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 gross substitutes from each firm's standpoint. We also generalize Gale and Shapley's [3] result that the equilibrium to which the adjustment process converges is biased in favor of agents on the side of the market that makes offers, beyond the class of economies to which it was extended by Crawford and Knoer [1]. Finally, we use our techniques to establish the existence of equilibrium in a wider class of markets, and some sensible comparative statics results about the effects of adding agents to the market are obtained. THE ARROW-DEBREU THEORY of general economic equilibrium has long been recognized as a powerful and elegant tool for the analysis of resource allocation in market economies. Not all markets fit equally well into the Arrow-Debreu framework, however. Consider, for example, the labor market-or the housing market, which provides an equally good example for most of our purposes. Essential features of the labor market are pervasive uncertainty about market opportunities on the part of participants, extensive heterogeneity, in the sense that job satisfaction and productivity generally differ (and are expected to differ) interactively and significantly across workers and jobs, and large set-up costs and returns to specialization that typically limit workers to one job. All of these features can be fitted formally into the Arrow-Debreu framework. State-contingent general equilibrium theory, for example, provides a starting point for studying the effects of uncertainty. But this analysis has been made richer and its explanatory power broadened by the examination of equilibrium with incomplete markets, search theory, and market signaling theory. The purpose of this paper is to attempt some improvements in another dimension: we study the outcome of competitive sorting processes in markets where complete heterogeneity prevails (or may prevail). To do this, we take as given the implications of set-up costs and returns to specialization by assuming that, while firms can hire any number of workers, workers can take at most one job. We also return to the simplification of perfect information. In the customary view of competitive markets, agents take market prices as given and respond noncooperatively to them. In this framework equilibrium cannot exist in general unless the goods traded in each market are truly homogeneous; heterogeneity therefore generally requires a very large number of markets. And since these markets are necessarily extremely thin-in many cases containing only a single agent on each side-the traditional stories supporting the plausibility of price-taking behavior are quite strained.

[Competitive adjustment processes in labor markets where firms and workers are heterogeneous but well informed are studied. A natural notion of equilibrium for such markets is defined, and a plausible adjustment process is shown under reasonable assumptions always to converge to an equilibrium; this allows a generalization of several existence results in the literature. Finally, the relationship between market institutions (such as who makes offers) and which of the range of equilibria that heterogeneity makes possible arises, is studied. Generalizing results of Gale and Shapley and Shapley and Shubik, it is shown that all agents on a given side of the market agree on which is the best equilibrium, and that the equilibrium that emerges is the one most favored by the agents on the side of the market that makes offers in the adjustment process. The process can also be viewed as an algorithm for transportation and optimal assignment problems.]

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 interface that allowed them to look up hidden payoffs as often as desired, one at a time, while automatically recording their look-ups. Monitoring information search allows tests of game theory's implications for cognition as well as decisions, and subjects' deviations from search patterns suggested by equilibrium analysis help to predict their deviations from equilibrium decisions.

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. Subjects' decisions and searches show that most subjects understood the games and sought to maximize payoffs, but many had simplified models of others' decisions that led to systematic deviations from equilibrium. The predictable component of their deviations is well explained by a structural nonequilibrium model of initial responses based on level-k thinking.

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 and Eyster and Rabin's (2005) “cursed equilibrium,” and evaluate the model's potential to explain nonequilibrium bidding in auction experiments. The level-k model generalizes many insights from equilibrium auction theory. It allows a unified explanation of the winner's curse in common-value auctions and overbidding in those independent-private-value auctions without the uniform value distributions used in most experiments.

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 between their strategy choices players can bring about. The authors show that optimality is nevertheless consistent with subgame-perfect equilibrium. Examples are analyzed in which players use precedents as focal points to achieve and maintain coordination, and in which they play dominated strategies with positive probability in early stages in the hope of generating a useful precedent.

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 simple form, in which S partitions the support of the (scalar) variable that represents his private information and introduces noise into his signal by reporting, in effect, only which element of the partition his observation actually lies in. We show under further assumptions that before S observes his private information, the equilibrium whose partition has the greatest number of elements is Pareto-superior to all other equilibria, and that if agents coordinate on this equilibrium, R's equilibrium expected utility rises when agents' preferences become more similar. Since R bases his choice of action on rational expectations, this establishes a sense in which equilibrium signaling is more informative when agents' preferences are more similar.

This paper proposes a model of cab drivers' labor supply, building on Henry S. Farber's (2005, 2008) empirical analyses and Botond Kőszegi 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, estimated with Farber's data, reconciles his finding that stopping probabilities are significantly related to hours but not income with Colin Camerer et al.'s (1997) negative “wage” elasticity of hours; and avoids Farber's criticism that estimates of drivers' income targets are too unstable to yield a useful model of labor supply.

“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 Rubinstein, Tversky, and others whose designs model nonneutral landscapes, in which subjects deviate systematically from equilibrium in response to them. Comparing alternative explanations theoretically and econometrically suggests that the deviations are well explained by a structural nonequilibrium model of initial responses based on “level-k” thinking, suitably adapted to nonneutral landscapes.

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 deviate systematically from equilibrium, and that structural nonequilibrium “level-k” or “cognitive hierarchy” models often out-predict equilibrium. Even when learning is possible and converges to equilibrium, such models allow better predictions of history-dependent limiting outcomes. This paper surveys recent theory and evidence on strategic thinking and illustrates the applications of level-k models in economics.