Vincent Paul Crawford

• PhD Massachusetts Institute of Technology
• Drummond Professor of Political Economy Emeritus at University of Oxford

Most applications of game theory assume equilibrium, justified by presuming either that learning will have converged to one, or that equilibrium approximates people's strategic thinking even when a learning justification is implausible. Yet several recent experimental and empirical studies suggest that people's initial responses to games often devi...

Competitive adjustment processes in labor markets with perfect information but heterogeneous firms and workers are studied. Generalizing results of Shapley and Shubik [7], and of Crawford and Knoer [1], we show that equilibrium in such markets exists and is stable, in spite of workers' discrete choices among jobs, provided that all workers are gros...

This paper develops a model of strategic communication, in which a better-informed Sender (S) sends a possibly noisy signal to a Receiver (R), who then takes an action that determines the welfare of both. We characterize the set of Bayesian Nash equilibria under standard assumptions, and show that equilibrium signaling always takes a strikingly sim...

We derive nonparametric sufficient and asymptotically necessary conditions for the existence of reference-dependent preferences, as in Kőszegi and Rabin's (2006) structural implementation of Kahneman and Tversky's (1979) prospect theory, that can rationalize some consumer demand choices that violate the conditions for a neoclassical rationalization...

This paper revisits Myerson and Satterthwaite's (1983) classic analysis of mechanism design for bilateral trading, replacing equilibrium with a level-k model of strategic thinking and focusing on direct mechanisms. The revelation principle fails for level-k models, so restricting attention to direct mechanisms and imposing incentive-compatibility a...

This review discusses selected work in experimental game theory. My goals are to further the dialogue between theorists and empiricists that has driven progress in economics and game theory and to guide future experimental work. I focus on experiments whose lessons are relevant to establishing and maintaining coordination and cooperation in human r...

Traditional game theory assumes that if framing does not affect a game's payoffs, it will not influence behavior. However, Rubinstein and Tversky (1993), Rubinstein, Tversky, and Heller (1996), and Rubinstein (1999) reported experiments eliciting initial responses to hide-and-seek and other types of game, in which subjects’ behavior responded syste...

Market design seeks to translate economic theory and analysis into practical solutions to real-world problems. By redesigning both the rules that guide market transactions and the infrastructure that enables those transactions to take place, market designers can address a broad range of market failures. In this paper, we illustrate the process and...

In this paper, I discuss the state of progress in applications of game theory in economics and try to identify possible future developments that are likely to yield further progress. To keep the topic manageable, I focus on a canonical economic problem that is inherently game-theoretic, that of fostering efficient coordination and cooperation in re...

Rubinstein and Tversky (1993), Rubinstein, Tversky, and Heller (1996), and Rubinstein (1999) reported experiments that elicited initial responses to coordination, discoordination, and hide and seek games with non-neutral decision labelings, in which behavior responded to labeling. Crawford and Iriberri (2007ab) proposed a level-k model to account f...

The paper is a comment on the article by R. Harstad and R. Selten and considers the tradeoff between bounded rationality and optimization models in the game-theoretic context. The author shows that in most of the models elements of opimization are still retained and that it is thus more productive to further improve the optimization-based modeling...

When the editors invited me to contribute an essay to Eminent Economists II: Their Life Philosophies, I found the adjective intimidating. My hesitance grew as I reviewed the list of contributors to the first Eminent Economists volume and reread their magnificent, moving essays. I wondered, “Why not Salient Economists? That I could live with.” My mu...

Harstad and Selten's article in this forum performs a valuable service by highlighting the dominance of optimization-based models over boundedly rational models in modern microeconomics, and questioning whether optimization-based models are a better way forward than boundedly rational models. This article complements Rabin's response to Harstad and...

There is a large body of evidence of apparently spontaneous mimicry in humans. This phenomenon has been described as "automatic imitation" and attributed to a mirror neuron system, but there is little direct evidence that it is involuntary rather than intentional. Cook et al. supplied the first such evidence in a unique strategic game design that g...

This paper begins to explore behavioral mechanism design, replacing equilibrium by a model based on "level-k" thinking, which has strong support in experiments. In representative examples, we consider optimal sealed-bid auctions with two symmetric bidders who have independent private values, assuming that the designer knows the distribution of leve...

This paper compares the leading models of strategic thinking with subjects' initial responses to Van Huyck, Battalio, and Beil (1990, 1991) coordination games. mong the refined “equilibrium plus noise” models we compare, payoff-dominant equilibrium performs better than risk-dominant or maximin equilibrium. Among the individualistic models we compar...

