do soccer players play the mixed strategy nash equilibrium mixed strategy nash equilibrium msne is a commonly used solution concept in game theoretic models in various fields in economics management and other disciplines but the experimental results whether the msne predicts well actual play in games is mixed consequently the evidence for naturally occurring games in which the msne predicts the outcome well is of great importance as it can justify the vast use of msne in models the game between the kicker and the goalkeeper in soccer penalty kicks is a real world game that can be used to examine the application of the msne concept or its accuracy because payoffs are a common knowledge the players have huge incentives to play correctly the game is simple enough to analyse its nash equilibrium is in mixed strategies and players actions can be observed we collected and analysed the data on the direction of kicks and jumps in penalty kicks in various top leagues and tournaments our analysis suggests that the msne predictions are the closest to the act

costs and benefits of investment in electronic design abstract appraising any investment requires reliable quantification of the costs and benefits associated with the project this paper addresses the measurement of the value of investment in design in electronic industries it discusses a staged approach to the measurement of costs and benefits within the design activity itself and resulting from changes in downstream activities in manufacturing and test it considers the problems of estimating revenues resulting from strategic implications of investment in design and suggests a possible approach to evaluating those benefits difficult to quantity

loss aversion and learning to bid bidding challenges learning theories even with the same bid experiences vary stochastically the same choice can result in either a gain or a loss in such an environment the question arises of how the nearly universally documented phenomenon of loss aversion affects the adaptive dynamics we analyse the impact of loss aversion in a simple auction using the experienced weighted attraction model of learning our experimental results suggest that individual learning dynamics are highly heterogeneous and affected by loss aversion to different degrees apart from that the experiment shows that loss aversion is not specific to rare decision making

flexibility and uncertainty the preserving of flexibility when faced with uncertainty is a neglected aspect of behaviour under risk yet it is an important factor in decisions to hold liquid assets or delay irreversible investment this paper formalizes the notion of flexibility in a sequential decision context and relates its value to the amount of information an agent expects to receive a rudimentary money demand model is developed embodying these ideas and the history of flexibility as an economic concept is traced choices are frequently made between alternatives that imply different degrees of future commitment between a short term investment that leaves future options open for example and a long term one that by its very nature forecloses those options the relative attractiveness of the two depends on their probability distributions of payoffs over time a basic consideration in this choice is the recognition that beliefs about the risks governing these payoffs may change current doubts may be partially resolved in the near future this prospect decreases the attractiveness of the longer term commitment in that one is able to respond less fully to new information and even if it does not directly affect the risks associated with shorter term choices enhances their appeal this paper formalizes the above remarks by establishing connections between the following two partial orderings the first is an ordering based on variability of beliefs one set of beliefs is more variable than another if more final risk is resolved at an intermediate stage the more one expects to learn by an intermediate period relative to what one knows today the more variation one is anticipating in beliefs about the final outcome the second is an ordering of current actions or positions based on flexibility one position is more flexible than another if it leaves available a larger set of future positions at any given level of cost these two orderings are incorporated in a simple sequential decision model to suggest the following behavioural principle the more variable are a decision maker s beliefs the more flexible is the position he will choose this principle potentially applies whenever i there will be opportunities to act after further information is received and ii current actions influence either the attractiveness or availability of different future actions

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

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

voters as fiscal conservatives voters penalize federal and state spending growth this is the central result of my analysis of voting behavior in presidential senatorial and gubernatorial elections from 1950 1988 the composition of federal spending growth seems irrelevant the vote loss to the president s party from an extra dollar of defense or nondefense spending is the same however in gubernatorial elections expansion of state welfare spending exacts a disproportionate political price deficit financing of federal or state spending does not appear to matter politically i conclude by discussing the obvious question of why government budgets have grown in the face of this voter hostility

