on the robustness of equilibrium refinements abstract the philosophy of equilibrium refinements is that the analyst if he knows things about the structure of the game can reject some nash equilibria as unreasonable the word know in the preceding sentence deserves special emphasis if in a fixed game the analyst can reject a particular equilibrium outcome but he cannot do so for games arbitrarily close by then he may have second thoughts about rejecting the outcome we consider several notions of distance between games and we characterize their implications for the robustness of equilibrium refinements

submarkets and the evolution of market structure we construct a model of industry evolution in which the central force for change is the creation and destruction of submarkets firms expand when they are able to exploit new opportunities that arrive in the form of submarkets they contract and ultimately exit when the submarkets in which they operate are destroyed this simple framework can transparently explain a wide range of well known regularities about industry dynamics most notably the subtle relationships between size age growth and survival data on the laser industry where submarkets are prominent further illustrate the ability of the model to explain distinctive patterns in the evolution of industries and firms

comparing behavioral models using data from experimental centipede games the centipede game posits one of the most well known paradoxes of backward induction in the literature of experimental game theory given that deviations from the unique subgame perfect nash equilibrium generates a pareto improvement several theoretical models have been employed in order to rationalize this kind of behavior in this social dilemma the available explanations range from social preferences including fairness altruism or cooperation motives errors in playing inability to perform backward induction or different depths of reasoning in the present study we use the blavatskyy s theoretical contribution and relax the assumptions of expected utility maximization and risk neutral attitudes to test an alternative explanation we compare various probabilistic decision theory models in terms of their descriptive in sample and predictive out of sample fit performance using data from experimental centipede games we find that introducing non expected utility preferences to the quantal response equilibrium model along with a nonlinear utility function provides a better explanation compared to alternative specifications such as the level k or the quantal response equilibrium model with altruistic motives jel c72 c92 d81 d82

credit market constraints consumption smoothing and the accumulation of durable production assets in low income countries investments in bullocks in india in this paper we formulate and estimate a finite horizon structural dynamic model of agricultural investment behavior that incorporates the major features of low income agricultural environments income uncertainty constraints on borrowing and rental markets and the use of investment assets to generate income and smooth consumption the model is fit to longitudinal indian household data on farm profits bullock stocks and pump sets the estimated structural parameters are used to assess the effects on the life cycle accumulation of bullocks agricultural profits and welfare associated with complete markets and bullock liquidity and with second best policies that provide assured sources of income to farmers and weather insurance

a survey of agricultural household models recent findings and policy implications semicommercial farms that produce multiple crops make up a large part of the agricultural sector in developing economies these farms or agricultural households combine two fundamental units of microeconomic analysis the household and the firm traditional economic theory has dealt with these units seperately but in developing economies in which peasant farms dominate their interdependence is of crucial importance researchers have developed models of agricultural households that combine producer and consumer behavior in a theoretically consistent fashion recent empirical applications of these models have extended them and expanded the range of policy issues which can be investigated using this general framework this article reports the results of empirical applications of this model in india indonesia japan the republic of korea malaysia nigeria senegal sierra leone taiwan and thailand it provides a comparative analysis of the policy implications of the approach for such matters as the welfare of farm households the size of marketed surplus the demand for nonagricultural goods and services and for hired labor and the availability of budget revenues and foreign exchange

firm dynamics and financial development abstract using comprehensive firm level datasets this paper studies the impact of cross country variation in financial market development on firms financing choices and growth in less financially developed economies small firms grow faster and have lower leverage than large firms as financial development improves the growth difference between small and large firms shrinks while the leverage difference rises the paper then develops a quantitative model where financial frictions drive firm growth and debt financing through the availability of credit and default risk the model explains the observed cross country variations in firm size leverage and growth in response to changes in financial frictions

age effects leverage and firm growth abstract recent theories of firm dynamics emphasize the role of financial variables as determinants of firm growth empirically examining these relationships has been difficult since there is a lack of financial data on the small young and private firms using a unique administrative data set this paper considers the growth of new firms in canadian manufacturing from a financial perspective we find that financial factors such as leverage and initial financial size impact growth rates for new firms further the inclusion of leverage has little impact on the economic significance of the conditional age and size relationships with firm growth

agricultural household models extensions applications and policy this book presents the basic model of an agricultural household that underlies most of the case studies undertaken so far the model assumes that households are price takers and is therefore recursive the decisions modeled include those affecting production and the demand for inputs and those affecting consumption and the supply of labor comparative results on selected elasticities are presented for a number of economies the empirical significance of the approach is demonstrated in a comparison of models that treat production and consumption decisions separately and those in which the decisionmaking process is recursive the book summarizes the implications of agricultural pricing policy for the welfare of farm households marketed surplus the demand for nonagricultural goods and services the rural labor market budget revenues and foreign exchange earnings in addition it is shown that the basic model can be extended in order to explore the effects of government policy on crop composition nutritional status health saving and investment and to provide a more comprehensive analysis of the effects on budget revenues and foreign exchange earnings methodological topics primarily the data requirements of the basic model and its extensions along with aggregation market interaction uncertainty and market imperfections are discussed the most important methodological issues the question of the recursive property of these models is also discussed

