492. Price Manipulation, Dynamic Informed Trading and Tame Equilibria: Theory and Computation

Shino Takayama, School of Economics Discussion Paper No. 492 September 2013, School of Economics, The University of Queensland. Australia.

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Abstract

This paper studies a dynamic version of the model proposed in Glosten and Milgrom (1985) with a long-lived informed trader. When the same individual can buy, and then sell, the same asset, the trader may profit from price manipulation. We make a fundamental contribution by clarifying the conditions under which a unique equilibrium exists, and in what situations this equilibrium involves price manipulation. We propose a concept that we refer to as a “tame” equilibrium, and derive a bound for the number of trading rounds under (or over) which a unique equilibrium exists (or multiple equilibria exist) for a sufficiently low probability of informed trading. We characterize and compute tame equilibria. Further, we provide a necessary and sufficient condition under which manipulation arises. We contend that we can extend our analysis to a continuous-time setting and thereby provide a reference framework in a discrete-time setting with a unique equilibrium.