The following is a simple definition: A Nash eqilibirum exisits when each player is doing the best she can given what the other player is doing. In other words, neither wishes to change strategies so long as the other player doesn't.

   Consider the payoff matrix we saw before, shown again to the right. If Firm 2 plays High Firm 1 will play Low. As it turns out, if Firm 1 plays Low Firm 2 will wish to play High. For Firm 1 Low is only best if Firm 2 plays High and for Firm 2 High is best only if Firm 1 plays Low. Firm 1 Low, Firm 2 High is a Nash equilibrium because each is doing the best possible given what the other is doing. Can you see that this game has two Nash eqilibria?

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