testing mixed strategy equilibria when players are heterogeneous the case of penalty kicks in soccer the concept of mixed strategy is a fundamental component of game theory and its normative importance is undisputed however its empirical relevance has sometimes been viewed with skepticism the main concern over the practical usefulness of mixed strategies relates to the indifference property of a mixedstrategy equilibrium in order to be willing to play a mixed strategy an agent must be indifferent between each of the pure strategies that are played with positive probability in the mixed strategy as well as any combination of those strategies given that the agent is indifferent across these many strategies there is no bene t to selecting precisely the strategy that induces the opponent to be indifferent as required for equilibrium why an agent would in the absence of communication between players choose exactly one particular randomization is not clear of course whether agents in real life actually play nash equilibrium mixed strategies is ultimately an empirical question the evidence to date on this issue is based almost exclusively on laboratory experiments e g barry o neill 1987 amnon rapoport and richard b boebel 1992 dilip mookherjee and barry sopher 1994 jack ochs 1995 kevin a mccabe et al 2000 the results of these experiments are mixed o neill 1987 concludes that his experimental evidence is consistent with nash mixed strategies but that conclusion was contested by james n brown and robert w rosenthal 1990 with the exception of mccabe et al 2000 which looks at a three person game the other papers generally reject the nash mixedstrategy equilibrium while much has been learned in the laboratory there are inherent limitations to such studies it is sometimes argued that behavior in the simpli ed arti cial setting of games played in such experiments need not mimic real life behavior in addition even if individuals behave in ways that are inconsistent with optimizing behavior in the lab market forces may discipline such behavior in the real world finally interpretation of experiments rely on the assumption that the subjects are maximizing the monetary outcome of the game whereas there may be other preferences at work among subjects e g attempting to avoid looking foolish that distort the results tests of mixed strategies in nonexperimental data are quite scarce in real life the games played are typically quite complex with large strategy spaces that are not fully speci ed ex ante in addition preferences of the actors may not be perfectly known we are aware of only one paper in a similar spirit to our own research using data from classic tennis matches mark walker and john wooders 2001 test whether the probability the player who serves the ball wins the point is equal for serves to the right and chiappori department of economics university of chicago 1126 east 59th street chicago il 60637 levitt department of economics university of chicago groseclose graduate school of business stanford university 518 memorial way stanford ca 94305 the paper was presented at games 2000 in bilbao and at seminars in paris and chicago we thank d braun j m conterno r guesnerie d heller d mengual p reny b salanie and especially j l ettori for comments and suggestions and m mazzocco and f bos for excellent research assistance any errors are ours 1 the theoretical arguments given in defense of the concept of mixed strategy equilibria relate either to puri cation john c harsanyi 1973 or to the minimax property of the equilibrium strategy in zero sum games for recent elaborations on these ideas see authur j robson 1994 and phil reny and robson 2001 2 the ultimatum game is one instance in which experimental play of subjects diverges substantially from the predicted nash equilibrium robert slonim and alvin e roth 1998 demonstrate that raising the monetary payoffs to experiment participants induces behavior closer to that predicted by theory although some disparity persists

a predictive index for the flypaper effect abstract it is well established that lump sum public grants boost local government spending more than an equivalent increase in private income the flypaper effect one shortcoming of the related literature is that it presumes all communities have an identical propensity to consume from an intergovernmental grant this paper is one attempt to allow for a heterogeneous response the working conjecture is that government expenditure on administrative overhead is a gauge of voter control over fiscal decisions high overhead spending implies a lower provision of public services and a stronger role for revenue maximizing forces in the budget setting process as such the flypaper effect should be more marked in high overhead communities an overhead index is applied to a sample of pennsylvania communities in the philadelphia metropolitan area it is difficult to understand these governments spending propensities from various windfall revenues without the help of the overhead index supportive evidence for this approach because overhead data is widely available the technique here can be used to address important policy questions such as predicting variations in state government responses to the recently created lump sum welfare grants

an experiment to evaluate bayesian learning of nash equilibrium play abstract we report on an experiment designed to evaluate the empirical implications of jordan s model of bayesian learning in games of incomplete information a finite example is constructed in which the model generates unique predictions of subjects choices in nearly all periods when the true game defined by players private information was one with a unique equilibrium in pure strategies the experimental subjects play converged to the equilibrium as jordan s theory predicts even when the subjects had not attained complete information about one another but when there were two pure strategy equilibria the theory s predictions were not consistent with observed behavior journal of economic literature classification numbers d83 c72 c92

does electoral accountability affect economic policy choices evidence from gubernatorial term limits this paper analyzes the behavior of u s governors from 1950 to 1986 to investigate a reputation building model of political behavior we argue that differences in the behavior of governors who face a binding term limit and those who are able to run again provides a source of variation in discount rates that can be used to test a political agency model we find evidence that taxes spending and other policy instruments respond to a binding term limit if a democrat is in office the result is a fiscal cycle in term limit states which lowers state income when the term limit binds

