Endogenous monetary commitment

We develop an asynchronous framework in which each player can optimally select the frequency of his moves based on cost-benefit considerations. To demonstrate how such ability to commit can alleviate coordination problems, we apply the framework to monetary policy.     

Monotone equilibria in Bayesian games of strategic complementarities

For Bayesian games of strategic complementarities, we provide a constructive proof of the existence of a greatest and a least Bayesian Nash equilibrium, each one in strategies that are monotone in type. Our main assumptions, besides strategic complementarities, are that each player's payoff displays increasing differences in own action and the profile of types and that each player's interim beliefs are increasing in type with respect to first-order stochastic dominance (e.g., types are affiliated). The result holds for general action and type spaces (single-, multi-, or infinite-dimensional; continuous or discrete) and no prior is assumed. We also provide the following comparative statics result: the greatest and least equilibria are higher if there is a first-order stochastic dominant shift in the interim beliefs. We apply this result to strategic information revelation in games of voluntary disclosure.     

Interim Bayesian Nash equilibrium on universal type spaces for supermodular games

We prove the existence of a greatest and a least interim Bayesian Nash equilibrium for supermodular games of incomplete information. There are two main differences from the earlier proofs and from general existence results for non-supermodular Bayesian games: (a) we use the interim formulation of a Bayesian game, in which each player's beliefs are part of his or her type rather than being derived from a prior; (b) we use the interim formulation of a Bayesian Nash equilibrium, in which each player and every type (rather than almost every type) chooses a best response to the strategy profile of the other players. There are no restrictions on type spaces and action sets may be any compact metric lattices.     

MACROECONOMIC STABILIZATION POLICIES IN THE EMU: SPILLOVERS, ASYMMETRIES AND INSTITUTIONS

This paper studies the institutional design of the coordination of macroeconomic stabilization policies within a monetary union in the framework of linear quadratic differential games. A central role in the analysis plays the partitioned game approach of the endogenous coalition formation literature. The specific policy recommendations in the European Economic and Monetary Union (EMU) context depend on the particular characteristics of the shocks and the economic structure. In the case of a common shock, fiscal coordination or full policy coordination is desirable. When anti‐symmetric shocks are considered, fiscal coordination improves the performance but full policy coordination does not produce further gains in policymakers' welfare.     

Correlated equilibria and local interactions

Summary This paper shows that Nash equilibria of a local-interaction game are equivalent to correlated equilibria of the underlying game.This work was done while George Mailath and Larry Samuelson were visiting the University of Bonn, whose hospitality is gratefully acknowledged. We thank Ken Binmore for helpful discussions. This is a revision of Section 2 of Mailath, Samuelson, and Shaked [6]. Financial support from the National Science Foundation and the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 303 at the University of Bonn, is gratefully acknowledged.     

Dynamic group formation in the repeated prisoner?s dilemma

We consider dynamic group formation in repeated n-person prisoner?s dilemma. Agreements in coalitional bargaining are self-binding in that they are supported as subgame perfect equilibria of repeated games. Individuals are allowed to renegotiate the cooperating group agreement through a process of voluntary participation. We prove that a cooperating group forms as an absorbing state of a Markov perfect equilibrium after a finite number of renegotiations if and only if the group is Pareto efficient, provided that individuals are patient. The cooperating group can only expand.     

Exclusion via Non‐Exclusive Contracts

We establish that non‐linear vertical contracts can allow an incumbent to exclude an upstream rival in a setting that does not rely on the exclusivity of the incumbent's contracts with downstream firms or any limits on distribution channels available to the incumbent or rival. The optimal contract we describe is a three‐part quantity discounting contract that involves the payment of an allowance to a downstream distributor and a marginal wholesale price below the incumbent's marginal cost for sufficiently large quantities. The optimal contract is robust to allowing parties to renegotiate contracts in case of entry.     

Fiscal leadership and central bank design

Abstract.  This article investigates the impact, on economic performance, of the timing of moves in a policy game between the government and the central bank for a government that has both redistributional and stabilization objectives. It is shown that both inflation and income inequality are reduced without sacrificing output growth if the government assumes a leadership role compared with a regime in which monetary and fiscal policy are determined simultaneously. Further, it is shown that government leadership benefits both the fiscal and monetary authorities through the enhanced coordination that this arrangement implies.     

Robust control and model misspecification

A decision maker fears that data are generated by a statistical perturbation of an approximating model that is either a controlled diffusion or a controlled measure over continuous functions of time. A perturbation is constrained in terms of its relative entropy. Several different two-player zero-sum games that yield robust decision rules are related to one another, to the max-min expected utility theory of Gilboa and Schmeidler [Maxmin expected utility with non-unique prior, J. Math. Econ. 18 (1989) 141-153], and to the recursive risk-sensitivity criterion described in discrete time by Hansen and Sargent [Discounted linear exponential quadratic Gaussian control, IEEE Trans. Automat. Control 40 (5) (1995) 968-971]. To represent perturbed models, we use martingales on the probability space associated with the approximating model. Alternative sequential and nonsequential versions of robust control theory imply identical robust decision rules that are dynamically consistent in a useful sense.     

