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22
Gaming Prediction Markets: Equilibrium Strategies with a Market Maker
 ALGORITHMICA
, 2008
"... 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 ..."
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Cited by 27 (13 self)
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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 nonmyopic strategies and examine what information structures lead to truthful betting by traders. Specifically, we analyze the behavior of riskneutral traders with incomplete information playing in a dynamic game. We consider finitestage and infinitestage 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 finitestage 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
Nonmyopic strategies in prediction markets
 In Second Workshop on Prediction Markets (held at EC ’07
, 2007
"... 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 garne ..."
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Cited by 11 (2 self)
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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 nonmyopic 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.
When Do Markets with Simple Agents Fail?
"... 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 meaningf ..."
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Cited by 7 (5 self)
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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
An InDepth Analysis of Information Markets with Aggregate Uncertainty
 ELECTRONIC COMMERCE RESEARCH
, 2006
"... The novel idea of setting up Internetbased 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 ..."
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Cited by 5 (1 self)
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The novel idea of setting up Internetbased 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?
Theoretical investigation of prediction markets with aggregate uncertainty
 In Proceedings of the Seventh International Conference on Electronic Commerce Research (ICECR7
, 2004
"... 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 t ..."
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Cited by 4 (3 self)
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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
Designing informative securities
 In UAI
, 2012
"... We create a formal framework for the design of informative securities in prediction markets. These securities allow a market organizer to infer the likelihood of events of interest as well as if he knew all of the traders’ private signals. We consider the design of markets that are always informativ ..."
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Cited by 3 (3 self)
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We create a formal framework for the design of informative securities in prediction markets. These securities allow a market organizer to infer the likelihood of events of interest as well as if he knew all of the traders’ private signals. We consider the design of markets that are always informative, markets that are informative for a particular signal structure of the participants, and informative markets constructed from a restricted selection of securities. We find that to achieve informativeness, it can be necessary to allow participants to express information that may not be directly of interest to the market organizer, and that understanding the participants’ signal structure is important for designing informative prediction markets. 1
Security Design and Information Aggregation in Markets ∗
"... It has been wellrecognized that markets can aggregate lessthanperfect 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 m ..."
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Cited by 1 (0 self)
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It has been wellrecognized that markets can aggregate lessthanperfect 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
Predicting Uncertain Outcomes Using Information Markets ∗
"... 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 der ..."
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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. 1
Rational Market Making with Probabilistic Knowledge
"... A market maker sets prices over time for wagers that pay out contingent on the future state of the world. The market maker has knowledge of the probability of realizing each state of the world, and of how the price of a bet affects the probability that traders will accept it. We compare the optimal ..."
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A market maker sets prices over time for wagers that pay out contingent on the future state of the world. The market maker has knowledge of the probability of realizing each state of the world, and of how the price of a bet affects the probability that traders will accept it. We compare the optimal policy for riskneutral (expected utility maximizing) and Kelly criterion (expected logutility maximizing) market makers. Computing the optimal policy for a riskneutral market maker is relatively simple, while computing the optimal policy for a Kelly criterion market maker is challenging, requiring advanced techniques adapted from the computational economics literature to run efficiently. We show that while a riskneutral market maker has an optimal policy that does not depend on the market maker’s state, a Kelly criterion market maker’s optimal policy has an intricate dependence on both time and state. Counterintuitively, a Kelly criterion market maker may offer bets that are myopically irrational with respect to the market maker’s beliefs for the entire trading period. In contrast, a riskneutral market maker never offers a myopically irrational bet.