Question

Question 1: Rebel without a cause

Two drivers speed head-on toward each other and a collision is bound to occur unless one of them deviates at the last minute. If both deviate, everything is okay (they both win 1). If one deviates and the other does not, then it is a great success for the driver with iron nerves (he wins 2) and a great disgrace for the deviating driver (he loses 1). If both drivers have iron nerves, disaster strikes (both lose 2).

1. Write down the payoff matrix of this game.

2. Briefly (1-2 sentences) define the notion of Nash Equilibrium.

3. What are the Nash equilibria of this game?

Answer 1

1. The playoff matrix of this game would be:

2. In game theory, Nash equilibrium is a situation where no payer can do better by changing his or her strategy alone. In simpler terms, if all the players were told of the strategies of every other player, but each of them would not want to change their original strategy, then that strategy profile would e Nash equilibrium.

3. In the above strategies as per the payoff matrix, (-2,-2) is the worst strategy as both players stand to lose. (1,1) is not the best strategy for both players either as player 1 stands to gain better if he deviates and player 2 drives on - that is, (2, -1); and player 2 gains better if he drives on and player 1 deviates. That is if either player drives on while the other deviates, that is a better strategy than both deviating.

Thus, (2, -1) and (-1, 2) are both pure strategy Nash equilibrium strategies.