The Analysis of Pre-play Communication under Adaptive Conjectures

This paper examines the sets of strategies that are stable for a stochastic process in cheap talk 2×2 coordination games. Relaxing the rationality condition assumed in previous literature and instead assuming what we call adaptive conjecture, we show that efficient outcomes are more difficult to achieve in medium term analysis. In addition, the outcomes that survive in the long term are Evolutionary Stable Sets, and in the medium term they are Neutrally Stable Strategies. Periodically each agent has an opportunity to change her strategy to one deemed more successful against the current population based on conjectures that are not always identical to the true action off the equilibrium path. Even if the message set is large enough, both efficient and inefficient equilibrium outcomes are stable in contrast to the results of previous literature where only efficient outcomes are stable.