Gaming Prediction Markets: Equilibrium Strategies with a Market Maker

Abstract

We study the equilibrium behavior of informed traders interacting with market scoring rule (MSR) market makers. One attractive feature of MSR is that it is myopically incentive compatible: it is optimal for traders to report their true beliefs about the likelihood of an event outcome provided that they ignore the impact of their reports on the profit they might garner from future trades. In this paper, we analyze non-myopic strategies and examine what information structures lead to truthful betting by traders. Specifically, we analyze the behavior of risk-neutral traders with incomplete information playing in a dynamic game. We consider finite-stage and infinite-stage game models. For each model, we study the logarithmic market Preliminary versions of some of the results in this paper were presented in two conference papers, Chen et al. [10] and Dimitrov and Sami [13]. Algorithmica (2010) 58: 930-969 931scoring rule (LMSR) with two different information structures: conditionally independent signals and (unconditionally) independent signals. In the finite-stage model, when signals of traders are independent conditional on the state of the world, truthful betting is a Perfect Bayesian Equilibrium (PBE). Moreover, it is the unique Weak Perfect Bayesian Equilibrium (WPBE) of the game. In contrast, when signals of traders are unconditionally independent, truthful betting is not a WPBE. In the infinite-stage model with unconditionally independent signals, there does not exist an equilibrium in which all information is revealed in a finite amount of time. We propose a simple discounted market scoring rule that reduces the opportunity for bluffing strategies. We show that in any WPBE for the infinite-stage market with discounting, the market price converges to the fully-revealing price, and the rate of convergence can be bounded in terms of the discounting parameter. When signals are conditionally independent, truthful betting is the unique WPBE for the infinite-stage market with and without discounting.

Decision Markets with Good Incentives

“…As mentioned in Section 1.1, previous work on prediction markets has demonstrated that myopic incentives are sufficient to aggregate information for Bayesian experts in equilibrium under certain conditions [4,15]. While we do not extend these results directly to decision markets, we show a correspondence between the perfect Bayesian equilibria of a strictly proper decision market and a set of strictly proper prediction markets, suggesting current aggregation results may generalize to decision markets, too.…”

“…While myopic incentive compatibility does not guarantee that an expert who participates in multiple rounds will predict consistent with its beliefs in every round, previous work has shown that myopic incentives are sufficient to aggregate experts' private information at perfect Bayesian equilibria under certain conditions [4,15]. Although we do not directly discuss information aggregation in decision markets, we establish a correspondence between the perfect Bayesian equilibria of any strictly proper decision market and a corresponding strictly proper prediction market.…”

“…However, while a market using a strictly proper scoring rule is myopic incentive compatible, it is not incentive compatible in general. An expert participating in multiple rounds may provide a prediction inconsistent with its belief, with the intention to mislead other experts and later capitalize on their mistakes [4]. Despite such possible manipulations by forward-looking Bayesian experts, previous work has shown that under certain conditions prediction markets that are myopic incentive compatible can fully aggregate information in finite rounds [4] or in the limit [15].…”

“…An expert participating in multiple rounds may provide a prediction inconsistent with its belief, with the intention to mislead other experts and later capitalize on their mistakes [4]. Despite such possible manipulations by forward-looking Bayesian experts, previous work has shown that under certain conditions prediction markets that are myopic incentive compatible can fully aggregate information in finite rounds [4] or in the limit [15]. In this paper, when considering myopic incentive compatibility of decision markets, we do not restrict experts to be Bayesian but allow arbitrary beliefs.…”

Instructor Rating Markets

“…There has been little systematic work in this area. While much of the literature on liquidity provision discusses the pitfalls and advantages of different algorithms [6,20,21,22], only recently have there been attempts to simultaneously compare market microstructures in controlled experimental designs involving human traders (such as the work of Brahma et al [4]). However, Brahma et al make these comparisons using short, ten-minute experiments.…”