Dynamic Semi-Consistency

The behaviour of dynamically consistent agents who follow through with any ex ante optimal plan, whether it involves mixed strategies or not, cannot be distinguished from the behaviour of Bayesian agents. I develop the notion of dynamic semi-consistency to allow for learning models in which the assumption of ambiguity aversion generates different predictions while at the same time not veering too far from the normatively appealing principle of dynamic consistency.

Dynamically semi-consistent agents follow through with ex ante optimal pure strategies. They do, however, not update their preferences upon learning randomisation outcomes. They therefore do not follow through with any ex ante optimal mixed strategy. I show that the equilibria of games with ambiguity averse agents may differ substantially from the equilibria of Bayesian games if we assume dynamically semi-consistent behavior. If we complement the assumption of ambiguity aversion with the assumption of dynamic consistency, the equilibrium sets of games with ambiguity averse agents coincide with the equilibrium sets of Bayesian games. I show that while the standard revelation principle for mechanism design applies in full force if agents are dynamically consistent a modification is required for semi-consistent agents.