One attractive feature of market scoring rules [Hanson, Information Systems Frontiers, 2003] is that they are myopically strategyproof: It is optimal for a trader to report her true belief about the likelihood of an event provided that we ignore the impact of her report on the profit she might garner from future trades. This does not rule out the possibility that traders may profit by first misleading other traders through dishonest trades and then correcting the errors made by other traders. In this paper, we describe a new approach to analyzing non-myopic strategies and the existence of myopic equilibria. We first use a simple model with two partially informed traders in a single information market to gain insight into the conditions under which different equilibrium behavior emerges. We prove that, under generic conditions, the myopically optimal strategy profile is not a weak Perfect Bayesian Equilibrium (PBE) strategy for the logarithmic market scoring rule. We show that our results extend to multiple traders and signals. We propose a simple discounted market scoring rule that reduces the opportunity for bluffing strategies. We show that in any weak PBE, myopic or otherwise, the market price converges to the optimal price, and the rate of convergence can be bounded in terms of the discounting parameter.

Much evidence supports that financial markets have the ability to aggregate information. When tied to a random variable, a financial market can forecast the value of the random variable. It then becomes a prediction market. We establish a model of prediction markets with aggregate uncertainty, and theoretically characterize some fundamental properties of prediction markets. Specifically, we have shown that a prediction market is guaranteed to converge to an equilibrium, where traders have consensus on the forecast. The best possible prediction a prediction market can make is the direct communication equilibrium. However, prediction markets do not always converge to it. We have proved that a sufficient condition for the convergence to the direct communication equilibrium under our model is that the private information of each trader, conditioned on the state of the world, is identically and independently distributed. Furthermore, if this condition is satisfied, the prediction market converges in at most two rounds. 1

We consider (prediction) markets where myopic agents sequentially interact with an automated market maker. We show a broad negative result: by varying the order of participation, the market’s aggregate prediction can converge to an arbitrary value. In other words, markets may fail to do any meaningful belief aggregation. On the positive side, we show that under a random participation model, steady state prices equal those of the traditional static prediction market model. We discuss applications of our results to the

The novel idea of setting up Internet-based virtual markets, information markets, to aggregate dispersed information and predict outcomes of uncertain future events has empirically found its way into many domains. But the theoretical examination of information markets has lagged relative to their implementation and use. This paper proposes a simple theoretical model of information markets to understand their information dynamics. We investigate and provide initial answers to a series of research questions that are important to understanding how information markets work, which are: (1) Does an information market converge to a consensus equilibrium? (2) If yes, how fast is the convergence process? (3) What is the best possible equilibrium of an information market? and (4) Is an information market guaranteed to converge to the best possible equilibrium?

It has been well-recognized that markets can aggregate less-than-perfect information across market participants. With two differently designed securities, this work examines the impact of security design on the information aggregation ability of markets in laboratory experiments. Results show that markets with one security aggregate information significantly better than markets with the other security, implying that information aggregation ability of markets is affected by the security design. Behavior of individual participants is then investigated to understand the observed market behavior. JEL Classification: C92; C91; D80

In this paper, information markets are introduced as a promising mechanism for predicting uncertain outcomes. A model of information markets is proposed. Some fundamental properties on when information markets will converge to the most desirable equilibrium, direct communication equilibrium, are derived.

Sigatures are on file in the Graduate School. iii In almost all walks of life, predicting uncertain future events plays an essential role in decision-making processes. However, information related to future events frequently exists only as dispersed opinions, insights, and intuitions of individuals. Each individual only knows a little, but aggregating the dispersed information together may make considerable contribution to decision making. This is typical in many domains including business, politics, and entertainment. Therefore, how to aggregate such dispersed information for useful decision support is a crucial task. Markets have shown great potential as one of the most effective mechanisms for gathering distributed information and generating accurate forecasts, often surpassing many existing methods in practice. This research studies information markets, markets that are specially designed for information aggregation and forecasting, from four different perspectives: theoretical examination, experimental evaluation, empirical analysis, and design.

with aggregate uncertainty

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 scoring 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

We investigate the problem of truthfully eliciting an expert’s assessment of a property of a probability distribution, where a property is any real-valued function of the distribution such as mean or variance. We show that not all properties are elicitable; for example, the mean is elicitable and the variance is not. For those that are elicitable, we provide a representation theorem characterizing all payment (or “score”) functions that induce truthful revelation. We also consider the elicitation of sets of properties. We then observe that properties can always be inferred from sets of elicitable properties. This naturally suggests the concept of elicitation complexity; the elicitation complexity of property is the minimal size of such a set implying the property. Finally we discuss applications to prediction markets.