Alejandro Neme

On group strategy-proof mechanisms for a many-to-one matching model

Abstract.For the many-to-one matching model in which firms have substitutable and quota q−separable preferences over subsets of workers we show that the workers-optimal stable mechanism is group strategy-proof for the workers. Therefore, in centralized markets like entry-level professional labor markets if the proposed matching is the workers-optimal stable matching then, no group of workers can never benefit by reporting untruthfully their preference relations. We exhibit an example showing that this property fails if the preferences of firms are substitutable but not quota q−separable.

An algorithm to compute the full set of many-to-many stable matchings

The paper proposes an algorithm to compute the full set of many-to-many stable matchings when agents have substitutable preferences. The algorithm starts by calculating the two optimal stable matchings using the deferred-acceptance algorithm. Then, it computes each remaining stable matching as the firm-optimal stable matching corresponding to a new preference profile, which is obtained after modifying the preferences of a previously identified sequence of firms.

The strength of a little perfection

The paper deals with three related issues.1.It introduces a measure of partial subgame perfection for equilibria of repeated games.2.It illustrates that the folk-theorem discontinuity generated by small complexity costs, as exhibited by Abreu and Rubinstein, does not exist in the presence of any level of perfection.3.It shows that reactive strategy equilibria, such as tit-for-tat, cannot be subgame perfect, even partially so. As a corollary, this shows a need to use full automata rather than exact automata when studying complexity and perfection in repeated games.

Maximal Domain of Preferences in the Division Problem

The division problem consists of allocating an amount of a perfectly divisible good among a group of n agents. Sprumont (1991) showed that if agents have single-peaked preferences over their shares, then the uniform allocation rule is the unique strategy-proof, efficient, and anonymous rule. We identify the maximal set of preferences, containing the set of single-peaked preferences, under which there exists at least one rule satisfying the properties of strategy-proofness, efficiency, and strong symmetry. In addition, we show that our characterization implies a slightly weaker version of Ching and Serizawas (1998) result. Journal of Economic Literature Classification Numbers: D71, D78, D63.

The multiple-partners assignment game with heterogeneous sales and multi-unit demands: competitive equilibria

A multiple-partners assignment game with heterogeneous sales and multi-unit demands consists of a set of sellers that own a given number of indivisible units of potentially many different goods and a set of buyers who value those units and want to buy at most an exogenously fixed number of units. We define a competitive equilibrium for this generalized assignment game and prove its existence by using only linear programming. In particular, we show how to compute equilibrium price vectors from the solutions of the dual linear program associated to the primal linear program defined to find optimal assignments. Using only linear programming tools, we also show (i) that the set of competitive equilibria (pairs of price vectors and assignments) has a Cartesian product structure: each equilibrium price vector is part of a competitive equilibrium with all optimal assignments, and vice versa; (ii) that the set of (restricted) equilibrium price vectors has a natural lattice structure; and (iii) how this structure is translated into the set of agents’ utilities that are attainable at equilibrium.

Stability and voting by committees with exit

Abstract.We study the problem of a society choosing a subset of new members from a finite set of candidates (as in Barberà et al. 1991). However, we explicitly consider the possibility that initial members of the society (founders) may want to leave it if they do not like the resulting new society. We show that, if founders have separable (or additive) preferences, the unique strategy-proof and stable social choice function satisfying founder’s sovereignty (on the set of candidates) is the one where candidates are chosen unanimously and no founder leaves the society.

On Exiting After Voting

We consider the problem of a society whose members must choose from a finite set of alternatives. After knowing the chosen alternative, members may reconsider their membership by either staying or exiting. In turn, and as a consequence of the exit of some of its members, other members might now find undesirable to belong to the society as well. For general exit procedures we analyze the exit behavior of members after knowing the chosen alternative. For the case of monotonic preferences we propose, for each chosen alternative, an unambiguous and meaningful prediction of the subset of members that will exit

Bribe-proof rules in the division problem

The division problem consists of allocating an amount of a perfectly divisible good among a group of n agents with single-peaked preferences. A rule maps preference profiles into n shares of the amount to be allocated. A rule is bribe-proof if no group of agents can compen- sate another agent to misrepresent his preference and, after an appropri- ate redistribution of their shares, each obtain as trictly preferred share. We characterize all bribe-proof rules as the class of efficient, strategy- proof, and weak replacement monotonic rules. In addition, we identify the functional form of all bribe-proof and tops-only rules.

The division problem with voluntary participation

The division problem consists of allocating a given amount of a homogeneous and perfectly divisible good among a group of agents with single-peaked preferences on the set of their potential shares. A rule proposes a vector of shares for each division problem. The literature has implicitly assumed that agents will find acceptable any share they are assigned to. In this article we consider the division problem when agents’ participation is voluntary. Each agent has an idiosyncratic interval of acceptable shares where his preferences are single-peaked. A rule has to propose to each agent either to not participate or an acceptable share because otherwise he would opt out and this would require to reassign some of the remaining agents’ shares. We study a subclass of efficient and consistent rules and characterize extensions of the uniform rule that deal explicitly with agents’ voluntary participation.

An undominated Nash equilibrium for voting by committees with exit

We consider the problem of a society whose members choose, with a voting by committees, a subset of new members from a given set of candidates. After knowing the elected candidates, former members may decide either stay or exit the society. We analyze the voting behavior of members who take into account the effect of their votes not only on the elected candidates, but also on the final composition of the society. For additive and monotonic preferences with dichotomous bads we construct a strategy profile that is an undominated pure strategy Nash equilibrium of the induced voting game.