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Game theory - A Tutorial |
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Static: Battle of the Sexes |
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Alice and Bob must decide to go either to the opera or to a football game. The reward matrix is shown below. For instance, if Alice goes to the opera and Bob to the game, Alice gets a reward (satisfaction) equal to 2 and so does Bob. |
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This game has a unique Nask equilibrium that corresponds to Alice going to the opera and Bob to the game, as colored red in the figure. Indeed, neither Alice nor Bob want to deviate from this point, and it is the only pair of strategies with that property. Here, the Nash equilibrium is pure (deterministic). |
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O = Opera F = Football
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