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Describe what it means to say a strategic game played with 2 players is in a...

Describe what it means to say a strategic game played with 2 players is in a Nash equilibrium. Then, describe the standard trust game, and identify the Nash equilibrium. Explain why this equilibrium is a Nash Equilibrium. Finally, explain why people actually playing this game might not play as the Nash Equilibrium predicts.

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Answer #1

A Nash equilibrium of a strategic game is an action profile with the property that no player can increase her payoff by choosing a different action, given the other players' actions.

For example - Two firms are merging into two divisions of a large firm, and have to choose the computer system to use. In the past the firms have used different systems, A and B each prefers the system it has used in the past. They will both be better off if they use the same system then if they continue to use different systems.

We can model this situation by the two-player strategic game.

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To find the Nash equilibria, we examine each action profile in turn.

(X,X) :- Firm 2 can increase its payoff from 1 to 2 by choosing the action Y rather than the action X. Thus this action profile is not a Nash equilibrium.

(X,Y) :- Firm 1 can increase its payoff from 1 to 2 by choosing the action Y rather than the action X. Thus this action profile is not a Nash equilibrium.

(Y,X) :- Firm 1 can increase its payoff from 1 to 2 by choosing the action X rather than the action Y. Thus this action profile is not a Nash equilibrium.

(Y,Y) :- Firm 2 can increase its payoff from 1 to 2 by choosing the action X rather than the action Y. Thus this action profile is not a Nash equilibrium.

We conclude that the game has no Nash equilibrium.

Neither player can increase her payoff by choosing an action different from her current one. Thus this action profile is a Nash equilibrium.

The simple insight underlying Nash's idea is that one cannot predict the choices of multiple decision makers if one analyzes those decisions in isolation. Instead, one must ask what each player would do taking into account what she/he expects the others to do. Nash equilibrium requires that their choices be consistent.... no player wishes to undo his decision given what the others are deciding.

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