Simulations of Prediction Markets

Zheyuan (Ryan) Shi, Sindhu Kutty

Prediction Markets are a platform for aggregating information from a population. In these markets, agents trade contracts and receive payments according to the future state of the world [1]. Prediction markets are observed to be more accurate and efficient compared to traditional information aggregation methods such as opinion polls and peer reviews [2]. The Iowa Electronic Markets, a major market for political predictions, have outperformed most mainstream polls and predictions in the US presidential elections since its inception in 1988 [3]. Google, among many others, has successfully implemented internal prediction markets to help the management gather information from employees that is otherwise impossible due to hierarchies and corporate politics [4].

To aggregate information, incentive compatibility, that the traders are incentivized to truthfully and promptly report their belief, is a core problem. Chen et al. [6] construct a unique perfect Bayesian equilibrium (PBE) in a binary outcome market based on logarithmic market scoring rule (LMSR) with a finite signal space. Iyer, Johari and Moallemi [7] prove that in a prediction market proposed by [1] with finite signal space, a PBE must aggregate the traders' information. However, the existence of such PBE remains a question.

We perform market simulations on the exponential family models of prediction markets [5]. We verify the market dynamics and provide some extensions to the previous models. We then address the incentive compatibility problem using one of our simulated models. Our model allows for infinite signal and outcome spaces, at the cost of putting more restrictions on the strategy space. We show that while the market is guaranteed to achieve information aggregation, whether traders express their beliefs promptly depends on their beliefs and initial market state. 

[1] J. Abernethy, Y. Chen, and J. W. Vaughan, "Efficient market making via convex optimization, and a connection to online learning," ACM Trans. Econ. Comput., vol. 1, no. 2, pp. 12:1-12:39, May 2013.

[2] R. Hanson, "Combinatorial information market design," Information Systems Frontiers, vol. 5, no. 1, pp. 107-119, 2003.

[3] Iowa electronic markets - previous market performance. [Online]. Available:

[4] B. Cowgill and E. Zitzewitz, "Corporate prediction markets: Evidence from google, ford, and firm x," The Review of Economic Studies, p. rdv014, 2015.

[5] J. Abernethy, S. Kutty, S. Lahaie, and R. Sami, "Information aggregation in exponential family markets," in Proceedings of the fifteenth ACM conference on Economics and computation. ACM, 2014, pp. 395-412.

[6] Y. Chen, S. Dimitrov, R. Sami, D. M. Reeves, D. M. Pennock, R. D. Hanson, L. Fortnow, and R. Gonen, "Gaming prediction markets: Equilibrium strategies with a market maker," Algorithmica, vol. 58, no. 4, pp. 930-969, 2010.

[7] K. Iyer, R. Johari, and C. C. Moallemi, "Information aggregation in smooth markets," in Proceedings of the 11th ACM conference on Electronic commerce. ACM, 2010, pp. 199-206.