Equivalence of Resource/Opportunity Egalitarianism and Welfare Egalitarianism in Quasilinear Domains

We study the allocation of indivisible goods when monetary transfers are possible and preferences are quasilinear. We show that the only allocation mechanism (upto Pareto-indifference) that satisfies the axioms supporting resource and opportunity egalitarianism is the one that equalizes the welfares. We present alternative characterizations, and budget properties of this mechanism and discuss how it would ensure fair compensation in government requisitions and condemnations.egalitarianism, egalitarian-equivalence, no-envy, distributive justice, allocation of indivisible goods and money, fair auctions, the Groves mechanisms, strategy-proofness, population monotonicity, cost monotonicity, government requisitions, eminent domain

Equal-Budget Choice Equivalent Solutions in Exchange Economies

Given a family of linear budget sets, an allocation is equal opportunity equivalent (Thomson, 1994) if there exists a common budget set such that each agent is indi¤erent between the bundle that he gets and the best bundle he can obtain in the choice set. We first study therobustness properties of equal opportunity equivalent correspondences with respect to change in preferences. We impose independence to irrelevant preference changes and connect this property with the implementation of rules via some game-theoretic solution concept. We provide an equivalence result with the equal-income Walrasian rule. Next, we study robustness with respect to change in the number of agents and derive a haracterization of the equal-income Walrasian rule. Our results provide additional justifications for the equal-division of resources as a first step toward fairness.microeconomics ;

Revising claims and resisting ultimatums in bargaining problems

We propose a mechanism which implements a unique solution to the bargaining problem with two players in subgame-perfect equilibrium. Players start by making claims and accept a compromise only if they cannot gain by pursuing their claim in an ultimatum. The player offering the lowest resistance to his opponent’s claim can propose a compromise. The unique solution depends on the extent to which claims can be revised. If no revisions are allowed, compatible claims implement the Nash solution. If all revisions are allowed, maximal claims implement the Kalai-Smorodinsky solution.

Revising claims and resisting ultimatums in bargaining problems.

We propose a mechanism which implements a unique solution to the bargaining problem with two players in subgame-perfect equilibrium. Players start by making claims and accept a compromise only if they cannot gain by pursuing their claim in an ultimatum. The player offering the lowest resistance to his opponent’s claim can propose a compromise. The unique solution depends on the extent to which claims can be revised. If no revisions are allowed, compatible claims implement the Nash solution. If all revisions are allowed, maximal claims implement the Kalai-Smorodinsky solution.

Vickrey Auctions with Reserve Pricing

We generalize the Vickrey auction to allow for reserve pricing in a multiple item auction with interdependent values. By withholding quantity in some circumstances, the seller can improve revenues or mitigate collusion. In the Vickrey auction with reserve pricing, the seller determines the quantity to be made available as a function of the bidders' private information, and then efficiently allocates this quantity among the bidders. Truthful bidding is a dominant strategy with private values and an ex post equilibrium with interdependent values. If the auction is followed by resale, then truthful bidding remains an equilibrium in the auction-plus-resale game. In settings where resale exhausts all the gains from trade among the bidders, the Vickrey auction with reserve pricing maximizes seller revenues.Auctions, Vickrey Auctions, Multiple Item Auctions, Resale

Compensation and responsibility

This a chapter for the Handbook of Social Choice and Welfare. It deals with the theory of fairness applied to situations when individuals are partly responsible for their characteristics.fairness, responsibility, equal opportunity, compensation, handicap, talent, effort

On the reserve price in all-pay auctions with complete information and lobbying games

We show that the seller’s optimal reserve price in an all-pay auction with complete information is higher than in a standard auction. We use our results to re-consider some findings of the literature that models lobbying games as all-pay auctions. In particular, we show that the so-called Exclusion Principle appears to rely crucially on the implicit assumption of a “weak” (in terms of bargaining power) seller, and does not hold if she regards bidders’ valuations as iid according to a monotonic hazard rate. Our preliminary results for the case of independent but asymmetric bidders make it even more suspicious.all-pay auctions; reserve price; economic theory of lobbying

Bargaining and the theory of cooperative games: John Nash and beyond

This essay surveys the literature on the axiomatic model of bargaining formulated by Nash ("The Bargaining Problem," Econometrica 28, 1950, 155-162).Nash's bargaining model, Nash solution, Kalai-Smorodinsky solution, Egalitarian solution

The Optimality of Being Efficient

In an optimal auction, a revenue-optimizing seller often awards goods inefficiently, either by placing them in the wrong hands or by withholding goods from the market. This conclusion rests on two assumptions: (1) the seller can prevent resale among bidders after the auction; and (2) the seller can commit to not sell the withheld goods after the auction. We examine how the optimal auction problem changes when these assumptions are relaxed. In sharp contrast to the no resale assumption, we assume perfect resale: all gains from trade are exhausted in resale. In a multiple object model with independent signals, we characterize optimal auctions with resale. We prove generally that with perfect resale, the seller's incentive to misassign goods is destroyed. Moreover, with discrete types, any misassignment of goods strictly lowers the seller's revenue from the optimum. In auction markets followed by perfect resale, it is optimal to assign goods to those with the highest values.Auctions; Multiple Object Auctions; Resale