For the following situation, come up with a game (in normal form – the matrix re

Question

For the following situation, come up with a game (in normal form – the matrix representation we have been using) to describe the situation. Determine the pure strategy Nash equilibria. a. Two gentlemen are engaged in a duel. They each have two choices: shoot straight (to try to kill the other) or duck (to try to avoid being killed). If they both shoot straight, they both die; if they both duck, they live, but both lose some "face". If one ducks and one shoots straight, they both live, but the one who shoots earns "honor" and "respect" from his peers, while the one who ducks loses "face" and is branded a coward. Shooting and living gives a higher reward than ducking and living, regardless of what the other person does.

Explanation / Answer

The game is played by two players: Player 1 and Player 2. The strategy set faced by each player is {Shoot, Duck}

Assign a payoff of $10 to the one who shoots (if he survives) and $5 to the one who ducks. A payoff of $0 is given to one who dies. After assigning the payoffs, construct the payoff matrix akin to the one described below:

Player 2

Player 1

Shoot

Duck

Shoot

(0, 0)

(10, 5)

Duck

(5, 10)

(5, 5)

The game certainly has no dominant strategy for any player. Note that when Player 1 choses shooting, Player 2 is better off in choosing ducking since survival gives a payoff of $5 while death gives nothing. When Player 1 choses duck, Player 2 is better off in choosing shoot. In a similar manner, when Player 2 choses shoot, Player 1 is better off in choosing duck and when Player 2 choses duck, Player 1 is better off in choosing shoot.

So there are two pure strategy Nash equilibria: (shoot, duck) and (duck, shoot)

Player 2

Player 1

Shoot

Duck

Shoot

(0, 0)

(10, 5)

Duck

(5, 10)

(5, 5)

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