In a two-player, one-shot simultaneous-move game each player can choose strategy

Question

In a two-player, one-shot simultaneous-move game each player can choose strategy A or strategy B. If both players choose strategy A, each earns a payoff of $500. If both players choose strategy B, each earns a payoff of $100. If player 1 chooses strategy A and player 2 chooses strategy B, then player 1earns $0 and player 2 earns $650. If player 1 chooses strategy B and player 2 chooses strategy A, then player 1 earns $650 and player 2 earns $0.

a. Write the above game in normal form.
b. Find each player’s dominant strategy, if it exists.
c. Find the Nash equilibrium (or equilibria) of this game.

Explanation / Answer

This is the standard Prisoner's Dilemma. ...........................Player 1 Player 2.......A....A.....| A...B... ...................500, 500.| 0, 650 --------------------------------------… ...................B....A.....| B...B... ...................650, 0.....| 100, 100 b. The dominant strategy for each player is to choose B. 100>0 & 650>500 c. Nash equilbrium is for each to choose B. This is because no matter what the row player does, if the column player picks B, they'll get a better result.

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