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 1 earns 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.
d) Rank strategy pairs by aggregate payoff (highest to lowest).
e) Can the outcome with the highest aggregate payoff be sustained in equilibrium? Why or why not?

Answer 1

a) The normal-form game with the two-player, one-shot, simultaneous–move game with each player choosing strategy A or strategy B along with the possible outcome is given by: (see attached image)

b) Dominant strategy is the strategy of a player which provides maximum payoff to the player irrespective of other player's actions.

Player 1 dominant strategy = when he chooses strategy B

Player 2 dominant strategy = when he chooses strategy B

c) Nash equilibrium is the strategy set of the players in which no individual player can be better off by deviating from their own strategy, given the other player's strategy.

Strategy A is the Nash equilibrium

d) AA = $800

AB , BA = $700

BB = $400

e) Yes because the Nash equilibrium is the same as the highest ranking strategy pair (AA = $800)