the dynamic in stability of backwards induction abstract the evolutionary basis for predicting the backwards induction solution in finite extensive form games with perfect information is examined evolution is modelled using the replicator dynamic in combination with rare perturbations that introduce a small change in the proportion of each strategy the criterion for our judgement is whether this dynamic stabilizes over time at the subgame perfect equilibrium outcome we find that the backwards induction solution is fully justified by this process only in very simple games examples of more complex games are given in which this process does not select between the subgame perfect equilibrium outcome and alternative nash equilibrium outcomes journal of economic literature classification numbers c72 c79

the role of bounded rationality and imperfect information in subgame perfect implementation an empirical investigation in this paper we conduct a laboratory experiment to test the extent to which moore and repullo s subgame perfect implementation mechanism induces truth telling in practice both in a setting with perfect information and in a setting where buyers and sellers face a small amount of uncertainty regarding the good s value we nd that moore repullo mechanisms fail to implement truth telling in a substantial number of cases even under perfect information about the valuation of the good this failure to implement truthtelling is due to beliefs about the irrationality of one s trading partner therefore although the mechanism should in theory provide incentives for truth telling many buyers in fact believe that they can increase their expected monetary payo by lying the deviations from truth telling become signicantly more frequent and more persistent when agents face small amounts of uncertainty regarding the good s value our results thus suggest that both beliefs about irrational play and small amounts of uncertainty about valuations may constitute important reasons for the absence of moore repullo mechanisms in practice

is there a hold up problem most literature on the hold up problem starts from the assumption that ex post bargaining outcomes are insensitive to prior investment costs we argue that this approach is unsatisfactory if the bargaining procedure is relatively symmetric it typically admits multiple perfect equilibria some of which give the investor a high enough payofi to sustain e cient investment even if the bargaining procedure is asymmetric and rigged against the investor there may be investment if agents are driven by moral concerns or if communication creates commitment laboratory experiments indicate that communication is necessary and su cient for agents to coordinate on e cient outcomes when the bargaining game is symmetric when the bargaining game is rigged against the investor the hold up problem is mitigated but not eliminated by moral behavior communication is quite credible and we flnd that promises are more believable than threats

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

rationality in extensive form games let us adopt the classical point of view that a theory of games is a description of rational behavior consequently equipped with a book entitled theory of games any individual in any strategic situation need only consult the book to make a rational decision one of the questions to address in this context is indeed whether or not strategies other than those provided by backward induction can ever appear in such a book in offering an answer we shall also explore the logical limits within which any theory of games must operate

the relationship between firm growth size and age estimates for 100 manufacturing industries this study uses a sample of all firms operating in 100 manufacturing industries to examine some aspects of firm dynamics it finds that firm growth the variability of firm growth and the probability that a firm will fail decrease with firm age it also finds that firm growth decreases at a diminishing rate with firm size even after controlling for the exit of slow growing firms from the sample gibrat s law therefore fails although the severity of the failure decreases with firm size copyright 1987 by blackwell publishing ltd

is the general public licence a rational choice open source projects are networks of developers distributors and end users of non proprietary created knowledge goods it has been argued that this form of organization has some advantages over the firm or market coordination i show that for sufficiently convex and modular projects proprietary licences are not able to sustain sequential knowledge production which however can be carried out if the project is run on the open source basis

transition and enterprise restructuring the development of individual farming in romania economic reforms have induced enterprise restructuring in transition countries in agriculture the most dramatic form of restructuring is the break up of state and collective farms into individual farms the development of individual farming varies strongly between countries regions and households this paper uses household level data from a 1996 survey in romania to analyze which household and regional characteristics determine the shift to individual farming individual farming is influenced by several household characteristics such as the human capital education age farming experience physical capital endowments ownership of land buildings machinery livestock and access to other finance sources off farm wages pensions furthermore environmental factors such as infrastructure local access to inputs and the pre reform importance of individual farming in the region all affect the development of individual farming

the bayesian foundations of solution concepts of games abstract we transform a noncooperative game into a bayesian decision problem for each player where the uncertainty faced by a player is the strategy choices of the other players the priors of other players on the choice of other players the priors over priors and so on we provide a complete characterization between the extent of knowledge about the rationality of players and their ability to successively eliminate strategies which are not best responses this paper therefore provides the informational foundations of iteratively undominated strategies and rationalizable strategic behavior b d bernheim econometrica 52 1984 1007 1028 d pearce econometrica 52 1984 1029 1050 sufficient conditions are also found for nash equilibrium behavior and a result akin to r j aumann econometrica 55 1987 1 18 on correlated equilibria is derived with different hypotheses

interest rates and credit risk this paper explores the effects of shifts in interest rates on corporate leverage and default we develop a dynamic model in which the relationship between firms and their outside financiers is affected by a moral hazard problem and entrepreneurs initial wealth is scarce the link between leverage and default risk comes from the lower incentives of overindebted entrepreneurs to guarantee firm survival the need to finance new investment with outside funding pushes firms leverage ratio above some state contingent target towards which they gradually adjust through earnings retention the dynamic response of leverage and default to interest rate rises and cuts is both asymmetric and heterogeneously distributed across firms both rises and cuts increase the aggregate default rate in the short run however a higher interest rate reduces firms target leverage and hence produces lower default rates in the longer run this helps rationalize some evidence regarding the risk taking channel of monetary policy

