Asymmetrically fair rules for an indivisible good problem with a budget constraint

We study a particular restitution problem where there is an indivisible good (land or property) over which two agents have rights: the dispossessed agent and the owner. A third party, possibly the government, seeks to resolve the situation by assigning rights to one and compensate the other. There is also a maximum amount of money available for the compensation. We characterize a family of asymmetrically fair rules that are immune to strategic behavior, guarantee minimal welfare levels for the agents, and satisfy the budget constraint.     

An algorithm for envy-free allocations in an economy with indivisible objects and money

This paper studies envy-free allocations for economies with indivisible objects, quasi-linear utility functions, and an amount of money. We give a polynomially bounded algorithm for finding envy-free allocations. Connectedness of envy-graphs, which are used in the algorithm, characterizes the extreme points of the polytopes of sidepayments corresponding with envy-free allocations. Received: 22 October 1997/Accepted: 19 January 1999     

Smith and Rawls share a room: stability and medians

We consider one-to-one, one-sided matching (roommate) problems in which agents can either be matched as pairs or remain single. We introduce a so-called bi-choice graph for each pair of stable matchings and characterize its structure. Exploiting this structure we obtain as a corollary the “lone wolf” theorem and a decomposability result. The latter result together with transitivity of blocking leads to an elementary proof of the so-called stable median matching theorem, showing how the often incompatible concepts of stability (represented by the political economist Adam Smith) and fairness (represented by the political philosopher John Rawls) can be reconciled for roommate problems. Finally, we extend our results to two-sided matching problems.     

On the exhaustiveness of truncation and dropping strategies in many-to-many matching markets

We consider two-sided many-to-many matching markets in which each worker may work for multiple firms and each firm may hire multiple workers. We study individual and group manipulations in centralized markets that employ (pairwise) stable mechanisms and that require participants to submit rank order lists of agents on the other side of the market. We are interested in simple preference manipulations that have been reported and studied in empirical and theoretical work: truncation strategies, which are the lists obtained by removing a tail of least preferred partners from a preference list, and the more general dropping strategies, which are the lists obtained by only removing partners from a preference list (i.e., no reshuffling). We study when truncation/dropping strategies are exhaustive for a group of agents on the same side of the market, i.e., when each match resulting from preference manipulations can be replicated or improved upon by some truncation/dropping strategies. We prove that for each stable mechanism, dropping strategies are exhaustive for each group of agents on the same side of the market (Theorem 1), i.e., independently of the quotas. Then, we show that for each stable mechanism, truncation strategies are exhaustive for each agent with quota 1 (Theorem 2). Finally, we show that this result cannot be extended neither to individual manipulations when the agent’s quota is larger than 1 (even when all other agents’ quotas equal 1—Example 1), nor to group manipulations (even when all quotas equal 1—Example 2).     

Manipulability in matching markets: conflict and coincidence of interests

We study comparative statics of manipulations by women in the men-proposing deferred acceptance mechanism in the two-sided one-to-one marriage market. We prove that if a group of women weakly successfully manipulates or employs truncation strategies, then all other women weakly benefit and all men are weakly harmed. We show that these results do not appropriately generalize to the many-to-one college admissions model.     

Outsourcing with identical suppliers and shortest-first policy: a laboratory experiment

We study experimentally in the laboratory two 2-player games that mimic a decentralized decision-making situation in which firms repeatedly outsource production orders to multiple identical suppliers. The first game has a unique (inefficient) equilibrium in mixed strategies, while the second game has two (efficient) equilibria in pure strategies and an infinite number of (inefficient) equilibria in mixed strategies. In both games, the optimal social costs can also be obtained via dominated strategies. We find that only in the second game subjects manage to reach an efficient outcome more often when matched in fixed pairs than when randomly rematched each round. Surprisingly, this is because subjects coordinate on dominated strategies (and not an efficient pure strategy equilibrium). We show theoretically that preferences for efficiency cannot explain our experimental results. Inequality aversion, on the other hand, cannot be rejected.     

Tax reform: Dreaming about tough realities

This paper discusses four papers concerned with tax reform. It is concluded that tax reform has had a rather limited impact on behaviour so far but that governments should press ahead with gradual improvement and not expect dramatic results.