The lack of meaning of words in games

Let us imagine a community of fishermen who make daily fishing trips onto the lake in small two-man boats. Occasionally, one fisherman notices a rock in the water which requires his partner to take evasive action. In such a situation, the observer needs to warn his partner. It would appear that the observer has only to shout “Be careful” in order to transmit the information about the obstacle. But why is “Be careful” indeed interpreted by his partner in the way we understand the phrase rather than as “Here is a fish” or as “What a beautiful day it is”? This is the question addressed in this chapter.

The situation is an interactive one in which the meaning of a statement depends on what the speaker thinks that the listener understands, which in turn depends, in a circular way, on what the listener thinks that the speaker has in mind. Thus, the situation can be analyzed in a game-theoretic framework. The basic situation will be viewed as a symmetric game. A player can either be an observer or a listener. A strategy is a plan of action for reacting to an obstacle in front of the boat and responding to the partner's cry while rowing the boat. Note (at this stage informally) that the situation has one “equilibrium” in which the cry is made in the case of an obstacle being spotted and is interpreted correctly.