Trees and extensive forms

This paper addresses the question of what it takes to obtain a well-defined extensive form game. Without relying on simplifying finiteness or discreteness assumptions, we characterize the class of game trees for which all pure strategy combinations induce unique outcomes. The generality of the set-up covers “exotic” cases, like stochastic games or decision problems in continuous time (differential games). We find that the latter class, though a well-defined problem, fails this test.     

Proposal power and majority rule in multilateral bargaining with costly recognition

This paper studies a sequential bargaining model in which agents expend efforts to be the proposer. In equilibrium, agents’ effort choices are influenced by the prize and cost effects. The (endogenous) prize is the difference between the residual surplus an agent obtains when he is the proposer and the payment he expects to receive when he is not. Main results include: (1) under the unanimity voting rule, two agents with equal marginal costs propose with equal probabilities, regardless of their time preferences; (2) under a nonunanimity rule, however, the more patient agent proposes with a greater probability; (3) while, under the unanimity rule, the social cost decreases in group heterogeneity, it can increase under a nonunanimity rule; and (4) when agents are identical, the unanimity rule is socially optimal.     

Fiscal policy under loose commitment

Due to time-inconsistency or political turnover, policymakers' promises are not always fulfilled. We analyze an optimal fiscal policy problem where the plans made by the benevolent government are periodically revised. In this loose commitment setting, the properties of labor and capital income taxes are significantly different than under the full-commitment and no-commitment assumptions. Because of the occasional reoptimizations, the average capital income tax is positive even in the long-run. Also, the autocorrelation of taxes is lower, their volatility with respect to output increases and the correlation between capital income taxes and output changes sign. Our method can be used to analyze the plausibility and the importance of commitment in a wide-class of dynamic problems.     

Species survival and evolutionary stability in sustainable habitats

Abstract. Whoever exists belongs to a species, which did not become extinct, has a (geno-)type, which should be well adjusted, and lives in a habitat which has been sustainable for a long time. We do not only analyze interspecies competition and the conditions for species survival, but also intraspecies competition of (geno-)types as in evolutionary biology and game theory. Survival in inter- and intraspecies competition together with sustainability define ecological stability, a concept which we illustrate by an example of solitary and social grazers who compete for food supply and who are endangered by the same predators. Although our approach is inspired by empirical evidence, no systematic attempt is made to apply it to some specific ecology.     

The supercore for normal-form games

This paper analyzes the supercore of a system derived from a normal-form game. For the case of a finite game with pure strategies, we define a sequence of games and show that the supercore coincides with the set of Nash equilibria of the last game in that sequence. This result is illustrated with the characterization of the supercore for the n-person prisoner's dilemma. With regard to the mixed extension of a normal-form game, we show that the set of Nash equilibrium profiles coincides with the supercore for games with a finite number of Nash equilibria.     

Community enforcement when players observe partners' past play

I investigate whether a large community can sustain cooperation in the repeated prisoner's dilemma by having cheaters punished not by their victims but by third parties. In the setting where players can observe their partners' past play only, I show that cooperation can be sustained by an equilibrium that has the following two properties: players choose their actions independently of their own past play, and they are indifferent between cooperation and defection at all histories. This equilibrium carries over to the finite-population setting and is robust to noise in the process of choosing actions or of recording past play.     

Higher order game dynamics

Continuous-time game dynamics are typically first order systems where payoffs determine the growth rate of the players? strategy shares. In this paper, we investigate what happens beyond first order by viewing payoffs as higher order forces of change, specifying e.g. the acceleration of the players? evolution instead of its velocity (a viewpoint which emerges naturally when it comes to aggregating empirical data of past instances of play). To that end, we derive a wide class of higher order game dynamics, generalizing first order imitative dynamics, and, in particular, the replicator dynamics. We show that strictly dominated strategies become extinct in n-th order payoff-monotonic dynamics n   orders as fast as in the corresponding first order dynamics; furthermore, in stark contrast to first order, weakly dominated strategies also become extinct for n?2$n?2$. All in all, higher order payoff-monotonic dynamics lead to the elimination of weakly dominated strategies, followed by the iterated deletion of strictly dominated strategies, thus providing a dynamic justification of the well-known epistemic rationalizability process of Dekel and Fudenberg [7]. Finally, we also establish a higher order analogue of the folk theorem of evolutionary game theory, and we show that convergence to strict equilibria in n-th order dynamics is n orders as fast as in first order.     

Bayesian coalitional rationalizability

In this paper we extend Ambrus's [A. Ambrus, Coalitional rationalizability, Quart. J. Econ. 121 (2006) 903-929] concept of “coalitional rationalizability (c-rationalizability)” to situations where, in seeking mutually beneficial interests, players in groups (i) make use of Bayes' rule in expectation calculations and (ii) contemplate various deviations, i.e., the validity of deviation is checked against any arbitrary sets of strategies, and not just only against restricted subsets of strategies. We offer an alternative notion of Bayesian c-rationalizability suitable for such complex social interactions. We show that Bayesian c-rationalizability possesses nice properties similar to those of conventional rationalizability.