Exchange of indivisible goods and indifferences: The Top Trading Absorbing Sets mechanisms

There is a wide range of economic problems that involve the exchange of indivisible goods with no monetary transfers, starting from the housing market model of the seminal paper by Shapley and Scarf (1974) to problems such as the kidney exchange or the school choice problem. The classical solution to many of these models is to apply a mechanism called Top Trading Cycles, attributed to David Gale, which satisfies good properties for the case of strict preferences. In this paper, we propose a family of mechanisms, called Top Trading Absorbing Sets mechanisms, which generalize the Top Trading Cycles to the general case in which individuals are allowed to report indifferences, while preserving a maximal possible set of its desirable properties.     

Incentive compatibility in a market with indivisible goods

In a market in which each trader's initial endowment is one unit of an indivisible good, there exists an incentive compatible procedure for reaching a competitive allocation. This contrasts with some recent results for similar problems.     

Approximate cores of games and economies with clubs

We introduce the framework of parameterized collections of games with and without sidepayments and provide three nonemptiness of approximate core theorems. The parameters bound (a) the number of approximate types of players and the size of the approximation and (b) the size of nearly effective groups of players and their distance from exact effectiveness. Our theorems are based on a new notion of partition-balanced profiles and approximately partition-balanced profiles. The results are applied to a new model of an economy with clubs. In contrast to the extant literature, our approach allows both widespread externalities and uniform results. A fundamental new mathematical result, the partition-balancing effect of large numbers, which promises to have further applications, is contained in Appendix A.     

Characterizations of bargaining solutions in production economies with unequal skills

In production economies with unequal skills, this paper characterizes bargaining solutions by using axioms on allocation rules rather than axioms on classical bargaining solutions. We introduce a new axiom, consistency w.r.t. technological innovations, so that the non-welfaristic characterizations of bargaining solutions in the production economies are provided. By the characterizations, we can classify the three bargaining solutions (the Nash, the Kalai-Smorodinsky, and the Egalitarian solutions) from the viewpoint of responsibility and compensation discussed by Dworkin.     

Group incentive compatibility in a market with indivisible goods

In a market where each trader has one unit of an indivisible good, there are procedures for exchanging goods which result in competitive allocations. One of these procedures, the top trading cycle, has the property that it is in each trader's best interest to report his true preferences over the set of goods. This note shows that no subset of traders can misrepresent their preferences and improve the allocation for all members of the subset. Additionally, if there are no indifferences in the preferences, then some traders in a subset that misrepresents preferences do worse.     

Market structure and matching with contracts

Ostrovsky (2008) [9] develops a theory of stability for a model of matching in exogenously given networks. For this model a generalization of pairwise stability, chain stability, can always be satisfied as long as agents' preferences satisfy same side substitutability and cross side complementarity. Given this preference domain I analyze the interplay between properties of the network structure and (cooperative) solution concepts. The main structural condition is an acyclicity notion that rules out the implementation of trading cycles. It is shown that this condition and the restriction that no pair of agents can sign more than one contract with each other are jointly necessary and sufficient for (i) the equivalence of group and chain stability, (ii) the core stability of chain stable networks, (iii) the efficiency of chain stable networks, (iv) the existence of a group stable network, and (v) the existence of an efficient and individually stable network. These equivalences also provide a rationale for chain stability in the unrestricted model. The (more restrictive) conditions under which chain stability coincides with the core are also characterized.     

An impossibility result for virtual implementation with status quo

In this paper, virtual implementation is restricted to deliver, on the equilibrium path, either a socially optimal outcome or a status quo: an outcome fixed for all preference profiles. Under such a restriction, for any unanimous and implementable social choice function there is a dictator, who obtains her most preferable outcome as long as all agents prefer this outcome to the status quo. Further restrictions on the lottery space and the range of social choice functions allow the dictator to impose her most preferred outcome even when other agents prefer the status quo to this outcome.     

The Nash bargaining solution in general n-person cooperative games

We present a noncooperative foundation for the Nash bargaining solution for an n-person cooperative game in strategic form. The Nash bargaining solution should be immune to any coalitional deviations. Our noncooperative approach yields a new core concept, called the Nash core, for a cooperative game based on a consistency principle. We prove that the Nash bargaining solution can be supported (in every subgame) by a stationary subgame perfect equilibrium of the bargaining game if and only if the Nash bargaining solution belongs to the Nash core.     

