Gaming Dynamic Parimutuel Markets

We study the strategic behavior of risk-neutral non-myopic agents in Dynamic Parimutuel Markets (DPM). In a DPM, agents buy or sell shares of contracts, whose future payoff in a particular state depends on aggregated trades of all agents. A forward-looking agent hence takes into consideration of possible future trades of other agents when making its trading decision. In this paper, we analyze non-myopic strategies in a two-outcome DPM under a simple model of incomplete information and examine whether an agent will truthfully reveal its information in the market. Specifically, we first; characterize a single agent's optimal trading strategy given the payoff uncertainty. Then, we use a, two-player game to examine whether an agent will truthfully reveal its information when it only participates in the market once. We prove that truthful betting is a Nash equilibrium of the two-stage game in our simple setting for uniform initial market probabilities. However, we show that there exists some initial market probabilities at which the first player has incentives to mislead the other agent in the two-stage game. Finally, we briefly discuss when an agent can participate more than once in the market whether it will truthfully reveal its information at its first play in a three-stage game. We find that in some occasions truthful betting is not a Nash equilibrium of the three-stage game even for uniform initial market probabilities.