Rajiv Vohra

Coalitional Power and Public Goods

We study the provision of public goods when all agents have complete information and can write binding agreements. This framework is in deliberate contrast to a traditional view of the free‐rider problem based on hidden information or voluntary provision. We focus on coalition formation as a potential source of inefficiency. To this end, we develop a notion of an equilibrium coalition structure, based on the assumption that each coalition that forms does so under a rational prediction of the society‐wide coalition structure. In a simple model, we characterize the (unique) equilibrium coalition structure. Only in some cases does the equilibrium involve full cooperation, resulting in efficient provision of the public good. In other cases, the equilibrium consists of several coalitions and inefficient provision. However, the degree of inefficiency and the number of possible coalitions are bounded.

Incentives and the core of an exchange economy: a survey

This paper provides a general overview of the literature on the core of an exchange economy with asymetric information. Incentive compatibility is emphasized in studying core concepts at the ex ante and the interim stage.The analysis includes issues of non emptiness of the core as wellas core convergence to price equilibrium allocations.

Nash implementation through elementary mechanisms in economic environments

This paper identifies a class of mechanisms, called elementary mechanisms, which are (in a precisely defined sense) the “simplest” mechanisms that can implement efficient outcomes in economic environments. The class of social choice correspondences that can be implemented by elementary mechanisms is completely characterized in a variety of different economic contexts.

A consistent bargaining set

Abstract Both the core and the bargaining set fail to satisfy a natural requirement of consistency. In excluding imputations to which there exist objections, the core does not assess the “credibility” of such objections. The bargaining set goes a step further. Only objections which have no counterobjections are considered justified. However, the credibility of counterobjections is not similarly assessed. We formulate a notion of a consistent bargaining set in which each objection in a “chain” of objections is tested in precisely the same way as its predecessor. Various properties of the consistent bargaining set are also analyzed.

An Extension of the Second Welfare Theorem to Economies with Nonconvexities and Public Goods

In this paper we report a generalization of the results of Foley and Guesnerie on the second welfare theorem to economies with arbitrary nonconvex production sets. The nature of marginal cost prices in such economies is clarified through the use of the Clarke tangent cones.

Multiplicity of Mixed Equilibria in Mechanisms: A Unified Approach to Exact and Approximate Implementation

We characterize full implementation of social choice sets in mixed strategy Bayesian equilibrium. Our results concern both exact and virtual mixed implementation. For exact implementation, we identify a strengthening of Bayesian monotonicity, which we refer to as mixed Bayesian monotonicity. It is shown that, in economic environments with at least three agents, mixed Bayesian implementation is equivalent to mixed Bayesian monotonicity, incentive compatibility and closure. For implementing a social choice function, the case of two-agents is also covered by these conditions and mixed Bayesian monotonicity reduces to Bayesian monotonicity. Following parallel steps, mixed virtual implementation is shown to be equivalent to mixed virtual monotonicity, incentive compatibility and closure. The key condition, mixed virtual monotonicity, is argued to be very weak. In particular, it is weaker than Abreu-Matsushima’s measurability, thereby implying that: (1) virtual implementation in mixed Bayesian equilibrium is more permissive than virtual implementation in iteratively undominated strategies, and (2) non-regular mechanisms are essential for the implementation of rules in that gap.

On a general existence theorem for marginal cost pricing equilibria

We report a generalization of recent results on the existence of marginal cost pricing equilibria (MCPE) in economies with an increasing returns to scale industry. Our result makes no ad hoc assumptions which force the equilibrium to be on the efficiency frontier of the aggregate production possibility set. We also present an additional condition under which our MCPE are productivity efficient in the aggregate.

The Ex Ante Incentive Compatible Core in the Absence of Wealth Effects

In a differential information economy with quasi-linear utilities, monetary transfers facilitate the fulfillment of incentive compatibility constraints: the associated ex ante core is generically non-empty. However, we exhibit a wellbehaved exchange economy in which this core is empty, even if goods are allocated through random mechanisms.

On Kakutani's fixed point theorem, the K-K-M-S theorem and the core of a balanced game*

SummaryWe provide elementary proofs of Scarfs theorem on the non-emptiness of the core and of the K-K-M-S thoerem, based on Kakutanis fixed point theorem. We also show how these proofs can be modified to apply a coincidence theorem of Fan instead of Kakutanis fixed point theorem, for some additional simplicity.

An existence theorem for a bargaining set

Abstract This paper considers non-transferable utility games and provides sufficient conditions for the existence of the bargaining set introduced in Mas-Colell (1989). Our main assumption is weak balancedness. This assumption is weaker than balancedness and is satisfied in all transferable utility games and all three-player games. The proof of our main result is based on an application of a coincidence theorem of Fan (1969).