Ingame theory, theLewis signaling game is a type ofsignaling game that features perfectcommon interest between players. It is named for the philosopherDavid Lewis who was the first to discuss this game in his Ph.D. dissertation, and later book,Convention.[1]
The underlying game has two players, thesender and thereceiver. The world can be in any of a number of states and the sender is aware of that state. The sender has at its disposal a fixed set ofsignals that it can send to the receiver. The receiver can observe the signal sent, but not the state of the world, and must take some action. For each state, there is a unique correct action and both the sender and receiver prefer that the receiver take the correct action in every state. Because both the sender and receiver prefer the same outcomes as one another, this game is a game of perfect common interest.
The simplest version of this game (pictured above) has two states, two signals, and two acts.
This game has manyNash equilibria. A few of them stand out where the sender sends a different signal in each state and the receiver takes the appropriate action in every state. Lewis dubbed thesesignaling systems.[1] But there are also other equilibria. In some the sender sends the same signal in every state and the receiver takes the action that is best to take given no additional information about the state of the world (pooling equilibria).
Also, when there are more than two states, signals, and acts, there arepartial pooling equilibria where some information is conveyed, but some states are also pooled.[2][3]
