3. Consider the following non-cooperative, 2-player game. Each player is a manag

Question

3. 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?

Explanation / Answer

The Nash Equilibrium is a strategy where both the players will have a higher payoff if any single player changed the strategy unilaterally it will be facing a loss. Here, the Nash equilibrium is Both the player will work and the other Nash equilibrium is both the players go Nasty.

Both works = when both the players are working their return are 20,7 if any player changes the strategy i.e. goes nasty his return will end up being 6 and 4 respectively, which is less than 20 and 7. They will remain at the point.

Both Nasty = When both the players are nasty their return is 5 and 3 if any player changes the strategy i.e. works their return will be 2 and 5 respectively, which is less than the previous return. They will remain at the point.

No, none of the players have any dominant strategy. The dominant strategy is a point in which a player can follow irrespective of what the other player is doing.

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