6.853 Topics in Algorithmic Game Theory September 20, 2011 Lecture 4

We have seen that Nash equilibria in two-player zero-sum games (and generalizations thereof) are polynomial-time tractable from a centralized computation perspective. We have also seen that the payoff matrix of a zero-sum game determines a unique value for the row player and a unique value for the column player (summing to zero), which specify their payoffs in all equilibria of the game. In this lecture, we investigate whether Nash equilibria can arise as a result of the distributed interaction between the players of a zero-sum game, and whether the values of the players in the game are descriptive of their long-term payoffs in the course of their interaction. Clearly, if the players are aware of the details of the game (i.e. the game’s payoff matrix), they can compute their min-max strategies on the side and just use these strategies forever. We envision a much weaker distributed scenario, of completely-uncoupled dynamics as follows: