7 May 2013, Logic Tea, Elliott Wagner

Abstract

The conventions of semantic meaning have long posed a philosophical problem. It is commonly believed that for agents to be governed by a convention, they must agree to abide by that convention. But how can we agree to any conventions of semantic meaning if our vocalizations and gestures do not already carry some semantic meaning with which we can express our agreement?

This puzzle goes back at least as far as Democritus, but a partial answer was proposed by David Lewis in Convention (1969). According to Lewis, signals have conventional meaning in certain Nash equilibria of signaling games. So if agents can learn to use one of these Nash equilibrium strategy profiles, then they will have learned a system of semantic meaning. Unfortunately, Lewis's framework assumes that the communicators in the signaling game share total common interest in communicating, and in real life this assumption is often not correct: actual individuals often have an incentive to deceive and manipulate.

In this LogicTea I will show one way in which Lewis's framework can be extended to cover these situations. Namely, I will demonstrate that in a class of games known as persuasion games (introduced by Milgrom and Roberts (1986)), a finite population of players who learn by proportional imitation of success will develop a system of semantic meaning with high probability even though the temptation to deceive is so strong that semantic meaning is not a Nash equilibrium.