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11
A Practical LiquiditySensitive Automated Market Maker
 IN PROCEEDINGS OF THE 11TH ACM CONFERENCE ON ELECTRONIC COMMERCE (EC
, 2010
"... 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. ..."
Abstract

Cited by 19 (6 self)
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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 costfunctionbased sampling method.
Price Updating in Combinatorial Prediction Markets with Bayesian Networks
"... To overcome the #Phardness of computing/updating prices in logarithm market scoring rulebased (LMSRbased) combinatorial prediction markets, Chen et al. [5] recently used a simple Bayesian network to represent the prices of securities in combinatorial prediction markets for tournaments, and showed ..."
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Cited by 6 (3 self)
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To overcome the #Phardness of computing/updating prices in logarithm market scoring rulebased (LMSRbased) combinatorial prediction markets, Chen et al. [5] recently used a simple Bayesian network to represent the prices of securities in combinatorial prediction markets for tournaments, and showed that two types of popular securities are structure preserving. In this paper, we significantly extend this idea by employing Bayesian networks in general combinatorial prediction markets. We reveal a very natural connection between LMSRbased combinatorial prediction markets and probabilistic belief aggregation, which leads to a complete characterization of all structure preserving securities for decomposable network structures. Notably, the main results by Chen et al. [5] are corollaries of our characterization. We then prove that in order for a very basic set of securities to be structure preserving, the graph of the Bayesian network must be decomposable. We also discuss some approximation techniques for securities that are not structure preserving. 1
An Efficient MonteCarlo Algorithm for Pricing Combinatorial Prediction Markets for Tournaments
 PROCEEDINGS OF THE TWENTYSECOND INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE
, 2011
"... Computing the market maker price of a security in a combinatorial prediction market is #Phard. We devise a fully polynomial randomized approximation scheme (FPRAS) that computes the price of any security in disjunctive normal form (DNF) within an ɛ multiplicative error factor in time polynomial in ..."
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Cited by 5 (2 self)
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Computing the market maker price of a security in a combinatorial prediction market is #Phard. We devise a fully polynomial randomized approximation scheme (FPRAS) that computes the price of any security in disjunctive normal form (DNF) within an ɛ multiplicative error factor in time polynomial in 1/ɛ and the size of the input, with high probability and under reasonable assumptions. Our algorithm is a MonteCarlo technique based on importance sampling. The algorithm can also approximately price securities represented in conjunctive normal form (CNF) with additive error bounds. To illustrate the applicability of our algorithm, we show that many securities in Yahoo!’s popular combinatorial prediction market game called Predictalot can be represented by DNF formulas of polynomial size.
Inventorybased versus Priorbased Options Trading Agents ∗
, 2012
"... Options are a basic, widelytraded form of financial derivative that offer payouts based on the future price of an underlying asset. The finance literature gives us optiontrading algorithms that take into consideration information about how prices move over time but do not explicitly involve the tr ..."
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Cited by 1 (1 self)
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Options are a basic, widelytraded form of financial derivative that offer payouts based on the future price of an underlying asset. The finance literature gives us optiontrading algorithms that take into consideration information about how prices move over time but do not explicitly involve the trades the agent made in the past. In contrast, the prediction market literature gives us automated marketmaking agents (like the popular LMSR) that are eventindependent and price trades based only on the inventories the agent holds. We simulate the performance of five trading agents inspired by these literatures on a large database of recent historical option prices. We find that a combination of the two approaches produced the best results in our experiments: a trading agent that keeps track of previouslymade trades combined with a good prior distribution on how prices move over time. The experimental success of this synthesized trader has implications for agent design in both financial and prediction markets. 1
ProfitCharging Market Makers with Bounded Loss, Vanishing Bid/Ask Spreads, and Unlimited Market Depth
"... Automated market makers are algorithmic agents that price fixedodds bets with traders. Four key qualities for automated market makers have appeared in the artificial intelligence literature: (1) bounded loss, (2) the ability to make a profit, (3) a vanishing bid/ask spread, and (4) unlimited market ..."
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Cited by 1 (0 self)
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Automated market makers are algorithmic agents that price fixedodds bets with traders. Four key qualities for automated market makers have appeared in the artificial intelligence literature: (1) bounded loss, (2) the ability to make a profit, (3) a vanishing bid/ask spread, and (4) unlimited market depth. Intriguingly, market makers that satisfy any three of these desiderata have appeared in the literature. However, it is an open question as to whether there exist market makers which can simultaneously satisfy all four of these properties; the issue is not simple to resolve because several of the qualities are oppositional, particularly in tandem. In this paper, we answer the open question in the affirmative by constructing market makers that satisfy all four qualities.
Eliciting Forecasts from Selfinterested Experts: Scoring Rules for Decision Makers
, 1106
"... Scoring rules for eliciting expert predictions of random variables are usually developed assuming that experts derive utility only from the quality of their predictions (e.g., score awarded by the rule, or payoff in a prediction market). We study a more realistic setting in which (a) the principal i ..."