the robustness of equilibria to incomplete information a number of papers have shown that a strict nash equilibrium action profile of a game may never be played if there is a small amount of incomplete information see for example carlsson and van damme 1993a we present a general approach to analyzing the robustness of equilibria to a small amount of incomplete information a nash equilibrium of a complete information game is said to be robust to incomplete information if every incomplete information game with payoffs almost always given by the complete information game has an equilibrium which generates behavior close to the nash equilibrium we show that many games with strict equilibria have no robust equilibrium and examine why we get such different results from existing refinements if a game has a unique correlated equilibrium it is robust a natural many player many action generalization of risk dominance is a sufficient condition for robustness

correlated equilibrium as an expression of bayesian rationality if it is common knowledge that the players in a game are bayesian utility maximizers who treat uncertainty about other players actions like any other uncertainty then the outcome is necessarily a correlated equilibrium random strategies appear as an expression of each player s uncertainty about what the others will do not as the result of willful randomization use is made of the common prior assumption according to which differences in probability assessments by different individuals are due to the different information that they have where information may be interpreted broadly to include experience upbringing and genetic makeup copyright 1987 by the econometric society

towards a renaissance of economic theory in his penetrating essay theory and experiment vernon smith observes that subject behavior often diverges from game theoretic predictions and asserts that minor fudging with theory is unlikely to solve our problems because circumstances unknown to us are responsible for the explanatory failures of neoclassical economic theory i deal precisely with these issues in thebounds of reason 2009a my remarksheredrawupon several themes fromthis book relevant to specifying a refocused research agenda for the study of human strategic interaction the core of economic theory is the rational actor model which holds that individuals have preferences over outcomes beliefs called subjectivepriors linking choices to the relativeprobability of alternativeoutcomes and theymaximize their expected payoffs given these preferences and beliefs subject towhatevermaterial informational and other constraints they face many observers consider the experimental work of daniel kahneman and others kahneman et al 1982 gigerenzer and todd 1999 as destructive of the rational actormodel in fact however their research has considerably strengthened the rational actor model s explanatory power albeit at the expense of increasing its complexity gintis 2009a chs 1 and 12 most important these studies have shown the value of modeling using heuristics that conserve on information processing and of including the current state physiological temporal and ownership of the individual as an argument of the preference ordering in the 1980s the core of economic theory was extended to include game theory viewed as the theory of the strategic interaction of bayesian rational actors game theory has become a centerpiece of microeconomic theory alongside the traditional walrasian model of general market equilibrium it is important to note however that this exalted position is quite recent the textbooks that expound the received wisdom of today s practicing economists were written in the early years of the game theory revival between 1988 and 1995 these textbooks include misconceptions promulgated in the 1980s that have been transmitted to the current generation of economists as i shall show some of these misconceptions have been repaired in more recent contributions to game theory contemporary experimentalists however generally rely on the more traditional body of outdated theory i here rely on more recent theoretical contributions especially those of robert aumann and adam brandenburger and their coworkers to bring game theory up to date i then argue that despite their analytical power game theory and the rational actor model provide only part of the theoretical toolkit needed to explain human strategic interaction moreover because individuals bring much of the complexity of society into the controlled conditions of the laboratory game theory and the rational actor model are insufficient to explain experimental results concretely i suggest that a these analytical tools must be supplemented by what i term the psycho social theory of norms b the correlated equilibrium should replace

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

pull and push individual farming in hungary this paper is motivated by the fact that part time individual farming is commonly observed among rural households in a number of transition economies but it is not clear prima facie if such resource allocation is optimal a conceptual model of household labor allocation between individual farming and off farm wage employment is developed the model explicitly accounts for the role of household endowments in labor allocation as the analysis is conditioned on the status of factor markets the hypotheses are empirically tested using 1998 data from a country representative survey of rural households in hungary an advanced transition country which only recently became eu member state results provide evidence that capital market imperfections still remain implications for the policies related to agricultural sector restructuring employment and rural development are discussed

backward induction normal form perfection and explicable equilibria a weakening of d kreps and r wilson s 1982 notion of sequential rationality is presented the motivation stems from the difficulty in justifying sequentially rational behavior in subgames reachable only through a violation of sequential rationality although the present notion of weak sequential rationality is based upon extensive form considerations it bears a close relation to r selten s 1975 normal form perfect equilibria backward induction outcomes can be achieved in generic games of perfect information with additional restrictions on beliefs an example with imperfect information shows that sequential rationality is not the consequence of equilibrium play and the absence of incredible threats copyright 1992 by the econometric society

a dual self model of impulse control we propose that a simple dual self model gives a unified explanation for several empirical regularities including the apparent time inconsistency that has motivated models of quasi hyperbolic discounting and rabin s paradox of risk aversion in the large and small the model also implies that self control costs imply excess delay as in the o donoghue and rabin models of quasi hyperbolic utility and it explains experimental evidence that increased cognitive load makes temptations harder to resist the base version of our model is consistent with the gul pesendorfer axioms but we argue that these axioms must be relaxed to account for the effect of cognitive load

