Current kidney exchange pools are of moderate size and thin, as they consist of many highly sensitized patients. Creating a thicker pool can be done by waiting for many pairs to arrive. We analyze a simple class of matching algorithms that search per
iodically for allocations. We find that if only 2-way cycles are conducted, in order to gain a significant amount of matches over the online scenario (matching each time a new incompatible pair joins the pool) the waiting period should be very long. If 3-way cycles are also allowed we find regimes in which waiting for a short period also increases the number of matches considerably. Finally, a significant increase of matches can be obtained by using even one non-simultaneous chain while still matching in an online fashion. Our theoretical findings and data-driven computational experiments lead to policy recommendations.
Correlated equilibrium (Aumann, 1974) generalizes Nash equilibrium to allow correlation devices. Aumann showed an example of a game, and of a correlated equilibrium in this game, in which the agents surplus (expected sum of payo s) is greater than th
eir surplus in all mixed-strategy equilibria. Following the idea initiated by the price of anarchy literature (Koutsoupias & Papadimitriou, 1999;Papadimitriou, 2001) this suggests the study of two major measures for the value of correlation in a game with non-negative payoffs: 1. The ratio between the maximal surplus obtained in a correlated equilibrium to the maximal surplus obtained in a mixed-strategy equilibrium. We refer to this ratio as the mediation value. 2. The ratio between the maximal surplus to the maximal surplus obtained in a correlated equilibrium. We refer to this ratio as the enforcement value. In this work we initiate the study of the mediation and enforcement values, providing several general results on the value of correlation as captured by these concepts. We also present a set of results for the more specialized case of congestion games (Rosenthal,1973), a class of games that received a lot of attention in the recent literature.
