Two individuals, A and B, who like each other, have arranged a date. They will meet either at a pop concert or at a techno party. However, they have not decided on which of the two.

A prefers techno whereas B prefers pop. However, they both prefer being at the same event as the other to going alone to the pop concert or to the techno party.

Suppose they cannot communicate, and therefore must decide separately. Then the game can be represented as in Figure E.7.1. The worst outcome is that they end up alone at their least preferred event. The best outcome for A is that they both go to the techno party, but that is only the second best outcome for B. The best outcome for B (and the second best for A) is that they both go to the pop concert.

a) What is a Nash equilibrium? Give a definition in words.

b) Find all Nash equilibria in the game.

c) To avoid this type of problems in the future, A and B decide on the following rule: If a game such as the one in Figure E.7.1 arises, then we go to the one that A prefers." Does that rule constitute an improvement for B?