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

equilibrium play and adaptive learning in a three person centipede game the two person centipede game is one of the most celebrated paradoxes of backward induction in complete information extensive form games an experimental investigation of a three person centipede game shows that the paradoxical results are strongly affected by the size of the stakes when the number of players in the game is increased from two to three and the game is played for unusually high stakes with group composition being randomly changed from trial to trial the paradox is considerably weakened as players approach equilibrium play with multiple iterations of the stage game when the game is played with low stakes there is no evidence for equilibrium play or learning across iterations of the stage game an adaptive learning model that assumes updating of the individual probabilities of choice outperforms alternative static and dynamic models in accounting for the major results observed in the high stake experiment

self confirming equilibrium and the lucas critique we examine the role of off path superstitions in macro economics and show how a false belief about off path play is the key element underlying both the lucas critique and the game theoretic concept of self confirming equilibrium however the impact of false beliefs in these two cases is different in the lucas case a policy maker s incorrect beliefs about off path play can lead to the adoption of mistaken policy innovation however the consequences of such an innovation provide evidence that the belief that motivated them was wrong in contrast play may never escape an undesirable self confirming equilibrium as the action implied by the mistaken belief does not generate data that contradicts it escape from the self confirming equilibrium requires that players do a sufficient amount of experimentation with off path actions

peasant household behaviour with missing markets some paradoxes explained a model of peasant household behavior under varying degrees of household specific food and labor market failures is constructed to show that these structural features can explain several well known patterns of peasant response which have often been attributed to peculiar motives presumed specific to peasants the model explains sluggish response to cash crops prices and high instability in perceived food and labor scarcities the key role of manufactured consumer goods prices in stimulating peasants effort in cash crops production the effectiveness of taxation as opposed to incentives in stimulating cash crops production and the key role of technological change in food production to enhance cash crop production results are obtained analytically in the case of one market failure and by numerical simulation with more than one

cycles of learning in the centipede game abstract this paper studies the evolutionary properties of the centipede game for this game the use of backward induction as a model of rational behavior has been consistently challenged by the experimental evidence our claim is that backward induction can still accurately predict the players behavior provided that they are given time enough to appreciate the strategic environment in which they operate we support this claim by proving convergence to the backward induction solution for all continuous time monotonic selection dynamics however we also show that this solution is intrinsically unstable and how this instability is positively related to the length of the game journal of economic literature classification numbers c72 c79

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

rationality nash equilibrium and backwards induction in perfect information games we say that a player is certain of an event a if she assigns probability 1 to a there is common certainty cc of a if the event a occurred each player is certain of a each player is certain that every other player is certain of a and so forth it is shown that in a generic perfect information game the set of outcomes that are consistent with common certainty of rationality ccr at the beginning of the game coincides with the set of outcomes that survive one deletion of weakly dominated strategies and then iterative deletion of strongly dominated strategies thus the backward induction outcome is not the only outcome that is consistent with ccr in particular cooperation in rosenthal s 1981 centipede game and fighting in selten s 1978 chainstore game are consistent with ccr at the beginning of the game next it is shown that if in addition to ccr there is cc that each player assigns a positive probability to the true strategies and beliefs of the other players and if there is cc of the support of the beliefs of each player then the outcome of the game is a nash equilibrium outcome

rural nonfarm employment and income diversification in colombia abstract using data for rural households from colombia we find that off farm employment contributes a significant share 45 on average to household income but that the importance of off farm income and returns to household labor vary over the income distribution analysis reveals significant gains from specialization but for households able to specialize no systematic differences in returns to labor between farm and nonfarm sources we conclude that in colombia there is no conflict between development of the farm and the nonfarm sector but that to maximize gains from nonfarm development and reduce the scope for undesirable distributional consequences policies enabling households to specialize might be called for

household composition labor markets and labor demand testing for separation in agricultural household models this paper tests the separation of farm labor supply and labor demand decisions using the observation that household composition is an important determinant of farm labor use with nonseparation after assessing the conditions under which the test has power against several alternatives an empirical model is developed to test the proposition that farm employment is independent of family composition the model is estimated on a data set from rural java the null hypothesis that farm labor allocation decisions are independent of household structure is not rejected the results are robust to different specifications of the labor demand function copyright 1992 by the econometric society

behavior in the centipede game a decision theoretical perspective the centipede game is a two player finite game of perfect information where a unique subgame perfect nash equilibrium appears to be intuitively unappealing and descriptively inadequate this paper analyzes behavior in the centipede game when a traditional game theoretical assumption that players maximize expected utility is relaxed we demonstrate the existence of a descriptively adequate subgame perfect equilibrium under two standard decision theoretical assumptions first players choose under uncertainty in a probabilistic manner as captured by embedding a core deterministic decision theory in a model of probabilistic choice second players adopt non linear decision weights and overweight the likelihood of rare events as captured for example by rank dependent utility or prospect theory

