Introduction and description of election futures markets The Iowa Electronic Markets are small-scale, real-money futures markets conducted by the University of Iowa College of Business. In this review we focus on the best known of these markets, The Iowa Political Markets. Contracts in these markets are designed so that prices should predict election outcomes. The data set contains the results of 49 markets covering 41 elections in 13 countries. The Iowa Markets operate 24-hours a day, using a continuous, double-auction trading mechanism. Traders invest their own funds, make their own trades, and conduct their own information search. The markets occupy a niche between the stylized, tightly controlled markets conducted in the laboratory and the information-rich environments of naturally occurring markets. By virtue of this design, the Iowa Markets provide data to researchers that is not otherwise available. Investments are typically limited to a $500 maximum per trader and general

We analyze the computational complexity of market maker pricing algorithms for combinatorial prediction markets. We focus on Hanson’s popular logarithmic market scoring rule market maker (LMSR). Our goal is to implicitly maintain correct LMSR prices across an exponentially large outcome space. We examine both permutation combinatorics, where outcomes are permutations of objects, and Boolean combinatorics, where outcomes are combinations of binary events. We look at three restrictive languages that limit what traders can bet on. Even with severely limited languages, we find that LMSR pricing is #P-hard, even when the same language admits polynomial-time matching without the market maker. We then propose an approximation technique for pricing permutation markets based on a recent algorithm for online permutation learning. The connections we draw between LMSR pricing and the vast literature on online learning with expert advice may be of independent interest.

Current automated market makers over binary events suffer from two problems that make them impractical. First, they are unable to adapt to liquidity, so trades cause prices to move the same amount in both thick and thin markets. Second, under normal circumstances, the market maker runs at a deficit. In this paper, we construct a market maker that is both sensitive to liquidity and can run at a profit. Our market maker has bounded loss for any initial level of liquidity and, as the initial level of liquidity approaches zero, worstcase loss approaches zero. For any level of initial liquidity we can establish a boundary in market state space such that, if the market terminates within that boundary, the market maker books a profit regardless of the realized outcome. Furthermore, we provide guidance as to how our market maker can be implemented over very large event spaces through a novel cost-function-based sampling method.

Abstract. We study the equilibrium behavior of informed traders interacting with two types of automated market makers: market scoring rules (MSR) and dynamic parimutuel markets (DPM). Although both MSR and DPM subsidize trade to encourage information aggregation, and MSR is myopically incentive compatible, neither mechanism is incentive compatible in general. That is, there exist circumstances when traders can benefit by either hiding information (reticence) or lying about information (bluffing). We examine what information structures lead to straightforward play by traders, meaning that traders reveal all of their information truthfully as soon as they are able. Specifically, we analyze the behavior of risk-neutral traders with incomplete information playing in a finite-period dynamic game. We employ two different information structures for the logarithmic market scoring rule (LMSR): conditionally independent signals and conditionally dependent signals. When signals of traders are independent conditional on the state of the world, truthful betting is a Perfect Bayesian Equilibrium (PBE) for LMSR. However, when signals are conditionally dependent, there exist joint probability distributions on signals such that at a PBE in LMSR traders have an incentive to bet against their own information—strategically misleading other traders in order to later profit by correcting their errors. In DPM, we show that when traders anticipate sufficiently better-informed traders entering the market in the future, they have incentive to partially withhold their information by moving the market probability only partway toward their beliefs, or in some cases not participating in the market at all. 1

We designed and built the Gates Hillman Prediction Market (GHPM) to predict the opening day of the Gates and Hillman Centers, the new computer science buildings at Carnegie Mellon University. The market ran for almost a year and attracted 169 active traders who placed almost 40,000 bets with an automated market maker. Ranging over 365 possible opening days, the market’s event partition size is the largest ever elicited in any prediction market by an order of magnitude. A market of this size required new advances, including a novel span-based elicitation interface. The results of the GHPM are important for two reasons. First, we uncovered two flaws of current automated market makers: spikiness and liquidity-insensitivity, and we develop the mathematical underpinnings of these flaws. Second, the market provides a valuable corpus of identity-linked trades. We use this data set to explore whether the market reacted to or anticipated official communications, how selfreported trader confidence had little relation to actual performance, and how trade frequencies suggest a power law distribution. Most significantly, the data enabled us to evaluate two competing hypotheses about how markets aggregate information, the Marginal Trader Hypothesis and the Hayek Hypothesis; the data strongly support the former.

We study combinatorial prediction markets where agents bet on the sum of values at any tree node in a hierarchy of events, for example the sum of page views among all the children within a web subdomain. We propose three expressive betting languages that seem natural, and analyze the complexity of pricing using Hanson’s logarithmic market scoring rule (LMSR) market maker. Sum of arbitrary subset (SAS) allows agents to bet on the weighted sum of an arbitrary subset of values. Sum with varying weights (SVW) allows agents to set their own weights in their bets but restricts them to only bet on subsets that correspond to tree nodes in a fixed hierarchy. We show that LMSR pricing is NP-hard for both SAS and SVW. Sum with predefined weights (SPW) also restricts bets to nodes in a hierarchy, but using predefined weights. We derive a polynomial time pricing algorithm for SPW. We discuss the algorithm’s generalization to other betting contexts, including betting on maximum/minimum and betting on the product of binary values. Finally, we describe a prototype we built to predict web site page views and discuss the implementation issues that arose.

Citing recent successes in forecasting elections, movies, products, and other outcomes, prediction market advocates call for widespread use of market-based methods for government and corporate decision making. Though theoretical and empirical evidence suggests that markets do often outperform alternative mechanisms, less attention has been paid to the magnitude of improvement. Here we compare the performance of prediction markets to conventional methods of prediction, namely polls and statistical models. Examining thousands of sporting and movie events, we find that the relative advantage of prediction markets is surprisingly small, as measured by squared error, calibration, and discrimination. Moreover, these domains also exhibit remarkably steep diminishing returns to information, with nearly all the predictive power captured by only two or three parameters. As policy makers consider adoption of prediction markets, costs should be weighed against potentially modest benefits.

We propose a model of prediction markets where participants are biased according to their social relationships. We relax the standard assumption of complete rationality and adopt an arguably more realistic model where agents are disproportionally influenced by their neighbors in a social network. We conduct extensive agent-based simulations of our model. We find that prices in prediction markets remain accurate even when participants are biased and irrational. Moreover, accuracy is robust to changes in many factors, including how individuals are motivated to participate in the market, the way that individuals use public information, individual utility functions, the topology of the social network, and the strength of social influences. Our model can explain the high volume of trade often observed in speculative markets that is hard or impossible to explain under standard market rationality assumptions. Our model can also explain the documented ability of prediction markets to succeed even in the face of biased and irrational participants.

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

1 Introduction and description of election futures markets The Iowa Electronic Markets are small-scale, 1 real-money futures markets conducted by the University of Iowa Henry B. Tippie College of Business. In this review, we focus on the best known of these markets, The Iowa Political Markets. 2 Contracts in these markets are designed so that prices should predict election outcomes. The