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

equilibrium political budget cycles political business cycle theories generally rely on nominal rigidities and voter myopia this paper offers an equilibrium theory that preserves some basic insights from earlier models though with significant refinements the political budget cycle emphasized here is in fiscal policy rather than output and inflation it arises via a multidimensional signal process one can consider the welfare implications of proposals to mitigate the cycle and the effects of altering the electoral structure copyright 1990 by american economic association

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

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

the power to tax analytical foundations of a fiscal constitution preface 1 taxation in constitutional perspective 2 natural government a model of leviathan 3 constraints on base and rate structure 4 the taxation of commodities 5 taxation through time income taxes capital taxes and public debt 6 money creation and taxation 7 the disposition of public revenues 8 the domain of politics 9 open economy federalism and taxing authority 10 toward authentic tax reform prospects and prescriptions epilogue notes selected bibliography index

flexible parametric estimation of duration and competing risk models in this paper we specify and estimate a flexible parametric proportional hazards model the model specification is flexibly parametric in the sense that the baseline hazard is non parametric while the effect of the covariates takes a particular functional form we also add parametric heterogeneity to the underlying hazard model specification we specify a flexible parametric proportional competing risks model which permits unrestricted correlation among the risks unemployment duration data are then analysed using the flexible parametric duration and competing risks specifications we find an important effect arising from the exhaustion of unemployment insurance and significantly different hazards for the two types of risks new jobs and recalls

an experimental investigation of unprofitable games we investigate behavior in two unprofitable games where maxmin strategies do not form a nash equilibrium yet guarantee the same payoff as nash equilibrium strategies that vary in the riskiness of the nash strategy we find that arguments for the implausibility of nash equilibrium are confirmed by our experiments however claims that this will lead to maxmin play are not neither solution concept accounts for more than 53 of choices in either game the results indicate that the tension between the nash and maxmin strategies does not resolve itself over the course of the experiment moreover the relative performance of the solution concepts is sensitive to the riskiness of the nash strategy journal of economic literature

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

the effects of payoff magnitude and heterogeneity on behavior in 2 2 games with unique mixed strategy equilibria the logit version of quantal response equilibrium predicts that equilibrium behavior in games will vary systematically with payoff magnitudes if all other factors are held constant including the nash equilibria of the game we explore this in the context of a set of asymmetric 2x2 games with unique totally mixed strategy equilibria the data provide little support for the payoff magnitude predictions of the logit equilibrium model we extend the theoretical quantal response equilibrium model to allow for heterogeneity and find that the data fit the heterogeneous version of the theory significantly better

what s to know about laboratory experimentation in economics abstract experimental economics has grown as a discipline from near non existence 50 years ago to a full fledged field within economics in the present much of experimental economics research involves experimental methods as a tool applied to problems in other fields of economics however some of this research is inward looking focusing on questions of the methodology of experimental economics in this note i briefly discuss two methodological issues in experimental economics that might benefit from meta analysis the pool from which experimental participants are drawn university undergraduate students versus other populations and the scale of monetary incentives faced by participants large small or hypothetical

an analysis of support for tax limitation referenda explanations for recent upsurges in support for tax reduction measures include 1 a desire to reduce the scope of government activity attiyeh and engle 1979 cbs 1978 1 2 a desire to cut taxes independent of changes in government services levy 1975 levy and zamola 1978 critin 1979 3 a dissatisfaction with the incidence of taxation reid 1979 decanio 1979 none of these explanations predicts when dissatisfaction with taxes will be great enough to cause citizens to act the literature suggests several catalysts that may produce or fail to produce a tax revolt first sales and income taxes produce less revolt since there is relatively little awareness of the amount being paid the incidence of the property tax is much more obvious enrick 1963 wagstaff 1965 gensemer 1965 wagner 1976 ordeshook 1979 a second catalyst is the recency of the assessment reassessment ordeshook 1979 argues that people do not compare their tax burdens with the burdens of others or with the level of government services provided they lack information for such an analysis rather taxpayers react when they experience recent and substantial changes in taxes this paper analyzes certain characteristics of people who sign a petition calling for a referendum to impose a tax limit and of their neighborhoods we hypothesize that

