been widely used to explain experimental data in this paper we use quantal response equilibrium as a homotopy method for equilibrium selection and study this in detail for 2 2 bimatrix coordination games we show that the risk dominant equilibrium need not be selected in the logarithmic game the limiting qre is the nash equilibrium with the larger sum of square root payoffs finally we apply the quantal response methods to the mini public goods game with punishment a cooperative equilibrium can be selected if punishment is strong enough

collusion in bertrand vs cournot competition a virtual bargaining approach how do firms manage to collude without communicating why do we find more collusion in price competition than in quantity competition why is collusion so hard to detect we examine strategic behavior in competitive interactions by developing and applying the concept of virtual bargaining when decision makers virtually bargain they mentally simulate and choose among agreements that they could reach if they were able to explicitly negotiate with each other virtual bargainers focus on agreements that offer some protection against the possibility that their counterparts may deviate and best respond to these agreements we develop a formal account of virtual bargaining and demonstrate that it leads to collusion in bertrand but not in cournot competition in this framework collusion is a result of virtual bargaining as a mode of reasoning and requires neither communication nor dynamic considerations such as rewards and punishments between the players this paper was accepted by manel baucells decisi

learning and noisy equilibrium behavior in an experimental study of imperfect price competition we consider a duopoly pricing game with a unique bertrand nash equilibrium the high price firm has a nonvanishing market share however and intuition suggests that observed prices may be positively related to this market share this relationship is implied by a model in which players make noisy logit best responses to expected payoff differences the resulting logit equilibrium model was used to design an experiment in which the high price firm s market share varies the model accurately predicts the final period price averages a naive learning model predicts the observed differences in the time paths of average prices

a test of stability in a linear altruism model linear altruism predicts the estimated preferences to be independent of the subject s position in the game if the role allocation is randomly determined because subjects in each role have the same preferences ex ante we test and reject this hypothesis

heterogeneous quantal response equilibrium and cognitive hierarchies we explore an equilibrium model of games where behavior is given by logit response functions but payoff responsiveness and beliefs about others responsiveness are heterogeneous we study two substantively different ways of extending quantal response equilibrium qre to this setting 1 heterogeneus qre where players share identical correct beliefs about the distribution of payoff responsiveness and 2 truncated qre where players have downward looking beliefs systematically underestimating others responsiveness we show that the cognitive hierarchy model is a special case of truncated qre we conduct experiments designed to differentiate these approaches we find significant evidence of payoff responsive stochastic choice and of heterogeneity and downward looking beliefs in some games

cooperation but no reciprocity individual strategies in the repeated prisoner s dilemma a recent advance in our understanding of repeated pds is the detection of a threshold d at which laboratory subjects start to cooperate predictively this threshold is substantially above the classic threshold existence of grim equilibrium and has been characterized axiomatically by blonski ockenfels and spagnolo 2011 bos in this paper i derive its behavioral foundations first i show that the threshold is equivalent to existence of a semi grim equilibrium s cc s cd s dc s dd it is cooperative s cc 0 5 non reciprocal s cd s dc and robust to imperfect monitoring belief free next i show that the no reciprocity condition s cd s dc also follows from robustness to random utility perturbations logit equilibrium finally i re analyze strategies in four recent experiments and find that the majority of subjects indeed plays semi grim when it is an equilibrium strategy which explains d s predictive success

monetary rewards and decision cost in experimental economics a survey of thirty one experimental studies which report data on the comparative effects of monetary rewards and opportunity cost shows 1 several studies in which increased rewards shift the central tendency of the data toward the predictions of rational models 2 in virtually all cases rewards reduce the variance of the data around the predicted outcome this is consistent with a model in which rewards are balanced against decision cost in agent behavior and explicates the argument that when rational models fail it can be attributed to low opportunity cost of deviations from the rational prediction

the evolution of walrasian behavior consider an evolutionary context where a given number of quantity setting oligopolists tend to mimic successful behavior occasionally experimenting with some small probability in this context it is shown that the unique long run outcome of the process has all firms playing walrasian i e choosing an output that maximizes profits when taking the market clearing price as given

strategic risk and coordination failure in blame games within a class of games that we call blame games we discuss how strategic risk may discourage play of a unique and efficient strictly dominance solvable equilibrium

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

information cascades in the laboratory when a series of individuals with private information announce public predictions initial conformity can create an information cascade in which later predictions match the early announcements this paper reports an experiment in which private signals are draws from an unobserved urn subjects make predictions in sequence and are paid if they correctly guess which of two urns was used for the draws if initial decisions coincide then it is rational for subsequent decisionmakers to follow the established pattern regardless of their private information rational cascades formed in most periods in which such an imbalance occurred copyright 1997 by american economic association

modeling the psychology of consumer and firm behavior with behavioral economics abstract marketing is an applied science that tries to explain and influence how firms and consumers behave in markets marketing models are usually applications of standard economic theories which rely on strong assumptions of rationality of consumers and firms behavioral economics explores the implications of the limits of rationality with the goal of making economic theories more plausible by explaining and predicting behavior more accurately while maintaining formal power this article reviews six behavioral economics models that are useful to marketing three models generalize standard preference structures to allow for sensitivity to reference points and loss aversion social preferences toward outcomes of others and preference for instant gratification the other three models generalize the concept of game theoretic equilibrium allowing decision makers to make mistakes encounter limits on the depth of strategic thinking and equilibrate by learning from feedback the authors also discuss a sp

signalling and adaptive learning in an entry limit pricing game in an experimental investigation of milgrom and roberts 1992 model play consistently converges to a unique equilibrium providing evidence of sophisticated strategic behavior that the theory predicts play starts with monopolists at their myopic maxima followed by an attempt to pool and then if no pooling equilibrium exists separation suggesting myopia rather than a forward looking process when both pure strategy equilibria and separating equilibria exist equilibrium selection is a function of the past history of play an adaptive learning model characterizes the major features of the data and provides predictions of intermediate term behavior that is otherwise lacking in the theory

