George J. Mailath

Learning, Mutation and Long Run Equilibria in Games

An evolutionary model with a finite number of players and with stochastic mutations is analyzed. The expansion and contraction of strategies is linked to their current relative success, but mutuation, perturbing the system from its deterministic evolution, are present as well. The focus is on the long run implications of ongoing mutations, which drastically reduce the set of equilibria. For 2 by 2 symmetric games with two symmetric strict Nash equilibria the risk dominant equilibrium is selected. In particular, if both strategies have equal security levels, the Pareto dominant Nash equilibrium is selected. In particular, if both strategies have equal security levels, the Pareto dominant Nash equilibrium is selected, even though there is another strict Nash equilibrium. Copyright 1993 by The Econometric Society.

Social Norms, Savings Behavior, and Growth

We argue that many goods and decisions are not allocated or made through markets. We interpret an agents status as a ranking device that determines how well he or she fares in the nonmarket sector. The existence of a nonmarket sector can endogenously generate a concern for relative position in, for example, the income distribution so that higher income implies higher status. Moreover, it can naturally yield multiple equilibria. It is thus possible to explain differences in growth rates across countries without recourse to differences in underlying preferences, technologies, or endowments. Different social organizations lead to different reduced-form preferences, which lead to different growth rates.

Incentive Compatibility in Signaling Games with a Continuum of Types

This paper provides two results that are useful in proving the exist ence of and characterizing separating equilibria in signaling games. A key element in the analysis of separating equilibria is the examina tion of the implied incentive compatibility constraints. It is shown that these constraints imply differentiability of strategies. In addi tion, a monotonicity condition (which is similar to the single crossi ng condition) is analyzed that is necessary and sufficient for there to be a strategy satisfying the incentive compatibility constraints. As a direct consequence of these two results, the analysis of Paul Milgrom and John Roberts (1982) is considerably strengthened. Copyright 1987 by The Econometric Society.

Collusion in second price auctions with heterogeneous bidders

Abstract We show that efficient collusion by any subset of bidders in second price private value auctions is possible, even when the bidders are heterogeneous. An important property of efficient collusion is that a bidders net payoff from participating in collusion is independent of her valuation. We show that the cooperative game whose characteristic function (evaluated at a coalition) is the ex ante collusive surplus (of that coalition) has a nonempty core. A feature of more technical interest is the mechanism characterization when the private information of agents does not enter in a linear (or even piecewise linear) manner.

Introduction: Symposium on evolutionary game theory

Abstract Interest in evolutionary game theory has recently increased dramatically. I present a brief overview of the subject and the symposium. An evolutionary model consists of a large population of myopic and unsophisticated players playing some game repeatedly through time. Strategies that are “good” replies to the distribution of actions chosen by the current population will be played by a larger fraction of the population in the next period. Thus, players learn from the experience of the population. Results on dynamics, convergence, and equilibrium concepts and their interpretation are discussed.

Efficient Non-Contractible Investments in Large Economies

Do investors making complementary investments face the correct incentives, especially when they cannot contract with each other prior to their decisions? We present a two-sided matching model in which buyers and sellers make investments prior to matching. Once matched, buyer and seller bargain over the price, taking into account outside options. Efficient decisions can always be sustained in equilibrium. We characterize the inefficiencies that can arise in equilibrium, and show that equilibria will be constrained efficient. We also show that the degree of diversity in a large market has implications for the extent of any inefficiency.

Extensive Form Reasoning in Normal Form Games

There is a tension between a belief in the strategic relevance of information sets and subgames and a belief in the sufficiency of the reduced normal form. The authors identify a prope rty of extensive form information sets and subgames termed strategic independence. Strategic independence is captured by the reduced norm al form and can be used to define normal form information sets and subgames. The authors prove a close relationship between these norma l form structures and their extensive form namesakes. They then motiva te and implement solution concepts corresponding to subgame perfection, sequential equilibrium, and forward induction entirely in the reduce d normal form. Copyright 1993 by The Econometric Society.

Imperfect Monitoring and Impermanent Reputations

We study the long-run sustainability of reputations in games with imperfect public monitoring. It is impossible to maintain a permanent reputation for playing a strategy that does not play an equilibrium of the game without uncertainty about types. Thus, a player cannot indefinitely sustain a reputation for non-credible behavior in the presence of imperfect monitoring.

Efficient Non-Contractible Investments in Finite Economies

Individuals making investments typically do not have incentives to invest efficiently when they cannot contract prior to their decisions. When they bargain over the surplus generated by their investments, they will usually not obtain the full fruits of the investment. Intuitively, this hold-up problem should be ameliorated if, in the bargaining stage, each agent has alternatives to the partner he is bargaining with. We characterize the matching and division of surplus in finite economies for any initial investment decisions. We provide conditions on those decisions that guarantee that each agent will capture the change in the aggregate social surplus that results from any investment change he makes. We further show that for any given problem, there exists a bargaining rule by which pairs split their surplus that will support efficient investment choices in equilibrium. We also show, however, that overinvestment or underinvestment can occur for natural bargaining rules.

Workers Versus Firms: Bargaining Over a Firm's Value

We introduce a distinction between a firm and its network of workers. In a competitive world, if networks are easily lured away, the workers must receive the entire value of their contribution to the firm. How then can service firms have equity value? A model is analysed in which workers are paid less as a group than their value, even in a competitive world. The workers are assumed to have a nonwage benefit for working at the current firm; this benefit is privately known. These privately known benefits make it impossible for the workers to agree on a division of their value should they leave the existing firm for a new enterprise. The result is that the workers may receive a total compensation that is less than their contribution to the firm.