Question

|3) The game below is called "Chicken"- players charge at each other at high speed, and whoever turns out of the way first loses. If both turn, their reputations suffer; if neither turns, things really don't end well. What is the solution to the game? What kind of game is it? Player 2 Head on Turn Head on -100, -100 2, Player 1 -1, - Turn 1,2

Answer 1

Answer : In the given game, there exists two Nash equilibrium. These are : (i) (-100, -100) and (ii) (-1, -1). Because only in these two cells both players gets same payoffs.

If player-1 select Head on and player-2 select Turn then there occur an incentive for player-2 to go to Head on strategy. Because by selecting Head on player-2 will be better off. Hence (2, 1) is not a Nash equilibrium.

Now, if player-1 select Turn and player-2 select Head on then there occur an incentive for player-1 to go to Head on strategy. Because by selecting Head on strategy player-1 will be better off. Hence (1, 2) is not a Nash equilibrium.

But if both players select Head on strategy then there occur no any incentive to any player to change their strategy. Similarly, if both players select Turn strategy then there occur no any incentive to any player to change their strategy. Hence there exists two Nash equilibrium (-100, -100) and (-1, -1). Here payoff -1 is better than payoff -100. Hence both players will select the strategy of Turn. As a result, the solution of the given game is (-1, -1).

The given game is a prisoner's dilemma game. Because the above written situations occur in case of prisoner's dilemma game. So, here the given game is an example of prisoner's dilemma game.