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

modeling bounded rationality in capacity allocation games with the quantal response equilibrium we consider a supply chain with a single supplier and two retailers the retailers choose their orders strategically and if their orders exceed the supplier s capacity quantities are allocated proportionally to the orders we experimentally study the capacity allocation game using subjects motivated by financial incentives we find that the nash equilibrium which assumes that players are perfectly rational substantially exaggerates retailers tendency to strategically order more than they need we propose a model of bounded rationality based on the quantal response equilibrium in which players are not perfect optimizers and they face uncertainty in their opponents actions we structurally estimate model parameters using the maximum likelihood method our results confirm that retailers exhibit bounded rationality become more rational through repeated game play but may not converge to perfect rationality as assumed by the nash equilibrium finally we consider several alternative behavioral theories and show that they do not explain our experimental data as well as our bounded rationality model this paper was accepted by loana popescu guest editor operations management

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

a new look at the classical bertrand duopoly abstract the paper provides necessary and sufficient conditions for the uniqueness of pure strategy nash equilibrium in the standard bertrand duopoly with a homogeneous product the main condition is elementary easy to interpret and nests all known sufficient conditions in the literature

on the political and fiscal determinants of income redistribution under federalism and democracy evidence from germany several recent studies suggest that transfers from central to regional governments are motivated by political considerations in this paper we examine if this is also the case for transfers from regional to central governments in the context of the german fiscal equalization system we examine the factors that contribute to differences in tax revenues across german states the evidence indicates that both fiscal incentives and political factors can explain these differences although in germany the former are more important moreover accounting for fiscal institutions has important consequences for the empirical assessment of political influences on taxation overall we find that the political affiliation of the state governor is an important factor in explaining differences in state tax revenues thus the right wing party cdu csu is effective in relaxing the tax burden at the state level in contrast partisan alignment between the state government and the federal government loses its importance once fiscal conditions enter the empirical model

cooperating over losses and competing over gains a social dilemma experiment evidence from studies in international relations the politics of reform collective action and price competition suggests that economic agents in social dilemma situations cooperate more to avoid losses than in the pursuit of gains to test whether the prospect of losses can induce cooperation we let experimental subjects play the traveler s dilemma in the gain and loss domain subjects cooperate substantially more over losses furthermore our results suggest that this treatment effect is best explained by reference dependent risk preferences and reference dependent strategic sophistication we discuss the implications of our results and relate our findings to other experimental games played in the loss domain

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

buyer search and price dispersion a laboratory study we study markets with costly buyer search in which sellers simultaneously post prices buyers costlessly observe one or with probability 1 q two of the posted prices and can accept one or pay to search again the experiment varies q the search cost and the number of buyers equilibrium theory predicts a unified very low high price for q 0 q 1 and predicts specific distributions of dispersed prices for q 1 3 and 2 3 actual prices conform closely to the predictions in some treatments buyers reservation prices are biased away from the extremes however and sellers prices have positive autocorrelation and cross sectional correlation

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

an experimental study of exclusive contracts abstract this paper reports results from a laboratory experiment based on exclusive contracts that may theoretically lead to inefficient naked exclusion of a potential rival the data indicate that changes in the number of buyers in the market have no significant effect on exclusion rates but the likelihood of inefficient exclusion is decreased both when a larger fraction of signed buyers are needed to deter a rival s entry and when buyers engage in non binding communication these results have antitrust implications both in terms of helping to identify at risk market characteristics and suggesting potential competition enhancing strategies a sub game of the experiment where buyers make signing decisions can be illustrated as a coordination game with the unique feature that payoffs are affected by a separate but interested party the incumbent seller i find that the height of the potential function and relevant basin of attraction especially when combined with quantal response estimation have larger predictive power in this sub game than several other equilibrium selection criteria

endogenous depth of reasoning we introduce a model of strategic thinking in games of initial response unlike standard models of strategic thinking in this framework the player s depth of reasoning is endogenously determined and it can be disentangled from his beliefs over his opponent s cognitive bound in our approach individuals act as if they follow a cost benet analysis the depth of reasoning is a function of the player s cognitive abilities and his payos the costs are exogenous and represent the game theoretical sophistication of the player the benet instead is related to the game payos behavior is in turn determined by the individual s depth of reasoning and his beliefs about the reasoning process of the opponent thus in our framework payos not only aect individual choices in the traditional sense but they also shape the cognitive process itself our model delivers testable implications on players chosen actions as incentives and opponents change we then test the model s predictions with an experiment we administer dierent treatments that vary beliefs over payos and opponents as well as beliefs over opponents beliefs the results of this experiment which are not accounted for by current models of reasoning in games strongly support our theory we also show that the predictions of our model are highly consistent both qualitatively and quantitatively with well known unresolved empirical puzzles our approach therefore serves as a novel unifying framework of strategic thinking that allows for predictions across games