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Cited by 1 (0 self)
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Scoring rules for eliciting expert predictions of random variables are usually developed assuming that experts derive utility only from the quality of their predictions (e.g., score awarded by the rule, or payoff in a prediction market). We study a more realistic setting in which (a) the principal is a decision maker and will take a decision based on the expert’s prediction; and (b) the expert has an inherent interest in the decision. For example, in a corporate decision market, the expert may derive different levels of utility from the actions taken by her manager. As a consequence the expert will usually have an incentive to misreport her forecast to influence the choice of the decision maker if typical scoring rules are used. We develop a general model for this setting and introduce the concept of a compensation rule. When combined with the expert’s inherent utility for decisions, a compensation rule induces a net scoring rule that behaves like a normal scoring rule. Assuming full knowledge of expert utility, we provide a complete characterization of all (strictly) proper compensation rules. We then analyze the situation where the expert’s utility function is not fully known to the decision maker. We show bounds on: (a) expert incentive to misreport; (b) the degree to which an expert will misreport; and (c) decision maker loss in utility due to such uncertainty. These bounds depend in natural ways on the degree of uncertainty, the local degree of convexity of net scoring function, and natural properties of the decision maker’s utility function. They also suggest optimization procedures for the design of compensation rules. Finally, we briefly discuss the use of compensation rules as market scoring rules for selfinterested experts in a prediction market. 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.
IOS Press Inventorybased versus Priorbased Options Trading Agents
"... Abstract. Options are a basic, widelytraded form of financial derivative that offer payouts based on the future price of an underlying asset. The finance literature gives us optiontrading algorithms that take into consideration information about how prices move over time but do not explicitly invo ..."
Abstract
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Abstract. Options are a basic, widelytraded form of financial derivative that offer payouts based on the future price of an underlying asset. The finance literature gives us optiontrading algorithms that take into consideration information about how prices move over time but do not explicitly involve the trades the agent made in the past. In contrast, the prediction market literature gives us automated marketmaking agents (like the popular LMSR) that are eventindependent and price trades based only on the inventories the agent holds. We simulate the performance of five trading agents inspired by these literatures on a large database of recent historical option prices. We find that a combination of the two approaches produced the best results in our experiments: a trading agent that keeps track of previouslymade trades combined with a good prior distribution on how prices move over time. The experimental success of this synthesized trader has implications for agent design in both financial and prediction markets.
Generalized Weighted Model Counting: An Efficient MonteCarlo MetaAlgorithm (Working paper)
"... Abstract. In this paper, we focus on computing the prices of securities represented by logical formulas in combinatorial prediction markets when the price function is represented by a Bayesian network. This problem turns out to be a natural extension of the weighted model counting (WMC) problem [15] ..."
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Abstract. In this paper, we focus on computing the prices of securities represented by logical formulas in combinatorial prediction markets when the price function is represented by a Bayesian network. This problem turns out to be a natural extension of the weighted model counting (WMC) problem [15], which we call generalized weighted model counting (GWMC) problem. In GWMC, we are given a logical formula F and a polynomialtime computable weight function. We are asked to compute the total weight of the valuations that satisfy F. Based on importance sampling, we propose a MonteCarlo metaalgorithm that has a good theoretical guarantee for formulas in disjunctive normal form (DNF). The metaalgorithm queries an oracle algorithm that computes marginal probabilities in Bayesian networks, and has the following theoretical guarantee. When the weight function can be approximately represented by a Bayesian network for which the oracle algorithm runs in polynomial time, our metaalgorithm becomes a fully polynomialtime randomized approximation scheme (FPRAS). 1
Combinatorial Prediction Markets: An Experimental Study
"... Abstract. Prediction markets produce crowdsourced probabilistic forecasts through a market mechanism in which forecasters buy and sell securities that pay off when events occur. Prices in a prediction market can be interpreted as consensus probabilities for the corresponding events. There is strong ..."
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Abstract. Prediction markets produce crowdsourced probabilistic forecasts through a market mechanism in which forecasters buy and sell securities that pay off when events occur. Prices in a prediction market can be interpreted as consensus probabilities for the corresponding events. There is strong empirical evidence that aggregate forecasts tend to be more accurate than individual forecasts, and that prediction markets are among the most accurate aggregation methods. Combinatorial prediction markets allow forecasts not only on base events, but also on conditional events (e.g., “A if B”) and/or Boolean combinations of events. Economic theory suggests that the greater expressivity of combinatorial prediction markets should improve accuracy by capturing dependencies among related questions. This paper describes the DAGGRE combinatorial prediction market and reports on an experimental study to compare combinatorial and traditional prediction markets. The experiment challenged participants to solve a “whodunit ” murder mystery by using a prediction market to arrive at group consensus probabilities for characteristics of the murderer, and to update these consensus probabilities as clues were revealed. A Bayesian