infrequent assessments distort property taxes theory and evidence abstract economists have long recognized that lags in property reassessment benefit infrequent movers because it reduces their property taxes but in addition reassessment lags can influence the level of property taxes selected under majority rule i show that short delays in community wide reassessment increase property tax collections because it reduces the tax price for a majority of voters however longer delays reduce property tax collections because the aggregate assessed base and thus the tax yield declines so much i formally characterize the cutoff between these regimes and show tax collections are generally above their socially optimal level this theory can help explain why many people believe property taxes are excessive and it also suggests that the american system of taxing capital gains at realization rather than on accrual might result in excessive rates i test this theory on a sample of pennsylvania municipalities in the philadelphia suburbs this is a suitable crucible for such an evaluation because community wide reassessments are infrequently performed in pennsylvania it is not possible to reject the theory s basic predictions and numerical estimates suggest that a 5 year delay in community wide reassessment increases government revenues by 6 however reassessment delays do not impose statistically significant social losses because they benefit infrequent movers

government credibility and policy choice evidence from the pennsylvania earned income tax abstract this paper considers the decision of pennsylvania communities whether to levy a 1 wage tax while a simple political economy model suggests this tax should be enacted when many residents are exempted from the tax the opposite pattern seems to hold one explanation is that residents may mistrust their government and fear that the new tax monies will be spent unwisely several implications of this credibility story are consistent with the data and non taxing communities tend to have low credibility as measured by three proxies in addition after controlling for credibility the proportion of exempt residents is positively associated with the probability of enacting the wage tax just as the political economy model suggests

learning about learning in games through experimental control of strategic interdependence we report experiments in which humans repeatedly play one of two games against a computer program that follows either a reinforcement learning or an experience weighted attraction algorithm our experiments show these learning algorithms detect exploitable opportunities more sensitively than humans also learning algorithms respond to detected payo increasing opportunities systematically however the responses are too weak to improve the algorithms payos human play against various decision maker types doesn t vary signicantly these factors lead to a strong linear relationship between the humans and algorithms action choice proportions that is suggestive of the algorithm s best response correspondence these properties are revealed only by our human versus computer experiments and not by our standard human versus human experiments nor our model simulations jel classication c72 c92 c81

expectation based loss aversion and strategic interaction abstract by extending the equilibrium concepts of k szegi and rabin 2006 k szegi and rabin 2007 this paper analyzes the strategic interaction of expectation based loss averse players for loss averse players with choice acclimating expectations the utility from playing a mixed strategy is not linear but convex in the probabilities they assign to their pure strategies as a consequence they are generally unwilling to randomize and an equilibrium may fail to exist for players with choice unacclimating expectations by contrast randomizing over their pure strategies may indeed constitute a credible best response and an equilibrium always exists building upon these insights we delineate how expectation based loss averse players differ in their strategic behavior from their counterparts with standard expected utility preferences derive novel strategic effects discuss equilibrium selection and derive equilibrium play for some simple games

property tax financing renting and the level of local expenditures the renter homeowner dichotomy has been systematically ignored in the local public goods literature the conventional justification for ignoring this dichotomy is that the only difference between the two groups of individuals is an innocuous accounting rule owners pay property taxes directly while renters pay property taxes indirectly via their rental payments to landlords 9 consequently when empirical studies after controlling for income and tastes find renter behavior that is discernably different from that of homeowners the explanation commonly offered is that renters are subject to fiscal illusion i e renters support higher levels of expenditures than homeowners because renters are unaware of the actual property tax burdens they bear 2 the fiscal illusion explanation despite its general acceptance is deficient on both empirical and theoretical grounds empirically the fiscal illusion hypothesis has not and probably cannot be directly tested 3 fiscal illusion is not so much a theory of renter behavior as it is a convenient ad hoc explanation for empirical results that are unexpected from the theory a revised theory of renter behavior cum illusion moreover would lack credibility to argue that even if time and again renters expectations are unfulfilled by experience i e they pay as much for increased services as owners when they expect not to yet renters consistently support higher levels of services would simply be untenable there are alternative possible explanations for renters behavior renters might have stronger preferences for public goods e g they may have a larger number of school age children renters

stationary concepts for experimental 2x2 games five stationary concepts for completely mixed 2 x 2 games are experimentally compared nash equilibrium quantal response equilibrium action sampling equilibrium payoff sampling equilibrium martin j osborne and ariel rubinstein 1998 and impulse balance equilibrium experiments on 12 games 6 constant sum games and 6 nonconstant sum games were run with 12 independent subject groups for each constant sum game and 6 independent subject groups for each nonconstant sum game each independent subject group consisted of four players 1 and four players 2 interacting anonymously over 200 periods with random matching the comparison of the five theories shows that the order of performance from best to worst is as follows impulse balance equilibrium payoff sampling equilibrium action sampling equilibrium quantal response equilibrium nash equilibrium