We consider the question of how collusion alters the quality of solutions obtained in competitive games. The price of anarchy aims to measure the cost of the lack of coordination by comparing the quality of a Nash equilibrium to that of a centrally designed optimal solution. However, this notion assumes that players act not only selfishly, but also independently. If a subset of players colludes, this can improve the social welfare of the participants, but they can also harm the welfare of those outside the coalition. The question we'll consider is what is the effect of such collusion on the overall solution quality.
We present joint work with Ara Hayrapetyan and Tom Wexler.