How to play (3×3)-games.: A strategy method experiment

Using the strategy method (Selten 1967) we elicit subjects' strategies for playing any 2-person 3x3-game with integer payoffs between 0 and 99. In each of 5 tournaments, every strategy pair plays 500000 games. The frequency of pure strategy equilibrium play increases from 51% in the first to 74% in the last tournament, with the equilibria that maximize joint payoff being preferred when multiple exist. For games without pure equilibria, strategies are typically based on elements of the best-reply cascade: MAP (maximize the expected payoff against uniformly randomizing opponents), BR-MAP (best reply to MAP), and BR-BR-MAP (best reply to BR-MAP).