Cooperative outcomes through noncooperative games (Q1342405)

Stable solution sets describe a reasonable outcome of a cooperative game, i.e., of a conflict in which participants are free to form coalitions. One might expect that if coalitions are not allowed, outcome will be different; sometimes outcomes are indeed different, but the paper under review gives a reasonable example of a non-cooperative game for which Nash equilibrium outcomes are exactly stable sets. In this game, in addition to non-cooperating players, we have a (sufficiently) large amount of ``principals''. All principals simultaneously make wage offers \(w_1,\dots, w_n\) to all the players. A player chooses the principal whose bid is the highest. For each resulting team \(S\), the gain is described by the value \(v(S)\) of a characteristic function, so that the resulting principal's profit is \(v(S)- \sum_{i\in S} w_i\). A similar result is proven for a slightly different game.