Divide-and-Permute

We construct "simple" games implementing in Nash equilibria several solutions to the problem of fair division. These solutions are the no-envy solution, which selects the allocations such that no agent would prefer someone else's bundle to his own, and several variants of this solution. Components of strategies can be interpreted as allocations, consumption bundles, permutations, points in simplices of dimensionalities equal to the number of goods or to the number of agents, and integers. We also propose a simple game implementing the Pareto solution and games implementing the intersections of the Pareto solution with each of these solutions.Nash implementation. No-envy. Divide-and-permute.

Fair Divisions as Attracting Nash Equilibria of Simple Games

We consider the problem of allocating a finite number of divisible homogeneous goods to N = 2 individuals, in a way which is both envy-free and Pareto optimal. Building on Thomson (2005 Games and Economic Behavior), a new simple mechanism is presented here with the following properties: a) the mechanism fully implements the desired divisions, i.e. for each preference profile the set of equilibrium outcomes coincides with the set of fair divisions; b) the set of equilibria is a global attractor for the best-reply dynamics. Thus, players myopically adapting their strategies settle down in an fair division. The result holds even if mixed strategies are used.Fair divisions, envy-free, implementation, best reply dynamics

Fairness under Uncertainty with Indivisibilities

I analyze an economy with uncertainty in which a set of indivisible objects and a certain amount of money is to be distributed among agents. The set of intertemporally fair social choice functions based on envy-freeness and Pareto efficiency is characterized. I give a necessary and sufficient condition for its non-emptiness and propose a mechanism that implements the set of intertemporally fair allocations in Bayes-Nash equilibrium. Implementation at the ex ante stage is considered, too. I also generalize the existence result obtained with envy-freeness using a broader fairness concept, introducing the aspiration function.aspiration function, envy-free social choice function, fairness, implementation, indivisible goods, uncertainty

Eliciting Socially Optimal Rankings from Unfair Jurors

A jury must provide a ranking of contestants (students applying for scholarships or Ph. D. programs, gymnasts in a competition, etc.). There exists a true ranking which is common knowledge among the jurors, but it is not verifiable. The socially optimal rule is that the contestants be ranked according to the true ranking. The jurors are not impartial and, for example, may have friends (contestants that they would like to benefit) and enemies (contestants that they would like to prejudice). We study necessary and sufficient conditions on the jury under which the socially optimal rule is Nash implementable. We also propose a simple mechanism that Nash implements the socially optimal rule under these conditions.Ranking of contestants; Implementation Theory; Nash Equilibrium

Fairness under uncertainty with indivisibilities

I analyze an economy with uncertainty in which a set of indivisible objects and a certain amount of money is to be distributed among agents. The set of intertemporally fair social choice functions based on envy-freeness and Pareto efficiency is characterized. I give a necessary and sufficient condition for its non-emptiness and propose a mechanism that implements the set of intertemporally fair allocations in Bayes-Nash equilibrium. Implementation at the ex ante stage is considered, too. I also generalize the existence result obtained with envy-freeness using a broader fairness concept, introducing the aspiration function

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 ;

Equity and economic theory: reflections on methodology and scope

This paper provides an introduction to the recent literature on ordinal distributive justice. Its objetive is to explain the process of the mathematical analysis of fairness and to consider its potential for solving real allocative problems by means of several illustrative examples

Equity and economic theory: reflections on methodology and scope.

This paper provides an introduction to the recent literature on ordinal distributive justice. Its objetive is to explain the process of the mathematical analysis of fairness and to consider its potential for solving real allocative problems by means of several illustrative examples.Fairness; Equity; Distributive justice;