Swap Dynamics in Single-Peaked House Markets.

This paper focuses on the problem of fairly and efficiently allocating resources to agents. We consider a restricted framework in which all the resources are initially owned by the agents, with exactly one resource per agent (house market). In this framework, and with strict preferences, the Top Trading Cycle (TTC) algorithm is the only procedure satisfying Pareto-optimality, individual rationality and strategy-proofness. When preferences are single-peaked, the Crawler enjoys the same properties. These two centralized procedures might involve long trading cycles. In this paper we focus instead on a procedure involving the shortest cycles: bilateral swap deals. In such a swap dynamics, the agents perform pairwise mutually improving deals until reaching a swap-stable allocation (no improving swap-deal is possible). We prove that on the single-peaked domain every swap-stable allocation is Pareto-optimal, showing the efficiency of the swap dynamics. Besides, both the outcome of TTC and the Crawler can always be reached by sequences of swaps. However, some Pareto-optimal allocations are not reachable through improving swap-deals. We further analyze the swap-deal procedure through the study of the average or minimum rank of the resources obtained by agents in the final allocation. We start by providing the price of anarchy of these procedures. Finally, we present an extensive experimental study in which different versions of swap dynamics as well as other existing allocation procedures are compared. We show that swap-deal procedures exhibit good results on average in this domain, under different cultures for generating synthetic data.