Vijay Krishna

Finitely repeated games

Etude systematique des equilibres parfaits de sous jeux pour des jeux repetes de facon finie avec information complete

A Model of Expertise

We study a model in which perfectly informed experts offer advice to a decision maker whose actions affect the welfare of all. Experts are biased and thus may wish to pull the decision maker in different directions and to different degrees. When the decision maker consults only a single expert, the expert withholds substantial information from the decision maker. We ask whether this situation is improved by having the decision maker sequentially consult two experts. We first show that there is no perfect Bayesian equilibrium in which full revelation occurs. When both experts are biased in the same direction, it is never beneficial to consult both. In contrast, when experts are biased in opposite directions, it is always beneficial to consult both. Indeed, in this case full revelation may be induced in an extended debate by introducing the possibility of rebuttal.

Asymmetric Information and Legislative Rules: Some Amendments

We reexamine the major tenets of the informational theory of legislative rules, focusing on the informational efficiency of rules with varying degrees of restrictiveness. When committees are heterogeneous, full efficiency is attainable under the unrestrictive open rule as well as the somewhat restrictive modified rule. In contrast, the restrictive closed rule always leads to inefficiencies. When committees are homogeneous, the situation is different. All equilibria are inefficient regardless of legislative rules, but the closed rule leads to greater informational efficiency than does the open rule. Furthermore, the efficiency gains under the closed rule more than offset distributional losses regardless of the degree of preference divergence. We also examine the incentives provided by the different rules for information acquisition and committee specialization.

Multiple-Object Auctions with Budget Constrained Bidders

A seller with two objects faces a group of bidders who are subject to budget constraints. The objects have common values to all bidders, but need not be identical and may be either complements or substitutes. In a simple complete information setting we show: (1) if the objects are sold by means of a sequence of open ascending auctions, then it is always optimal to sell the more valuable object first; (2) the sequential auction yields more revenue than the simultaneous ascending auction used recently by the FCC if the discrepancy in the values is large, or if there are significant complementarities; (3) a hybrid simultaneous- sequential form is revenue superior to the sequential auction; and (4) budget constraints arise endogenously.

The art of conversation: eliciting information from experts through multi-stage communication☆

We examine the strategic interaction between an informed expert and an uninformed decision maker, extending the analysis of Crawford and Sobel (Econometrica 50 (1982) 1431). We modify their model to allow for more extensive communication between the two parties and show that face-to-face communication between the expert and the uninformed decision maker followed by a written report from the expert leads to improved information transmission. In (almost) all cases, there exists an equilibrium in our modified model that ex ante Pareto dominates all of the equilibria identified by Crawford and Sobel. This remains true even if the experts bias is so great that in their model no information would be disclosed.

Dynamic Duopoly: Prices and Quantities

We study a dynamic model of duopoly in which firms choose both prices and quantities. If quantity (capacity) choices are relatively inflexible, firms generally carry excess (idle) capacity in equilibrium. Because of this enforcement cost, firms are unable to achieve monopoly levels. This contrasts with models in which which firms compete in either prices or quantities alone. On the other hand, if capacities are flexible firms may be able to sustain monopoly behaviour.

Renegotiation in Finitely Repeated Games

Perfect equilibria of finitely repeated games may be vulnerable to the possibility of renegotiation among players. The authors study the limiting properties of the set of payoffs from equilibria that are immune to renegotiation. Their main result is th at the limit of the set of payoffs from renegotiation-proof equilibria is either a singleton or a connected subset of the Pareto efficient frontier. A simple sufficient condition for the latter to occur is a lso provided. Copyright 1993 by The Econometric Society.

ON THE CONVERGENCE OF FICTITIOUS PLAY

We study the continuous time Brown-Robinson fictitious play process f or non-zero sum games. We show that, in general, fictitious play cannot converg e cyclically to a mixed strategy equilibrium in which both players use more tha n two pure strategies.

Voluntary voting: Costs and benefits☆

We compare voluntary and compulsory voting in a Condorcet-type model in which voters have identical preferences but differential information. With voluntary voting, all equilibria involve sincere voting and positive participation. Thus, in contrast to situations with compulsory voting, there is no conflict between strategic and sincere behavior. When voting is costless, voluntary voting is welfare superior to compulsory voting. Even when voting is costly, participation rates are such that, in the limit, the correct candidate is elected—that is, information fully aggregates. Because it economizes on costs, voluntary voting is again welfare superior to compulsory voting.

Overcoming Ideological Bias in Elections

We study a model in which voters choose between two candidates on the basis of both ideology and competence. While the ideology of the candidates is commonly known, voters are imperfectly informed about competence. Voter preferences, however, are such that it is a dominant strategy to vote according to ideology alone. When voting is compulsory, the candidate of the majority ideology prevails and this may be inefficient from a social perspective. However, when voting is voluntary and costly, we show that turnout adjusts endogenously so that the outcome of a large election is always first-best.