This paper proposes a model of cab drivers' labor supply, building on Henry S. Farber's (2005, 2008) empirical analyses and Botond Koszegi and Matthew Rabin's (2006; henceforth "KR") theory of reference-dependent preferences. Following KR, our model has targets for hours as well as income, determined by proxied rational expectations. Our model, est...

Human behavior theories are not unrelated to assumptions about cognition, as cognitive processes are believed to be involved in human decisionmaking processes. Through neuroeconomics, we find that making use of evidence regarding cognition and its aspects may lead us to come up with better theories of decisions. However, Gul and Pesendorfer assert...

Since Schelling, it has often been assumed that players make use of salient decision labels to achieve coordination. Consistent with previous work, we find that given equal payoffs, salient labels yield frequent coordination. However, given even minutely asymmetric payoffs, labels lose much of their effectiveness and miscoordination abounds. This r...

This paper reconsiders whether cabdrivers' labor supply decisions reflect reference-dependent preferences. Following Botond Koszegi and Matthew Rabin (2006), we construct a model with targets for hours as well as income, both determined by rational expectations. Estimating using Henry S. Farber's (2005, 2008) data, we show that the reference-depend...

This paper compares the leading models of strategic thinking with subjects' initial responses to Van Huyck, Battalio, and Beil (1990, 1991) coordination games. Among the refined “equilibrium plus noise” models we compare, payoff-dominant equilibrium performs better than risk-dominant or maximin equilibrium. Among the individualistic models we compa...

"Hide-and-seek" games are zero-sum two-person games in which one player wins by matching the other’s decision and the other wins by mismatching. Although such games are often played on cultural or geographic "landscapes" that frame decisions nonneutrally, equilibrium ignores such framing. This paper reconsiders the results of experiments by Rubinst...

Table A1 lists the choice frequencies from five additional RTH Treasure treatments with the same payoff structure as RTH-4 (Table 1), but labels with positive or negative connotations and/or focally labeled end locations. RTH-2 and RTH-5 are analogous to RTH-4 except for the connotations of the focal label. RTH-1 and RTH-3 are like RTH-4 except tha...

"Hide-and-seek" games are zero-sum two-person games in which one player wins by matching the other's decision and the other wins by mismatching. Although such games are often played on cultural or geographic "landscapes" that frame decisions nonneutrally, equilibrium ignores such framing. This paper reconsiders the results of experiments by Rubinst...

This paper proposes a structural nonequilibrium model of initial responses to incomplete-information games based on "level-k" thinking, which describes behavior in many experiments with complete-information games. We derive the model's implications in first- and second-price auctions with general information structures, compare them to equilibrium...

This paper reconsiders Joseph Farrell's (1987) and Matthew Rabin's (1994) analyses of coordination via preplay communication, focusing on Farrell's analysis of Battle of the Sexes. Replacing their equilibrium and rationalizability assumptions with a structural non-equilibrium model based on level-k thinking, I reevaluate FR's assumptions on how pla...

Identification in errors-in-variables regression models was recently extended to wide models classes by S. Schennach (Econometrica, 2007) (S) via use of generalized functions. In this paper the problems of non- and semi- parametric identification in such models are re-examined. Nonparametric identification holds under weaker assumptions than in (S)...

This paper reports an experiment that elicits subjects? initial responses to 16 dominance-solvable two-person guessing games. The structure is publicly announced except for varying payoff parameters, to which subjects are given free access. Varying the parameters allows very strong separation of the behavior implied by leading decision rules. Subje...

[eng] Transportation costs and monopoly location in presence of regional disparities. . This article aims at analysing the impact of the level of transportation costs on the location choice of a monopolist. We consider two asymmetric regions. The heterogeneity of space lies in both regional incomes and population sizes: the first region is endowed...

This paper proposes a structural non-equilibrium model of initial responses to incomplete-information games based on "level-k" thinking, which describes behavior in many experiments with complete-information games. We derive the model's implications in first- and second-price auctions with general information structures, compare them to equilibrium...

Most graduating medical students in the United States obtain hospital residencies through the National Resident Matching Program (“NRMP”). The NRMP, or “Match” as it is called, is a centralized procedure that begins each year with hospitals defining residency positions, including a fixed specification of the associated salaries. The Match has been...

Rubinstein, Tversky, and Heller elicited subjects' initial responses to games in which a Hider and a Seeker choose simultaneously among four locations, with the Seeker winning a given amount if he chooses the same location as the Hider and the Hider otherwise winning that amount. The game has a unique equilibrium, in which both players randomize un...

In Taipei we observed a dual Dutch fish auction, like a conventional Dutch auction with bundling, but with reversed roles of price and quantity. We study dual and conventional auctions with symmetric, independent private values, when agents' utilities are linear in money but strictly concave in fish. With known buyers' values, conventional and dual...