Serial cost sharing of excludable public goods: general cost functions

Summary. A group of individuals meet to share the cost and determine output allocations of a partial-excludable public good. We demonstrate that, for general cost functions and preferences that satisfy the Spence-Mirlees sorting condition, the serial cost-sharing formula (Moulin, 1994) has remarkable incentive properties. First, a direct economic mechanism that uses the serial formula is coalition strategy-proof, envy-free and satisfies the stand-alone property. Second, the serial mechanism involves partial exclusion, which is important for the reduction of the free-rider problem. Received: June 10, 1996; revised version; February 11, 1997     

Role of linking mechanisms in multitask agency with hidden information

We investigate the adverse selection problem where a principal delegates multiple tasks to an agent. We characterize the virtually implementable social choice functions by using the linking mechanism proposed by Jackson and Sonnenschein (2007) [20] that restricts the message spaces. The principal does not require any incentive wage schemes and can therefore avoid any information rent and welfare loss. We show the resemblance between the functioning of this message space restriction and that of incentive wage schemes. We also extend the results of the single-agent model to the multi-agent model.     

Contracting with externalities and outside options

This paper proposes a model of multilateral contracting where players are engaged in two parallel interactions: they dynamically form coalitions and play a repeated normal form game with temporary and permanent decisions. We show that when outside options are independent of the actions of other players all Markov perfect equilibrium without coordination failures are efficient, regardless of externalities created by interim actions. Otherwise, in the presence of externalities on outside options, all Markov perfect equilibrium may be inefficient. This formulation encompasses many economic models, and we analyze the distribution of coalitional gains and the dynamics of coalition formation in four illustrative applications.     

Median stable matching for markets with wages

We define the median stable matching for two-sided matching markets with wages and prove constructively that it exists.     

Stable schedule matching under revealed preference

Baiou and Balinski (Math. Oper. Res., 27 (2002) 485) studied schedule matching where one determines the partnerships that form and how much time they spend together, under the assumption that each agent has a ranking on all potential partners. Here we study schedule matching under more general preferences that extend the substitutable preferences in Roth (Econometrica 52 (1984) 47) by an extension of the revealed preference approach in Alkan (Econom. Theory 19 (2002) 737). We give a generalization of the Gale-Shapley algorithm and show that some familiar properties of ordinary stable matchings continue to hold. Our main result is that, when preferences satisfy an additional property called size monotonicity, stable matchings are a lattice under the joint preferences of all agents on each side and have other interesting structural properties.     

Collective choice under dichotomous preferences

Agents partition deterministic outcomes into good or bad. A mechanism selects a lottery over outcomes (time-shares). The probability of a good outcome is the canonical utility. The utilitarian mechanism averages over outcomes with largest “approval”. It is efficient, strategyproof, anonymous and neutral.We reach an impossibility if, in addition, each agent's utility is at least , where n is the number of agents; or is at least the fraction of good to feasible outcomes. We conjecture that no ex ante efficient and strategyproof mechanism guarantees a strictly positive utility to all agents, and prove a weaker statement.     

Symmetry-based compromise and the Nash solution to convex bargaining problems

A new axiom, symmetry-based compromise, is introduced to study solutions to convex bargaining problems. It is shown that any efficient solution that is also scale invariant and satisfies symmetry-based compromise must be Nash.     

Social orderings for the assignment of indivisible objects

In the assignment problem of indivisible objects with money, we study social ordering functions which satisfy the requirement that social orderings should be independent of changes in preferences over infeasible bundles. We combine this axiom with efficiency, consistency and equity axioms. Our result is that the only social ordering function satisfying those axioms is the leximin function in money utility.     

Bargaining foundations of the median voter theorem

We give a game-theoretic foundation for the median voter theorem in a one-dimensional bargaining model based on Baron and Ferejohn's [D. Baron, J. Ferejohn, Bargaining in legislatures, Amer. Polit. Sci. Rev. 83 (1989) 1181-1206] model of distributive politics. We prove that as the agents become arbitrarily patient, the set of proposals that can be passed in any pure strategy, subgame perfect equilibrium collapses to the median voter's ideal point. While we leave the possibility of some delay, we prove that the agents' equilibrium continuation payoffs converge to the utility from the median, so that delay, if it occurs, is inconsequential. We do not impose stationarity or any other refinements. Our result counters intuition based on the folk theorem for repeated games, and it contrasts with the known result for the distributive bargaining model that as agents become patient, any division of the dollar can be supported as a subgame perfect equilibrium outcome.