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

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

games of perfect information predatory pricing and the chain store paradox the thesis of this paper is that finite noncooperative games possessing both complete and perfect information ought to be treated like one player decision problems that is players ought to assign at every move subjective probabilities to every subsequent choice in the game and ought to make decisions via backward induction this view is in contrast with the gametheoretic approach of nash equilibrium after expanding on this view for games in the abstract in sections 2 and 3 attention is turned in section 4 to an example due to reinhard selten called the chain store paradox which possesses the flavor of a situation involving a predatory pricing monopolist it is argued that for the chain store game the decision analytic approach leads under certain assumptions to more realistic outcomes than the standard nash equilibrium approach

on price risk and the inverse farm size productivity relationship abstract the oft observed inverse relationship between farm size and productivity has elicited several explanations having important policy and theoretical implications using advances in the analysis of price risk effects on producer behavior and a simple two period model of an agricultural household that both produces and consumes under price uncertainty at the time labor allocation decisions are made this paper demonstrates analytically that a non degenerate land distribution and price risk can together produce an inverse relationship even absent any of the more common explanations empirical evidence from madagascar confirms the plausibility of this intuitive explanation for the phenomenon

payoff information and self confirming equilibrium abstract in a self confirming equilibrium each player correctly forecasts the actions that opponents will take along the equilibrium path but may be mistaken about the way that opponents would respond to deviations this paper develops a refinement of self confirming equilibrium in which players use information about opponents payoffs in forming beliefs about the way that opponents play off of the equilibrium path we show that this concept is robust to payoff uncertainty we also discuss its relationship to other concepts and show that it is closely related to assuming almost common certainty of payoffs in an epistemic model with independent beliefs journal of economic literature classification numbers c72 d84

rational behavior with payoff uncertainty abstract the iterated deletion of weakly dominated strategies has been advanced as a necessary requirement for rational play however this requirement relies on the assumption that the players have no doubts about their opponents payoffs we show that once such doubts are introduced all that can be justified by an appeal to rationality is one round of deletion of weakly dominated strategies followed by iterated deletion of strategies that are strongly dominated this extends the fudenberg kreps and levine j econ theory 12 1988 354 380 study of the robustness of nash equilibrium refinements to the robustness of solution concepts based only on rationality our results also clarify the relationship between various notions of what it means for payoff uncertainty to be small

on the effects of group identity in strategic environments abstract we examine differences in behavior between subjects interacting with a member of either the same or different identity group in both a centipede game and a series of stag hunt games we find evidence that subjects interacting with outgroup members are more likely to behave as though best responding to uniform randomization of the partner we conclude that group identity not only affects player s social preferences as identified in earlier research but also affects the decision making process independent of changes in the utility function

subgame perfect implementation under information perturbations we consider the robustness of extensive form mechanisms to deviations from common knowledge about the state of nature which we refer to as information perturbations first we show that even under arbitrarily small information perturbations the moore repullo mechanism does not yield even approximately truthful revelation and that in addition the mechanism has sequential equilibria with undesirable outcomes more generally we prove that any extensive form mechanism is fragile in the sense that if a non maskin monotonic social objective can be implemented with this mechanism then there are arbitrarily small information perturbations under which an undesirable sequential equilibrium also exists finally we argue that outside options can help improve efficiency in asymmetric information environments and that these options can be thought of as reflecting ownership of an asset

an experimental investigation of rating market regulation abstract we introduce a simple game theoretical model that captures the main aspects of the repeated interaction between an issuer and a credit rating agency it involves up front payments of issuer fees and direct publication of requested ratings due to pecuniary injuries for untruthful ratings the credit rating agency should always report truthfully in the subgame perfect equilibrium knowing this the issuer should never request a rating conducting laboratory experiments we find that behavior significantly deviates from the equilibrium prediction in favor of a cooperative solution issuers frequently do request ratings which is often reciprocated with untruthful good ratings

income strategies among rural households in mexico the role of off farm activities abstract off farm activities generate on average more than half of farm households incomes in the mexican ejido sector participation in these activities helps reduce poverty and contributes to greater equality in the distribution of income this paper analyzes the determinants of access to off farm sources of income across households we find that education plays a major role in accessing better remunerated nonagricultural employment adults of indigenous ethnic origin suffer from an educational lag and have less access to off farm nonagricultural employment than non indigenous adults at identical educational levels the regional availability of off farm employment strongly affects participation in addition women are differentially limited by distance to urban centers in their ability to gain off farm employment

prudence in bargaining the effect of uncertainty on bargaining outcomes abstract we investigate the outcome of bargaining when a player s pay off from agreement is risky we find that a risk averse player typically increases his equilibrium receipts when his pay off is made risky this is because the presence of risk makes individuals behave more patiently in bargaining strong analogies are drawn to the precautionary saving literature we show that the effect of risk on receipts can be sufficiently strong that a decreasingly risk averse player may be better off receiving a risky pay off than a certain pay off

subgame perfect cooperation in an extensive game abstract we propose a new solution concept for games in extensive form that incorporates both cooperation and subgame perfection from its definition and properties the new solution concept named the subgame perfect core is a refinement of the core of an extensive game in the same sense as the set of subgame perfect nash equilibria is a refinement of the set of nash equilibria to further characterize the subgame perfect core we show that each subgame perfect core payoff vector can be implemented as a non cooperative solution as it is a subgame perfect nash equilibrium payoff vector of an extensive form game that is closely related to the original game we also motivate and introduce a related concept of subgame perfect strong nash equilibrium of an extensive game that is coalition proof

