  This paper builds a model of interactive belief hierarchies to derive the
conditions under which judging an arbitrage opportunity requires Bayesian
market participants to exercise their higher-order beliefs. As a Bayesian, an
agent must carry a complete recursion of priors over the uncertainty about
future asset payouts, the strategies employed by other market participants that
are aggregated in the price, other market participants' beliefs about the
agent's strategy, other market participants beliefs about what the agent
believes their strategies to be, and so on ad infinitum. Defining this infinite
recursion of priors -- the belief hierarchy so to speak -- along with how they
update gives the Bayesian decision problem equivalent to the standard asset
pricing formulation of the question. The main results of the paper show that an
arbitrage trade arises only when an agent updates his recursion of priors about
the strategies and beliefs employed by other market participants. The paper
thus connects the foundations of finance to the foundations of game theory by
identifying a bridge from market arbitrage to market participant belief
hierarchies.
