A Social Choice Lemma on Voting over Lotteries with Applications to a Class of Dynamic Games

We prove a lemma characterizing majority preferences over lotteries on a subset of Euclidean space. Assuming voters have quadratic von Neumann-Morgenstern utility representations, and assuming existence of a majority undominated (or "core") point, the core voter is decisive: one lottery is majority-preferred to another if and only if this is the preference of the core voter. Several applications of this result to dynamic voting games are discussed

The Dynamic Reform of Political Institutions

This paper formulates a model of dynamic, endogenous reform of political institutions. Specifically, a class of dynamic political games (DPGs) is introduced in which institutional choice is both recursive and instrumental. It is recursive because future political institutions are decided under current ones. The process is instrumental because institutional choices do not affect payoffs or technology directly. DPGs provide a broad framework to address the question: which environments exhibit institutional reform? Which tend toward institutional stability? In any state, private (public) sector decisions are essential if, roughly, they cannot always be replaced by decisions in the public (private) sector. We prove that institutional reform occurs if public sector decisions are not essential. Conversely, private sector decisions are essential if institutional reform occurs. The results suggest that a relatively more effective public sector is conducive to institutional stability, while a more effective private sector is conducive to change. We also show that if the political rules satisfy a dynamic consistency property, then the game admits ``political fixed points" of a recursive map from future (state-contingent) decisions rules to current ones. Since existence of political fixed points is a necessary condition of equilibrium, we apply the result to prove two equilibrium existence theorems, one of which implies that private and public sector decision rules that are smooth functions of the economic state.institutional reform, recursive, instrumental, dynamic political games, political fixed points.

Markov Equilibrium in Models of Dynamic Endogenous Political Institutions

This paper examines existence of Markov equilibria in the class of dynamic political games (DPGs). DPGs are dynamic games in which political institutions are endogenously determined each period. The process of change is both recursive and instrumental: the rules for political aggregation at date t+1 are decided by the rules at date t, and the resulting institutional choices do not affect payoffs or technology directly. Equilibrium existence in dynamic political games requires a resolution to a “political fixed point problem” in which a current political rule (e.g., majority voting) admits a solution only if all feasible political rules in the future admit solutions in all states. If the class of political rules is dynamically consistent, then DPGs are shown to admit political fixed points. This result is used to prove two equilibrium existence theorems, one of which implies that equilibrium strategies, public and private, are smooth functions of the economic state. We discuss practical applications that require existence of smooth equilibria.Recursive, dynamic political games, political fixed points, dynamically consistent rules.

Regularity of Pure Strategy Equilibrium Points in a Class of Bargaining Games

For a class of n-player (n ? 2) sequential bargaining games with probabilistic recognition and general agreement rules, we characterize pure strategy Stationary Subgame Perfect (PSSP) equilibria via a finite number of equalities and inequalities. We use this characterization and the degree theory of Shannon, 1994, to show that when utility over agreements has negative definite second (contingent) derivative, there is a finite number of PSSP equilibrium points for almost all discount factors. If in addition the space of agreements is one-dimensional, the theorem applies for all SSP equilibria. And for oligarchic voting rules (which include unanimity) with agreement spaces of arbitrary finite dimension, the number of SSP equilibria is odd and the equilibrium correspondence is lower-hemicontinuous for almost all discount factors. Finally, we provide a sufficient condition for uniqueness of SSP equilibrium in oligarchic games.Local Uniqueness of Equilibrium, Regularity, Sequential Bargaining.

Communication and Bargaining in the Spatial Model

This paper studies collective choice by participants possessing private information about the consequences of policy decisions in policymaking institutions that involve cheap-talk communication and bargaining. The main result establishes a connection between the extent to which problems of this type posses fully-revealing equilibria that select policies in the full information majority rule core (when it is well-defined) and the extent to which a fictitious sender-receiver game possesses a fully revealing equilibria. This result allows us to extend Banks and Duggan's (2000) core equivalence results to the case of noisy policymaking environments with private information when some combination of nonexclusivity and preference alignment conditions are satisfied.

The Economics of Lotteries: An Annotated Bibliography

This paper presents an annotated bibliography of all papers relating to the economics of lotteries as of early to mid 2011. All published scholarly papers that could be identified by the authors are included along with the published abstract where available.lotto, lottery, public finance, gambling

Markov Equilibrium in Models of Dynamic Endogenous Political Institutions

This paper examines existence of Markov equilibria in the class of dynamic political games (DPGs). DPGs are dynamic games in which political institutions are endogenously determined each period. The process of change is both recursive and instrumental: the rules for political aggregation at date t+1 are decided by the rules at date t, and the resulting institutional choices do not affect payoffs or technology directly. Equilibrium existence in dynamic political games requires a resolution to a political fixed point problemin which a current political rule (e.g., majority voting) admits a solution only if all feasible political rules in the future admit solutions in all states. If the class of political rules is dynamically consistent, then DPGs are shown to admit political fixed points. This result is used to prove two equilibrium existence theorems, one of which implies that equilibrium strategies, public and private, are smooth functions of the economic state. We discuss practical applications that require existence of smooth equilibria.Recursive, dynamic political games, political fixed points, dynamically consistent rules