a response to glazer and rosenthal we are most grateful to glazer and rosenthal for the attention they have paid to our work abreu and matsushima 1992a b c in the process of criticizing our mechanism they have provided an elegant exposition of it which usefully supplements our own efforts the criticisms themselves we feel are misplaced and based on a close reading but narrow interpretation of our results glazer and rosenthal seek to show that in our mechanisms the iterative removal of strictly dominated strategies is or indeed ought to be controversial in terms of conventional decision theory the iterative logic is impeccable when iterative deletion leads to a unique profile that profile is the unique rationalizable profile the unique nash equilibrium and so on of course the logic of iterative dominance entails common knowledge of rationality the theoretical coherence of this assumption has been questioned in the context of backward programming in extensive form games see luce and raiffa 1957 pp 80 81 rosenthal 1981 basu 1988 reny 1992a 1992b bonanno 1991 binmore 1987a 1987b and gul 1989 among others these paradoxes of common knowledge of rationality have been highlighted in stylized examples such as the finitely repeated prisoners dilemma and rosenthal s centipede game which in fact has been a seminal inspiration for this recent literature 2 but our mechanisms are simultaneous there is no opportunity to demonstrate irrationality strategic or otherwise and therefore no scope to rationalize iteratively dominated behavior from a decision theory perspective the glazer and rosenthal critique might therefore be viewed as an elaborate revival of the indefensible claim that players in a one short prisoners dilemma will choose not to confess because they are both better off doing so than by both playing their dominant strategies within the standard game theory paradigm there is really nothing more to be said before turning to issues of bounded rationality we note that the glazer and rosenthal critique is essentially premised on the existence of a countervailing focal point but what is a focal point the notion is notoriously vague and we are aware of no widely accepted definition 3 this is not to deny that in very simple and particular games certain behavior may be focal frequently focalness is identified with a pareto dominating equilibrium and this is the point of view glazer and rosenthal seem to adopt 4 this is implicit in their acknowledgement that when the social choice function does satisfy pareto optimality our objection loses much of its immediate

information learning and wage rates in low income rural areas in this essay we present evidence that employers in rural areas of developing countries have imperfect information with regard to the productivity of heterogeneous workers in addition to obtaining direct measures of the completeness of employer information we consider the implications of information asymmetries for the structure of casual labor markets we then evaluate the extent to which casual labor markets do in fact exhibit these attributes we find that 1 there is adverse selection out of the time rate labor market 2 employers discriminate statistically given two workers with different observed characteristics but the same actual productivity the worker from the group with the higher average productivity will have a higher wage 3 employers exhibit learning over time the extent of employer ignorance is negatively related to labor market exposure on the part of the workers and 4 calorie consumption affects productivity but is not rewarded in the time rate labor market in concluding we argue that an analysis of wage and employment patterns and the implications of these patterns for human capital investment in rural areas of developing countries that ignored the role of information problems could yield misleading conclusions

transition and agricultural labor reforms have strongly affected agricultural employment in transition countries but in remarkably different ways we present a theoretical model and an empirical analysis to explain differences in labor adjustment during transition we show that the differences are due to a combination of variations in initial conditions and differences in reform policies and effects the removal of price distortions and subsidies caused wage and price adjustments during transition and a reduction in labor demand in agriculture surplus labor outflow from agriculture was further stimulated by the privatization of the farm assets as they improve incentives and remove constraints for optimal factor allocation and structural adjustment the shift to individual farms which was especially strong in labor intensive production systems with low labor productivity in agriculture has reduced the outflow of labor from agriculture by improving farm governance and labor efficiency although this effect was mitigated by losses in scale economies due to disruptions and market imperfections in transition in general labor outflow was considerably lower on individual farms than on corporate farms due to a combination of factors related to human capital access to finance and physical capital in the last section of the article we present a general framework for understanding labor adjustments in transition countries specifically we show that there are several patterns of labor transition in one pattern followed by e g the czech republic and hungary there is initially a strong survival of the restructured large scale corporate farms that have laid off many workers in the second phase of transition gradually the importance of individual farms increases in other countries such as romania the opposite has happened in these countries there is an immediate strong shift to individual farms while labor use increases on average in agriculture after this initial phase the shift to individual farms continues albeit more slowly and labor use in agriculture starts to decline finally our analysis shows that in countries such as russia and ukraine much of the surplus labor is still employed by little reformed former collective and state farms major adjustments await more progress in agricultural and general reforms

what happened to the three legged centipede game abstract in the last two decades several frameworks have been proposed to analyze the question of whether common knowledge of rationality is sufficient to justify the play of backward induction bi in games of perfect information three strands of literature have addressed this issue the literature on equilibrium refinements the literature on knowledge based epistemology and the literature on interactive epistemology this paper surveys seminal frameworks within the first two strands of research and assesses the extent to which they provide a satisfactory solution to the problem these approaches are illustrated using a three legged version of rosenthal s centipede game which is the classical example in the literature the paper argues that some of these frameworks provide sensible answers to the riddle of bi or at least succeed in bringing the paradox to another level the paper also points at consistency problems in the body of refinements of nash equilibrium revealed by the surveyed literature

