Strategies in dynamic parimutuel markets

Abstract

Prediction Markets are developed to aggregate information among people and have a long outstanding record for their accuracy of forecasting the future outcomes. The rapid progress of Internet, which allows wagering and hedging anywhere anytime makes a great number of such markets emerge prominently. Market models allowing sequential trades are most popular as such models enable to aggregate the information effectively even if there're few players. Dynamic Parimutuel Markets (DPM) is one of such models. It encourages players to reveal their information as early as possible and that its unfixed returning money attracts speculation and risk traders. At the first part of this thesis, I study the myopic behavior in DPM. Guidelines are proposed for traders on how much to buy or sell. As for the myopic version, information is aggregated effectively thus the market states that influenced by trader behavior are more important. I show that three types of actions (FPS, SPS, BOS) are payoff equivalent for both the involved player and the others currently but quite different in the long run. We show that the Buy-Only Strategy (BOS) achieves the highest market capitalization for the instant transaction and it always yields the fastest growth of market capitalization even in multiple stages. Simulation results also show that BOS is a better revelation of the traders' personal beliefs, though it exhibits a higher risk in traders' payoffs. At the second part, I move on to the strategic behavior of risk-neutral forwardlooking traders with incomplete information. In a DPM, agents' 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. I analyze non-myopic strategies in a two-outcome DPM and examine whether an agent will truthfully reveal its information in the market. Specifically, I first characterize one single agent's optimal trading strategy given the payoff uncertainty. Then, I use a two-player two-stage game to examine whether an agent will truthfully reveal its information when it only participates in the market once. I prove that truthful betting is a Nash equilibrium of the two-stage game in the symmetry setting for uniform initial market probabilities. I show numerically 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, I examine when an agent can participate more than once in the market whether it will truthfully reveal its information at its first play using a two-player three-stage game. I demonstrate that there exist signal distributions such that truthful betting is not a Nash equilibrium of the three-stage game even for uniform initial market probabilities.