Question

4. Consider the following non-cooperative, 2-player game. Each player is a middle 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?

Answer 1

A dominant strategy can be seen as when a certain player opt a specific strategy irrespective of the strategy selected by other player.

if Player 1 choose to work, in this situation play 2 will opt to work
if player 1 chooses to Nasty , in this situation player 2 choose to Nasty

as player 2 changes the strategy depending upon the strategy selected by player 1, thus it is clear that player 2 does not have any dominant strategy

if player 2 choose work, , in this situation player 1 will go for Nasty
if player 2 choose Nasty, , in this situation player 1 choose Nasty

In this case, player 1 has the dominant strategy as NASTY as he selects this strategy irrespective of the strategy selected by player 2.

if Player one is playing Nasty then player 2 will play Nasty so the Nash equilibrium is "Nasty, Nasty"