Starting from Hendricks and McAfee's (2000) example of the Allies' decision to feint at Calais and attack at Normandy on D-Day, this paper models misrepresentation of intentions to competitors or enemies. Allowing for the possibility of bounded strategic rationality and rational players' responses to it yields a sensible account of lying via costle...

In Taipei we observed a dual Dutch fish auction, like a conventional Dutch auction with bundling but with the roles of quantity and price reversed, and fish the numeraire rather than money. This paper uses a symmetric independent private values framework to study how duality interacts with auction form when agents' utility functions are linear in m...

This essay describes one economist’s view of how four extraordinary papers by John Nash, two on non-cooperative game theory [Proceedings of the National Academy of Sciences, USA 36 (1950b) 48–49; Annals of Mathematics 54 (1951) 286–295] and two on the theory of bargaining [Econometrica 18 (1950a) 155–162; Econometrica 21 (1953) 128–140], influenced...

Journal of Economic Literature Classification Numbers: C70, C92.

1 [1ST SCREEN] {Introduction} WELCOME! PLEASE WAIT UNTIL THE EXPERIMENTER TELLS YOU TO START You are about to participate in an experiment in interdependent decision making. Universities and research foundations have provided the funds for this experiment. If you follow the instructions and pass the Understanding Test, you will be allowed to contin...

This paper reports experiments designed to measure strategic sophistication, the extent to which players' behavior reflects attempts to predict others' decisions, taking their incentives into account. Subjects played normal-form games with various patterns of iterated dominance and unique pure-strategy equilibria without dominance, using a computer...

This paper reports experiments designed to measure strategic sophistication, the extent to which players' behavior reflects attempts to predict others' decisions, taking their incentives into account. Subjects played normal-form games with various patterns of iterated dominance and unique pure-strategy equilibria without dominance, using a computer...

This paper is a survey of experimental evidence on behavior in games with communication, focusing on environments where “talk is cheap” in the sense that players' messages have no direct payoff implications. Also considered are some environments in which communication was permitted throughout the game, in addition to those environments in which onl...

A model is proposed to explain the results of recent experiments in which subjects repeatedly played a coordination game, with the right to play auctioned each period in a larger group. Subjects bid the market-clearing price to a level recoverable only in the efficient equilibrium and then converged to that equilibrium, although subjects playing th...

This paper compares the leading theoretical approaches to equilibrium selection, both traditional and adaptive, in the light of recent experiments by Van Huyck, Battalio, and Beil (henceforth "VHBB") in which subjects repeatedly played coordination games, uncertain only about each other's strategy choices. The large strategy spaces of VHBB's design...

A model of the process by which players learn to play repeated coordination games is proposed with the goal of understanding the results of recent experiments. In those experiments, the dynamics of subjects' strategy choices and the resulting patterns of discrimination among equilibria varied systematically with the rule for determining payoffs and...

This paper studies the correspondence between Nash equilibrium and evolutionary stability in large and finite populations. Whenever the payoff function of the game that describes the simultaneous interaction of the individuals in the population, and thereby determines their fitnesses, is sufficiently continuous, an evolutionarily stable strategy (E...

This paper studies the comparative statics of adding agents to matching markets that generalize the marriage and college-admissions markets of D. Gale and L. S. Shapley [Am. Math. Month. 69, 9-15 (1962; Zbl 0109.244)]. It is shown, for the wide class of matching markets studied by A. Roth [Econometrica 52, 47-57 (1984; Zbl 0526.90012)], that adding...

This paper proposes an adaptive interpretation of the results of some recent experiments with repeated tacit coordination games. These experiments revealed several behavioral regularities, including a systematic discrimination between strict Nash equilibria in certain games, that appear to be driven by strategic uncertainty, and are not explained b...

This paper proposes a characterization of optimal strategies for playing certain repeated coordination games whose players have identical preferences. Players' optimal coordination strategies reflect their uncertainty about how their partners will respond to multiple-equilibrium problems; this uncertainty constrains the statistical relationships be...

This paper considers a strengthening of Maynard Smith's definition of an evolutionarily stable strategy, or “ESS”, discussed by Vickers & Cannings [Vickers, G. T. & Cannings, C. (1987). On the definition of an evolutionarily stable strategy. J. theor. Biol.129, 349–353]. Vickers & Cannings showed that the stronger definition was equivalent to Mayna...

Because players whose preferences violate the von neumann-Morgenstern independence axiom may be unwilling to randomize as mixed-strategy Nash equilibrium would require, a Nash equilibrium may not exist without independence. This paper generalizes Nash's definition of equilibrium, retaining its rational-expectations spirit but relaxing its requireme...