optimal lending contracts and firm dynamics we develop a general model of lending in the presence of endogenous borrowing constraints borrowing constraints arise because borrowers face limited liability and debt repayment cannot be perfectly enforced in the model the dynamics of debt are closely linked with the dynamics of borrowing constraints in fact borrowing constraints must satisfy a dynamic consistency requirement the value of outstanding debt restricts current access to short term capital but is itself determined by future access to credit this dynamic consistency is not guaranteed in models of exogenous borrowing constraints where the ability to raise short term capital is limited by some prespecified function of debt we characterize the optimal default free contract which minimizes borrowing constraints at all histories and derive implications for firm growth survival leverage and debt maturity the model is qualitatively consistent with stylized facts on the growth and survival of firms comparative statics with respect to technology and default constraints are derived borrowing constraints are an important determinant of firm growth and survival 1 such constraints may arise in connection to the financing of investment opportunities faced by firms or temporary liquidity needs such as those required to survive a recession this paper develops a theory of endogenous borrowing constraints and studies its implications for firm dynamics in our model debt is constrained by the firm s limited liability and option to default a lending contract specifies an initial loan size future financing and a repayment schedule the choice of these variables in turn determines future growth the firm s future borrowing capacity and its ability and willingness to repay hence borrowing constraints and firm dynamics are jointly determined we study this dynamic design problem our model builds on thomas and worral s 1994 model of foreign direct investment at time zero a risk neutral borrower firm or entrepreneur has a project which requires a fixed initial set up cost every period the project yields revenues that increase with the amount of 1 there is considerable evidence suggesting that financing constraints are important determinants of firm dynamics gertler and gilchrist 1994 argue that liquidity constraints may explain why small manufacturing firms respond more to a tightening of monetary policy than do larger manufacturing firms perez quiros and timmermann 2000 show that in recessions smaller firms are more sensitive to the worsening of credit market conditions as measured by higher interest rates and default premia evans and jovanovic 1989 show that the liquidity constraints are essential in the decision to become an entrepreneur fazzari hubbard and petersen 1988 among others view financial constraints as an explanation for the dynamic behaviour of aggregate investment and cabral and mata 1996 are able to fit reasonably well the size distribution of portuguese manufacturing firms by estimating a simple model of financing constraints for surveys see hubbard 1998 and stein 2003

common belief and the theory of games with perfect information abstract the statement it is common belief that player i is bayesian rational where bayesian rational means an expected utility maximizer is defined for two person games with perfect information it is shown that in most such games it is not possible for a theory so postulate the bayesian rationality of all players and to be common belief this bears directly upon the salience of standard solution concepts such as subgame perfect and sequential equilibria as well as upon the extensive form rationalizability theories of d bernheim econometrica 52 1984 1009 1028 and d pearce econometrica 52 1984 1029 1050 which rely heavily on the common belief of bayesian rationality journal of economic literature classification number c72

financial determinants of firm dynamics evidence from a european panel i use a panel of large european firms for the period 1999 2007 to study scale dependence in firm dynamics i find that scale dependence is much more pronounced when focusing on within firm rather than between firm variation and that scale dependence is a decreasing function of financial development

off farm work and capital accumulation decisions of farmers over the life cycle the role of heterogeneity and state dependence abstract this paper analyzes two principal simultaneous decisions of farm operators off farm labor supply and farm capital investment we first develop a theoretical model analyzing the effects of exogenous shocks on farmers decisions then we estimate jointly a multinomial probit model of farmers off farm labor supply and a switching regression model of farm capital using a two period panel data set from israel this method enables to account for both unobserved heterogeneity and structural state dependence the results demonstrate that farm capital investments during the 1970s which were enhanced by heavily subsidized credit prevented farmers from seeking off farm employment opportunities

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

education and off farm work an investigation is presented of the determinants of educational selectivity in a framework that emphasizes the coordination of household members sectoral time allocation is based on members comparative advantage which in turn depends on the utilization and returns to schooling in the farm and nonfarm sectors central to the model is a knowledge spillover hypothesis that workers who participate in off farm work may still contribute knowledge to farm management estimation of the model is based on cross sectional chinese farm household data collected in 1990 from 204 households in sichuan province it is concluded that schooling does not enhance labour productivity when carrying out routine tasks that the contribution to farm efficiency by the most educated members is not affected by their non farm participation and that schooling increases labour market wage rates these empirical results give comparative advantage for the better educated farmers to work off the farm

bargaining with history dependent preferences abstract two impatient players bargain over a pie of size one according to the infinite alternating offers procedure players payoffs depend not only on the outcome but also on the process of the bargaining specifically they prefer impasse to any agreement that gives them lower discounted utility than would have been derived from accepting earlier offers we characterize the essentially unique subgame perfect equilibrium path which consists of gradual concessions the more patient players are the longer it takes them to reach an agreement when players become infinitely patient the efficiency loss is substantial yet the equilibrium division converges to the nash solution

