Question

Consider an intersection of roads without any traffic light. Two cars A and B approach an intersection and they want to proceed as indicated by respective arrows in the following diagram. If both proceed without stopping and there is an accident, then A would have a payoff of -100 and B would have a payoff of -500 (since B is responsible for the accident). If one stops, and the other proceeds then the payoff is: -5 and 10, respectively. If both of them stop, then it takes a little longer to reach their respective destinations, they have a payoff of -5 each. Find the Pure Strategy Nash Equilibrium (PSNE) of the players (Car drivers). 

• A. (Car A, Car B) = (Stop, Stop)
• B. (Car A, Car B) = (Stop, Proceed)
• C. (Car A, Car B) = (Proceed, Stop)
• D. (Car A, Car B) = (Proceed, Proceed)

Hint:

In game theory, a Nash Equilibrium occurs when neither player can improve their payoff by unilaterally changing their strategy.

Answer 1

The Correct Option is B, C

We need to find the Nash Equilibrium where neither player has an incentive to change their strategy given the strategy of the other player. We will analyze the payoffs for each combination of strategies.
Step 1: Construct the payoff matrix.
- If both cars proceed without stopping, the payoffs are (-100, -500), indicating that both players are worse off.
- If one car stops and the other proceeds, the payoffs are (-5, 10) and (10, -5), respectively. The car that proceeds gains a higher payoff.
- If both cars stop, the payoffs are (-5, -5), indicating that both players are equally worse off.
Step 2: Analyze the strategies.
- If Car A stops, Car B should proceed to get the highest payoff (10 instead of -5).
- If Car A proceeds, Car B should stop to avoid the worst payoff (-500). Thus, (Proceed, Stop) is also a Nash equilibrium.
Step 3: Conclusion.
The Pure Strategy Nash Equilibriums (PSNE) are: (Stop, Proceed) and (Proceed, Stop).
Final Answer: (B) (Car A, Car B) = (Stop, Proceed)
Final Answer: (C) (Car A, Car B) = (Proceed, Stop)