This paper considers whether Maynard Smith's concept of an evolutionarily stable strategy, or “ESS”, can be used to predict long-run strategy frequencies in large populations whose members are randomly paired to play a game, and who adjust their strategies over time according to sensible learning rules. The existing results linking the ESS to stabl...

The theory of fair division is concerned with the design of procedures for allocating a bundle of goods among n persons who are perceived to have equal rights to the goods. Both equity (according to criteria discussed below) and efficiency are sought. The theory is of interest primarily because its approach to allocation problems enjoys some import...

The effect of short-term contracting on resource extraction is studied, in a two-country model of international trade in oil. Countries' planners are assumed to be fully rational, with perfect information and perfect foresight. Contracts are assumed perfectly enforceable and complete, except that short-term contracts do not allow commitments to act...

The theory of fair division is concerned with the design of procedures for allocating a bundle of goods among n persons who are perceived to have equal rights to the goods. Both equity (according to criteria discussed below) and efficiency are sought. The theory is of interest primarily because its approach to allocation problems enjoys some import...

Game-Theoretic Models of Bargaining provides a comprehensive picture of the new developments in bargaining theory. It especially shows the way the use of axiomatic models has been complemented by the new results derived from strategic models. The papers in this volume are edited versions of those given at a conference on Game Theoretic Models of Ba...

The article provides a survey and exposition of recent developments in dynamic noncooperative game theory and dynamic contract theory. In realistic models of economic relationships, complex long-term agreements may be mutually beneficial; legal enforcement of contracts is difficult or impossible; assymmetries of information place limits on the use...

The paper considers whether an adaptive justification, like those commonly available for non-interactive optimization models, can be found for the mixed-strategy Nash equilibrium. Although it is known that such a justification is frequently available for pure-strategy equilibria, it is shown that all members of a wide class of behaviorally plausibl...

This paper studies the limits of contracting as a method for achieving efficient allocation, with particular attention to how informational asymmetries interact with the timing of commitment to a mechanism. There are arguments to suggest, in the spirit of the Coase "Theorem," that if agents can agree on a mechanism before observing their private in...

This paper proposes a framework for the analysis of optimal strategic reserve policy when ability to withstand embargoes influences terms of trade in an exhaustible resource like oil. The mode embodies two stylized facts: competitive forces are not always strong enough to eliminate other influences on the negotiated price of oil, and long-term cont...

The effect of conventional and final-offer compulsory arbitration on negotiated settlements is characterized, using Nash's variable-threats bargaining solution, with particular attention to the interaction between arbitral risk and bargainers' risk preferences. When there is no arbitral risk, both schemes are shown to have the same effect on negoti...

This note shows that standard comparative statics techniques, properly reinterpreted, can be used to obtain correct qualitative results for irregular extrema, even though the conditions for application of the Implicit Function Theorem are not satisfied for them.

This paper proposes a simple theory to explain bargaining impasses, which is based on Schelling's view of the bargaining process as a struggle between bargainers to commit themselves to favorable bargaining positions. Because bargaining impasses are generally Pareto-inefficient, anything involving a positive probability of impasse is Pareto-ineffic...

Competitive adjustment processes in labor markets with perfect information but heterogeneous firms and workers are studied. Generalizing results of Shapley and Shubik [7], and of Crawford and Knoer [1], we show that equilibrium in such markets exists and is stable, in spite of workers' discrete choices among jobs, provided that all workers are gros...

A vast and often confusing economics literature relates competition to investment in innovation. Following Joseph Schumpeter, one view is that monopoly and large scale promote investment in research and development by allowing a firm to capture a larger fraction of its benefits and by providing a more stable platform for a firm to invest in R&D. Ot...

The effect of Social Security and private pensions on individual retirement decisions is modeled, relaxing in turn three commonly maintained assumptions—perfect capital markets, actuarial fairness, and certain lifetimes—which together imply that there is no effect. In each case, raising the contribution level can cause systematic changes (of either...

This article shows that the conclusions of the Zeuthen-Harsanyi theory of bargaining, which is widely regarded as an alternative justification for Nash's solution of the bargaining problem, can be extremely sensitive to small changes in the assumption that both bargainers have identical perceptions of the costs of disagreement. Whether this is the...

A mechanism that can implement any Pareto-efficient allocation in a two-person Edgeworth box economy when agents choose among uncertain alternatives by the maximin criterion is described. This, coupled with the association of maximin and its generalizations with complete ignorance, suggests that deliberately withholding information from agents abou...

It is shown that in Nash bargaining over division of a single good, when agents are allowed to distort their von Neumann-Morgenstern utility functions into any (weakly) concave form, reporting linear utility functions constitutes a unique dominant-strategy Nash equilibrium.