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

bargaining under strategic uncertainty the role of second order optimism this paper shows that bargainers may reach delayed agreements even in environments where there is no uncertainty about payoffs or feasible actions under such conditions delay may arise when bargainers face direct forms of strategic uncertainty that is uncertainty about the opponent s play the paper restricts the nature of this uncertainty in two important ways first it assumes on path strategic certainty bargainers face uncertainty only after surprise moves second it assumes battigalli and siniscalchi s 2002 rationality and common strong belief of rationality rcsbr a requirement that bargainers are strategically sophisticated the main result characterizes the set of outcomes consistent with on path strategic certainty and rcsbr it shows that these assumptions allow for delayed agreement despite the fact that the bargaining environment is one of complete information the source of delay is second order optimism bargainers do not put forward good offers early in the negotiation process because they fear that doing so will cause the other party to become more optimistic about her future prospects

labor supply the family and poverty the s shaped labor supply curve abstract the canonical model of labor supply is extended to account for subsistence needs and a frequently rigid division of labor within families gender various theories that have been put forward are thus reconciled in particular with respect to the distinct work choices of the poor the model predicts negative labor supply elasticities for secondary workers at low wage rates and positive ones at higher rates but near 0 for primary workers at all levels detailed time allocation data of the rural philippines support these conclusions as well as evidence from other studies including of industrialized countries policy implications are briefly discussed

the effects of human capital on wages and the determinants of labor supply in a developing country abstract the heckman procedure is used to correct for sample selection bias in estimating wage offer and net labor market supply equations the findings show that wages are affected by education and experience in addition the wage offer is influenced by other genetic and environmental influences captured in the wage of one s father calories as predicted by exogenous instruments are also shown to influence the wage offer suggesting that better nutrition increases labor productivity the probability of market labor participation as well as the amount of net market labor supply declined with the size of paddy landholding in addition to the net market supply elasticity increasing with the amount of land owned and being lower for urban than rural workers

iterated reasoning and welfare enhancing instruments in the centipede game abstract this paper investigates the effectiveness of two instruments designed to defer termination in the centipede game an insurance against termination by the opponent and an option to offer the opponent a bonus for not terminating the game the rational prediction in both cases is passing until close to the end empirically however only the bonus option is used by the subjects the results indicate that subjects readily understand the strategic effect of the bonus which once offered renders passing until close to the end the strictly dominant strategy for both players yet they fail to realise the slightly more involved strategic signal entailed in the insurance namely that passing until close to the end is a strictly dominant strategy for an insured player the results are compatible with the common finding that the majority of people exhibit only a limited degree of iterated reasoning

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

checkmate exploring backward induction among chess players it is difficult to overstate the profound impact that game theory has had on the economic approach and on the sciences more generally for that reason understanding how closely the assumptions that underpin game theoretic analysis conform to actual human decision making is a question of first order importance to economists in this spirit backward induction represents one of the most basic concepts in game theory backward induction played a prominent role in reinhard selten s 1965 development of perfect equilibrium and it has helped to shape the modern refinement literature although backward induction is a cornerstone of game theory existing empirical evidence suggests that economic agents engage in backward induction less frequently than theorists might hope backward induction has fared especially poorly in the centipede game which was introduced by robert w rosenthal 1981 and has since been extensively analyzed ken binmore 1987 robert j aumann 1988 philip j reny 1988 david m kreps 1990 geir b asheim and martin dufwenberg 2003 the original centipede game is a two player finite move game in which the subjects alternate choosing whether to end the game or to pass to the other player the subject s payoff to ending the game at a particular node is greater than the payoff he receives if the other player ends the game at the next node but less than the payoff earned if the other player elects not to end the game the player making the final choice gets paid more from stopping than from passing and thus would be expected to stop if the opponent will stop at the last node then conditional on reaching the penultimate node the player maximizes his earnings by stopping at that node following this logic further backward induction leads to the unique subgame perfect equilibrium the game is stopped at the first node as pointed out in prior research

irrationality and ambiguity in extensive games abstract based on a model where deviations from equilibrium play are assumed to identify irrational players who are characterized by ambiguous set valued strategies this paper introduces an equilibrium notion for extensive games with ambiguity averse players that yields a precise interpretation for the counterfactual reasoning usually associated with backward induction the resulting equilibria are always nash equilibria but may not satisfy the conditions required for various refinements of nash equilibrium including those for subgame perfection existence of such equilibria is proved for all two player games and for n player games with perfect information

does gibrat s law hold evidence from canadian retail and manufacturing firms this paper investigates the validity of gibrat s law holding for firms in manufacturing and retail trade sectors the object is to expand our knowledge of gibrat s law to include non manufacturing firms a unique longitudinal firm level database which contains information on canadian incorporated establishments enables the inter industry comparison the findings of the analysis are that gibrat s law is violated in both manufacturing and retail sectors violations of gibrat s law for both sectors include i growth rates that depend on firm size ii growth variability that depends on firm size and iii a negative persistence of firm growth finally age effects or selection effects are not the causes of these violations

the relation between farm size and farm productivity the role of family labor supervision and credit constraints abstract the paper shows that if the performance of hired farmhands is affected by supervision from family members and if the availability of credit is dependent on the amount of land owned then a systematic positive or negative relationship between per acre yields and farm size will prevail a model with no supervision effects on labor productivity would predict that yields are unaffected by farm size the paper also investigates the relation between land utilization and owned holding size when land rental possibilities are limited results are shown to be compatible with various observed patterns in ldcs