Luis C. Corchón

Implementation with State Dependent Feasible Sets and Preferences: A Renegotiation Approach

In this paper we present a model of implementation based on the idea that agents renegotiate unfeasible allocations. We characterize the maximal set of Social Choice Correspondences that can be implemented in Nash Equilibrium with a class of renegotiation functions that do not reward agents for unfeasibilities. This result is used to study the possibility of implementing the Walrasian Correspondence in exchange economies and several axiomatic solutions to problems of bargaining and bankruptcy.

Foundations for contest success functions

In the literature, the outcome of contests is either interpreted as win probabilities or as shares of the prize. With this in mind, we examine two approaches to contest success functions (CSFs). In the first, we analyze the implications of contestants’ incomplete information concerning the ‘type’ of the contest administrator. While in the case of two contestants this approach can rationalize prominent CSFs, we show that it runs into difficulties when there are more agents. Our second approach interprets CSFs as sharing rules and establishes a connection to bargaining and claims problems which is independent of the number of contestants. Both approaches provide foundations for popular CSFs and guidelines for the definition of new ones.“The strategic approach also seeks to combine axiomatic cooperative solutions and non-cooperative solutions. Roger Myerson recently named this task the ‘Nash program’.”(Rubinstein 1985, p. 1151)

On the competitive effects of divisionalization

In this paper, we assume that firms can create independent divisions which compete in quantities in a homogeneous good market. Assuming complete information, identical firms and constant returns to scale, we prove the following: 1) Subgame Perfect Nash Equilibrium (SPNE) implies Perfect Competition if the number of firms is beyond some critical Level 2) This Level is small (sometimes one) under reasonable circumstances. Assuming a fixed cost per firm, SPNE implies that even if this cost is arbitrarily small and the number of potential firms is arbitrary Large, 3) the number of active firms is small (sometimes a monopoly) and 4) the total number of divisions is bounded above. This implies that the market under consideration is a Natural Oligopoly. Next we study a model in which there is both a fixed cost and an upper bound on the maximum number of divisions which can be created. We show that 5) when this upper bound tends to infinity and the fixed cost tends to zero, SPNE may imply either Perfect Competition or a Natural Oligopoly. Finally 6) it is shown that the above results hold under incomplete information.

Welfare Losses Under Cournot Competition

We find that in a market for a homogeneous good where firms are identical, compete in quantities and produce with constant returns, the percentage of wel-fare losses (PWL) is small with as few as five competitors for a class of demand functions which includes linear and isoelastic cases. However with fixed costs and asymmetric firms PWL can be large. We provide exact formulae of PWL and robust constructions of markets were PWL is close to one in these two cases. We show that the market structure that maximizes PWL is either monopoly or dominant firm, depending on demand. Finally we prove that PWL is minimized when all firms are identical, a clear indication that the assumption of identical firms biases the estimation of PWL downwards.

On The Allocative Effects of Rent Seeking

We consider the effects of rent-seeking activities on resource allocation. Before rent-seeking activities take place, there are prior probabilities that an object will be given to one of several agents. The posterior probability depends on prior probabilities and the expenses incurred by all agents. In the case of two agents who equally value the object, prior and posterior probabilities coincide, and thus rent seeking has no effect on resource allocation. If there are two agents with different valuations of the object or we have more than two agents, rent seeking matters and posterior probabilities reflect the valuations of the agents. Copyright 2000 by Blackwell Publishing Inc.

The Scholarship Assignment Problem

Abstract There are n graduate students and n faculty members. Each student will be assigned a scholarship by the joint faculty. The socially optimal outcome is that the best student should get the most prestigious scholarship, the second-best student should get the second most prestigious scholarship, and so on. The socially optimal outcome is common knowledge among all faculty members. Each professor wants one particular student to get the most prestigious scholarship and wants the remaining scholarships to be assigned according to the socially optimal outcome. We consider the problem of finding a mechanism such that in equilibrium, all scholarships are assigned according to the socially optimal outcome. Journal of Economic Literature Classification Numbers: D70, D78.

Foundations for Contest Success Functions

We examine two approaches to contest success functions. In the first we analyze the implications of contestants´ incomplete information concerning the `type´ of the contest administrator. While in the case of two contestants this approach can rationalize prominent contest success functions, we show that it runs into difficulties when there are more agents. Our second approach interprets contest success functions as sharing rules and establishes a connection to bargaining and claims problems which is independent of the number of contestants. Both approaches provide foundations for popular contest success functions and guidelines for the definition of new ones.

Existence and Nash implementation of efficient sharing rules for a commonly owned technology

Abstract Suppose that a group of individuals owns collectively a technology which produces a consumption good by means of a (possibly heterogeneous) input. A sharing rule associates input contributions with a vector of consumptions that are technologically feasible. We show that the set of allocations obtained by any continuous sharing rule contains Pareto efficient allocations. We also present a mechanism that implements in Nash equilibrium the Pareto efficient allocations contained in an arbitrary sharing rule.

Comparative statics in Cournot free entry equilibrium

Abstract In this paper we study the effects of a change in an exogenous variable (the fixed cost or a parameter in the demand function) on the output and the number of active firms in a Symmetric Cournot Equilibrium with Free Entry (SCEFE). The results obtained here are different from those obtained in the Cournot model with a given number of firms. In particular, an increase in demand might yield a decrease in the output of the industry. We also show that any observation on prices, profits and number of firms is compatible with the assumption that the market is in a SCEFE. If fixed costs can be observed, there is a loose relationship between the profit rate and the number of active firms. This result is used as a warning against the use of the profit rate as a measure of an anticompetitive position and against the Structure–Conduct–Performance paradigm.

Peace Agreements Without Commitment

We present a model of rational and fully informed players. We show that in absence of binding agreements, in many cases, war can be avoided by transferring resources from one player into another. In most cases the rich country transfers money to the poor country. But when the military proficiency of the rich country is sufficiently high, the poor country stops the war by transferring part of its resources to the rich country. War cannot be avoided when inequality is sufficiently large or the cost of war is small enough,