The Collective Wisdom of Beauty Contests

This note uses techniques developed for aggregate games to characterize the set of equilib- ria for a beauty contest or prediction game in which the experts’ preferences are quadratic, but with an otherwise unrestricted information structure for private signals and the state variable. We show that, on aggregate, the experts’ collective estimate of the unknown parameter to be estimated is unbiased for every equilibrium.Aggregate games, beauty contests, prediction games

A necessary and sufficient condition for non-smooth linear-state optimal control problems

We present a set of necessary and sufficient conditions for a class of optimal control problems with pure state constraints for which the objective function is linear in the state variable but the objective function is otherwise only restricted to be upper semicontinuous in the control variable.Optimal control, non-smooth optimization, convex analysis

Barter relationships

We offer a simple economic model of repeated barter to explore current economic exchange in Russia: individuals trade with each other in a dynamic environment where the threat of dissolving the relationship constrains the incentives to cheat. We show how the value of future interactions affects the willingness of individuals to trade with each other; only when rates of interaction are large can trust compensate for an absence of money. Moreover, when trading relationships are asymmetric – either in the trading partners’ values for each other’s goods or in their relative bargaining power – the resulting barter allocations are distorted, as goods must be used for liquidity reasons. When third-party middlemen exist who can facilitate barter, they command a premium for their services, and have preferences for improved liquidity which may or may not correspond with the other traders in the barter economy. Fourth, we demonstrate that the restriction of trading to tight trading networks may be a socially efficient response to insufficient barter interactions. Finally, we consider how liquidity constraints affect pricing, and illustrate how the existence of a barter market can mute incentives to change prices in response to credit crunches.Barter, non-monetary exchange

Common Agency Equilibria with Discrete Mechanisms and Discrete Types

This paper characterizes the equilibrium sets of an intrinsic common agencygame with discrete types and direct revelation mechanisms. After presentinga general algorithm to find the pure-strategy equilibria of this game, we use itto characterize these equilibria when the two principals control activitieswhich are complements in the agent’s objective function. Some of thoseequilibria may entail allocative inefficiency. For the case of substitutes, wedemonstrate non-existence of such equilibria with direct mechanisms, butexistence may be obtained with indirect mechanisms. Finally, we relax theequilibrium concept and analyze quasi-equilibria. We show that existence isthen guaranteed and characterize the corresponding allocations.

The Revelation and Delegation Principles in Common Agency Games

In the context of common agency adverse-selection games weillustrate that the revelation principle cannot be applied to studyequilibria of the multi-principal games. We then demonstrate thatan extension of the taxation principle – what we term the“delegation principle” – can be used to characterize the set of allcommon agency equilibria.revelation principle, delegation principle, taxationprinciple, common agency, adverse selection.

Aggregate Representations of Aggregate Games

An aggregate game is a normal-form game with the property that each player’s payoff is a function only of his own strategy and an aggregate function of the strategy profile of all players. Aggregate games possess a set of purely algebraic properties that can often provide simple characterizations of equilibrium aggregates without first requiring that one solves for the equilibrium strategy profile. The defining nature of payoffs in an aggregate game allows one to project the n-player strategic analysis of a normal form game onto a lower-dimension aggregate-strategy space, thereby converting an n-player game to a simpler object – a self-generating single-person maximization program. We apply these techniques to a number of economic settings including competition in supply functions and multi-principal common agency games with nonlinear transfer functions.Aggregate games, common agency, asymmetric informa- tion, menu auctions

Barter, Liquidity and Market Segmentation

This paper explores the private and social benefits from barter exchange in a monetized economy. We first prove a no-trade theorem regarding the ability of firms with double-coincidences-of-wants to negotiate improvements in trade among themselves relative to the market outcomes. We then demonstrate that in the presence of liquidity shocks, introducing a non-monetary exchange avoids this limitation and enhances trade by (1) generating liquidity and (2) by segmenting the market place into low-demand and high-demand customers in a manner which is impossible with pure monetary exchange. We provide comparative statics illustrating the importance of each effect and relevant extensions.barter, exchange