Institute for Mathematical Behavioral Sciences

In Lewis signaling games [Lewis 1969], nature picks one of N possible states of the world at random and a player, the sender, observes the state and selects one of N signals to send to a receiver. The receiver observes the signal and selects one of N possible acts. There is exactly one act that is “right” for each state, in that both sender and receiver both get a payoff of one of the right act is done for the state and both get a payoff of zero otherwise. A sender’s strategy is a function from states to signals; a receiver’s from signals to acts. The two strategies form a signaling system equilibrium if they guarantee that the correct act is always taken. From any signaling system equilibrium, a permutation of signals (the same in both sender and receiver strategies) leads to another signaling system equilibrium with exactly the same payoff. This is why Lewis introduced these games as a model in which meaning of signals is purely conventional.