Reinterpreting Mixed Strategy Equilibria: A Unification of the Classical and Bayesian Views

We provide a new interpretation of mixed strategy equilibria that incorporates both von Neumann and Morgenstern's classical concealment role of mixing as well as the more recent Bayesian view originating with Harsanyi. For any two-person game, G, we consider an incomplete information game, IG, in which each player's type is the probability he assigns to the event that his mixed strategy in G is 'found out' by his opponent. We show that, generically, any regular equilibrium of G can be approximated by an equilibrium of IG in which almost every type of each player is strictly optimizing. This leads us to interpret i's equilibrium mixed strategy in G as a combination of deliberate randomization by i together with uncertainty on j's part about which randomization i will employ. We also show that such randomization is not unusual: For example, i's randomization is nondegenerate whenever the support of an equilibrium contains cyclic best replies.

On the origin of the family

We present a game theoretic model to explain why people form life long monogamous families. Three components are essential in our framework, paternal investment, fatherhood uncertainty, and, perhaps the most distinctive feature of all, the overlap of children of different ages. When all three conditions are present, monogamy is the most efficient form of sexual organization in the sense that it yields greater survivorship than serial monogamy, group marriage, and polygyny. Monogamy is also the only configuration that fosters altruistic ties among siblings. Finally, our result sheds light to the understanding of why most religions center around the monogamous fidelity family

Secret Contracts for Efficient Partnerships ∗

By allocating different information to team members, secret contracts can provide better incentives to perform with an intuitive organizational design. For instance, they may help to monitor monitors, and appoint secret principals. More generally, secret contracts highlight a rich duality between detection and enforcement with linear transfers. On the one hand, every disobedient deviation must be detectable to enforce an an outcome, but different behavior may be used to detect different deviations. On the other, every disobedient deviation must be attributable, i.e., some player can be identified as innocent after the deviation, to provide incentives with budget balance. JEL Classification: D21, D23, D82

Dynamic legislative policy making

Abstract We prove existence of stationary Markov perfect equilibria in an infinite-horizon model of legislative policy making in which the policy outcome in one period determines the status quo for the next. We allow for a multidimensional policy space and arbitrary smooth stage utilities, and we assume preferences and the status quo are subject to arbitrarily small shocks. We prove that all such equilibria are essentially in pure strategies and that proposal strategies are continuous almost everywhere. We establish upper hemicontinuity of the equilibrium correspondence, and we derive conditions under which each equilibrium of our model determines a unique invariant distribution characterizing long run policy outcomes. We provide a convergence theorem giving conditions under which the invariant distributions generated by stationary equilibria must be close to the core in a canonical spatial model

A network approach to public goods

Abstract We study settings where each agent can exert costly effort that creates nonrival, heterogeneous benefits for some of the others. For example, municipalities can forgo consumption to reduce pollution. How do the prospects for efficient cooperation depend on asymmetries in the effects of players' actions? We approach this question by analyzing a network that describes the marginal benefits agents can confer on one another. The first set of results explains how the largest eigenvalue of this network measures the marginal gains available from cooperating; as an application, we describe the players whose participation is essential to achieving any Pareto improvement on an inefficient status quo. Next, we examine mechanisms all of whose equilibria are Pareto efficient and individually rational; an outcome is called robust if it is an equilibrium outcome in every such mechanism. Robust outcomes exist and correspond to the Lindahl public goods solutions. The main result is a characterization of effort levels at these outcomes in terms of players' centralities in the benefits network. It entails that an outcome is robust if and only if agents contribute in proportion to how much they value the efforts of those who help them

For helpful comments, I thank Pierpaolo Battigalli, Aaron Bodoh-Creed, Subir Bose, Gabe Carroll,

This paper studies mechanism design when agents are maxmin expected utility maximizers. The …rst result gives a general necessary condition for a social choice rule to be implementable. The condition combines an inequality version of the standard envelope characterization of payo¤s in quasilinear environments with an approach for relating maxmin agents ’ subjective expected utilities to their objective expected utilities under any common prior. The condition is then applied to give an exact characterization of when e ¢ cient trade is possible in the bilateral trading problem of Myerson and Satterthwaite (1983), under the assumption that agents know each other’s expected valuation of the good (which is the information structure that emerges when the agents start with a common prior but are pessimistic about how the other agent might acquire information before participating in the mechanism). Whenever e ¢ cient trade is possible, it may be implemented by a relatively simple double auction format