Asked by Hailey Gallant on May 02, 2024
Verified
Two players are engaged in a game of Chicken.There are two possible strategies, Swerve and Drive Straight.A player who chooses to Swerve is called Chicken and gets a payoff of zero, regardless of what the other player does.A player who chooses to Drive Straight gets a payoff of 36 if the other player swerves and a payoff of 36 if the other player also chooses to Drive Straight.This game has two pure strategy equilibria and
A) a mixed strategy equilibrium in which each player swerves with probability .50 and drives straight with probability .50.
B) a mixed strategy equilibrium in which one player swerves with probability .50 and the other swerves with probability .50.
C) a mixed strategy in which each player swerves with probability .25 and drives straight with probability .75.
D) two mixed strategies in which players alternate between swerving and driving straight.
E) no mixed strategies.
Pure Strategy Equilibria
A situation in a game where players choose a single strategy and their choices result in an equilibrium.
Mixed Strategy
A decision-making strategy in game theory where a player chooses between possible moves according to a set of probabilities.
Payoff
The gain or benefit derived from an investment or action.
- Differentiate between pure strategy equilibria and mixed strategy equilibria in game theory.
Verified Answer
CW
Chaya WoodsMay 06, 2024
Final Answer :
A
Explanation :
In this game, both players have a dominant strategy of driving straight, as no matter what the other player does, they will get a higher payoff by driving straight. Therefore, the game has a unique Nash equilibrium where both players choose to drive straight. However, if both players randomly choose Swerve or Drive Straight with equal probability, then the expected payoff for each player is (0.5*0)+(0.5*36)=18, which is the same as the payoff for choosing to drive straight in the pure strategy equilibrium. Therefore, A is the best choice.
Learning Objectives
- Differentiate between pure strategy equilibria and mixed strategy equilibria in game theory.