externality from choosing the same action. The action choices are +1 and −1, as seen in the payoff matrix in Figure 1. This game has a potential function . If player 1 moves from −1 to +1, the payoff difference is . The change in potential is . The solution for player 2 is equivalent. Using numerical values , , , this example transforms into a simple battle of the sexes, as shown in Figure 2. The game has two pure Nash equilibria, and . These are also the local maxima of the potential function (Figure 3). The only stochastically stable equilibrium is , the global maximum of the potential function. A 2-player, 2-action game cannot be a potential game unless See also Congestion game Econophysics References External links Lecture notes of Yishay Mansour about Potential and congestion games Section 19 in: Non technical exposition by Huw Dixon of the inevitability of collusion Chapter 8, Donut world and the duopoly archipelago,Surfing Economics. Game theory game classes