Question

Consider the following non-cooperative, 2-player game. Each player is a manager who wishes to get a promotion. To get the promotion, each player has two possible strategies: earn it through hard work (Work) or make the other person look bad through unscrupulous means (Nasty). The payoff matrix describing this game is shown below. The payoffs for each player are levels of utility—larger numbers are preferred to smaller numbers. Player 1’s payoffs are listed first in each box.

Find the Nash equilibrium (or Nash equilibria) and describe how you found it/them. Does either player have a dominant strategy? If so, what is it for each player?

Nasty Work 4,6 Work 50,7 7,3 Nasty 6,2

Answer 1

(1)

When Player 2 chooses Work, Player 1's best strategy is Work since payoff is higher (50 > 6).

When Player 2 chooses Nasty, Player 1's best strategy is Work since payoff is Nasty (7 > 4).

When Player 1 chooses Work, Player 2's best strategy is Work since payoff is higher (7 > 6).

When Player 1 chooses Nasty, Player 2's best strategy is Nasty since payoff is Nasty (3 > 2).

There are 2 Nash equilibria: (Work, Work) and (Nasty, Nasty) [see below].

(2)

A dominant strategy is the strategy chosen by a player irrespective of strategy chosen by the other player.

When Player 2 chooses Work, Player 1's best strategy is Work since payoff is higher (50 > 6), but when Player 2 chooses Nasty, Player 1's best strategy is Work since payoff is Nasty (7 > 4). So Player 1 does not have a dominant strategy.

When Player 1 chooses Work, Player 2's best strategy is Work since payoff is higher (7 > 6), but when Player 1 chooses Nasty, Player 2's best strategy is Nasty since payoff is Nasty (3 > 2). So Player 2 does not have a dominant strategy.