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.

� We survey the literature on prediction mechanisms, including prediction markets and peer prediction systems. We pay particular attention to the design process, highlighting the objectives and properties that are important in the design of good prediction mechanisms. Mechanism design has been described as “inverse game theory. ” Whereas game theorists ask what outcome results from a game, mechanism designers ask what game produces a desired outcome. In this sense, game theorists act like scientists and mechanism designers like engineers. In this article, we survey a number of mechanisms created to elicit predictions, many newly proposed within the last decade. We focus on the engineering questions: How do they work and why? What factors and goals are most important in their

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

We contribute to the recently developed theory of asset pricing in decentralized markets. We extend this literature to characterize an environment in which some agents have superior private information. In our model, agents have an additional incentive to trade assets to learn information that other agents have. First, we show that uninformed agents can learn all the useful information the long run, and that the long-run allocations are Pareto efficient. In the long run, therefore, the allocations coincide with those of the standard centralized market equilibrium such as in Grossman-Stiglitz. Second, we show that agents with private information receive rents, and the value of information is positive. This is in contrast with the centralized markets in which prices fully reveal information and the value of information is zero. Finally, we provide characterization of the dynamics of the trades.

We provide an overview of recent research on belief and opinion dynamics in social networks. We discuss both Bayesian and non-Bayesian models of social learning and focus on the implications of the form of learning (e.g., Bayesian vs. non-Bayesian), the sources of information (e.g., observation vs. communication), and the structure of social networks in which individuals are situated on three key questions: (1) whether social learning will lead to consensus, i.e., to agreement among individuals starting with different views; (2) whether social learning will effectively aggregate dispersed information and thus weed out incorrect beliefs; (3) whether media sources, prominent agents, politicians and the state will be able to manipulate beliefs and spread misinformation in a society.

Options are a basic, widely-traded form of financial derivative that offer payouts based on the future price of an underlying asset. The finance literature gives us option-trading 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 market-making agents (like the popular LMSR) that are event-independent 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 previously-made 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

Abstract. We study the strategic behavior of risk-neutral non-myopic agents in Dynamic Parimutuel Markets (DPM). In a DPM, agents buy or sell shares of contracts, whose future payoff in a particular state depends on aggregated trades of all agents. A forward-looking agent hence takes into consideration of possible future trades of other agents when making its trading decision. In this paper, we analyze non-myopic strategies in a two-outcome DPM under a simple model of incomplete information and examine whether an agent will truthfully reveal its information in the market. Specifically, we first characterize a single agent’s optimal trading strategy given the payoff uncertainty. Then, we use a two-player game to examine whether an agent will truthfully reveal its information when it only participates in the market once. We prove that truthful betting is a Nash equilibrium of the two-stage game in our simple setting for uniform initial market probabilities. However, we show that there exists some initial market probabilities at which the first player has incentives to mislead the other agent in the two-stage game. Finally, we briefly discuss when an agent can participate more than once in the market whether it will truthfully reveal its information at its first play in a three-stage game. We find that in some occasions truthful betting is not a Nash equilibrium of the three-stage game even for uniform initial market probabilities. 1

job market paper

This paper studies price inference in small (finite) markets and investigates the effects of market size on the ability to aggregate private information. To account for trader heterogeneity, the presented model departs from the standard fundamentalvalue formulation of preferences. When trader values are heterogeneously correlated, a trade-off exists in information aggregation between small and large markets. As a result, equilibrium price can be more informative in small than in large markets in relevant economic environments. This paper identifies the sources of learning present in small—but not large—markets, which originate from non-negligibility of individual signals. Necessary and sufficient conditions for the monotonicity of price informativeness in market size are provided. The effects of empirically motivated aspects of heterogeneity in preference dependence on price informativeness are examined.

Abstract. Decision and prediction markets are designed to determine the likelihood of future events; prediction markets predict what will happen, and decision markets predict the results of a choice, or what would happen. Both allow multiple participants to review and make predictions, and participants are typically scored for improving the accuracy of the market’s prediction. Previous work has demonstrated prediction markets can reward accuracy improvements, as can a single participant informing a decision. We construct and characterize decision markets where all participants are scored for improving the market’s accuracy. These markets require the decision maker always risk taking an action at random, and reducing this risk increases its potential loss. We also relate these decision markets to sets of prediction markets, demonstrating a correspondence between their perfect Bayesian equilibria. 1