Arbitrage from a Bayesian's Perspective

TL;DR

This paper models the complex belief hierarchies in Bayesian markets to determine when arbitrage opportunities arise, linking market behavior to game theory and belief updates.

Contribution

It introduces a framework for understanding arbitrage through infinite belief hierarchies and shows arbitrage occurs when agents update their priors about others' strategies.

Findings

Arbitrage arises when agents update their priors about others' strategies.

The belief hierarchy framework connects finance foundations with game theory.

Infinite recursion of priors is key to understanding arbitrage conditions.

Abstract

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.