Sequential Equilibria in Bayesian Games with Communication

We study the effects of communication in Bayesian games when the players are sequentially rational but some combinations of types have zero probability. Not all communication equilibria can be implemented as sequential equilibria. We define the set of strong sequential equilibria (SSCE) and characterize it. SSCE differs from the concept of sequential communication equilibrium (SCE) defined by Myerson (1986) in that SCE allows the possibility of trembles by the mediator. We show that these two concepts coincide when there are three or more players, but the set of SSCE may be strictly smaller than the set of SCE for two-player games.Bayesian games, Communication, Communication equilibrium, Sequential communication equilibrium

Local agency costs of political centralization

We analyze a model of moral hazard in local public services which could be efficiently managed by officials under local democratic accountability, but not by officials who are appointed by the ruler of a centralized autocracy. The ruler might prefer to retain an official who diverted resources from public services but contributed part to benefit the ruler. The autocratic ruler would value better public services only when residents reduce taxable investments which become unprofitable without good public services. For local government to benefit local residents, they must have some decentralized power to punish an official who serves them badly even while serving the ruler well

Comparison of Scoring Rules in Poisson Voting Games

Scoring rules are compared by the equilibria that they generate for simple elections with three candidates and voters drawn from large Poisson distributions. A calculus for comparing pivot probabilities in Poisson voting games is applied. For a symmetric Condorcet cycle, nonsymmetric discriminatory equilibria exist under best-rewarding scoring rules like plurality voting. A candidate who is universally disliked may still not be out of contention under worst-punishing scoring rules like negative-plurality voting. In elections where two of three candidates have the same position, symmetric equilibria coincide with majority rule only for scoring rules that are balanced between best-rewarding and worst-punishing. When voters also care about continuous functions of vote shares, equilibria may still depend on pivot probabilities.

Sequential Equilibria in Bayesian Games with Communication

We study the effects of communication in Bayesian games when the players are sequentially rational but some combinations of types have zero probability. Not all communication equilibria can be implemented as sequential equilibria. We define the set of strong sequential equilibria (SSCE) and characterize it. SSCE differs from the concept of sequential communication equilibrium (SCE) defined by Myerson (1986) in that SCE allows the possibility of trembles by the mediator. We show that these two concepts coincide when there are three or more players, but the set of SSCE may be strictly smaller than the set of SCE for two-player games

Economic Analysis of Political Institutions: An Introduction

This paper surveys four game-theoretic models of politics, to offer an introduction to the analysis of political institutions. The first two models focus on electoral competition, to show how successful candidates' equilibrium strategies may differ under different electoral systems. The other two models probe the consequences of legislative bargaining under different constitutional structures.

Population Uncertainty and Poisson Games

A general class of models is developed for analyzing games with population uncertainty. Within this general class, a special class of Poisson games is defined. It is shown that Poisson games are uniquely characterized by properties of independent actions and enviornmental equivalence. The general definition of equilibrium for games with population uncertainty is formulated, and it is shown that the equilibria of Poisson games are invariant under payoff-irrelevant type splitting. An example of a large voting game is discussed, to illustrate the advantages of using a Poisson game model for large games.

Dual Reduction and Elementary Games

Consider the linear incentive constraints that define the correlated equilibria of a game. The duals of these constraints generate Markov chains on the players' strategy sets. The stationary distributions for these Markov chains can be interpreted as the strategies in a reduced game, which is called a dual reduction. Any equilibrium of a dual reduction is an equilibrium of the original game. We say that a game is elementary if all incentive constraints can be satisfied as strict inequalities in a correlated equilibrium. Any game can be reduced to an elementary game by iterative dual reduction.