We introduce a class of utility-based market makers that always accept orders at their risk-neutral prices. We derive necessary and sufficient conditions for such market makers to have bounded loss. We prove that hyperbolic absolute risk aversion utility market makers are equivalent to weighted pseudospherical scoring rule market makers. In particular, Hanson’s logarithmic scoring rule market maker corresponds to a negative exponential utility market maker in our framework. We describe a third equivalent formulation based on maintaining a cost function that seems most natural for implementation purposes, and we illustrate how to translate among the three equivalent formulations. We examine the tradeoff between the market’s liquidity and the market maker’s worst-case loss. For a fixed bound on worst-case loss, some market makers exhibit greater liquidity near uniform prices and some exhibit greater liquidity near extreme prices, but no market maker can exhibit uniformly greater liquidity in all regimes. For a fixed minimum liquidity level, we give the lower bound of market maker’s worst-case loss under some regularity conditions. 1

In the last three years, Google has conducted the largest corporate experiment with prediction markets we are aware of. In this paper, we illustrate how markets can be used to study how an organization processes information. We document a number of biases in Google’s markets, most notably an optimistic bias. Newly hired employees are on the optimistic side of these markets, and optimistic biases are significantly more pronounced on days when Google stock is appreciating. We find correlated trading among employees who sit within a few feet of one another and employees with social or work relationships. The results are interesting in light of recent research on the role of optimism in entrepreneurial firms, as well as recent work on the importance of geographic and social proximity in explaining information flows in firms and markets. 1

While a simple information market lets one trade on the probability of each value of a single variable, a full combinatorial information market lets one trade on any combination of values of a set of variables, including any conditional or joint probability. In laboratory experiments, we compare the accuracy of simple markets, two kinds of combinatorial markets, a call market and a market maker, isolated individuals who report to a scoring rule, and two ways to combine those individual reports into a group prediction. We consider two environments with asymmetric information on sparsely correlated binary variables, one with three subjects and three variables, and the other with six subjects and eight variables (and so 256 states). ∗ For their comments, we thank David Porter, Ryan Oprea, and participants of seminars at George Mason

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 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

Abstract. We study the problem of designing prediction markets for random variables with continuous or countably infinite outcomes on the real line. Our interval betting languages allow traders to bet on any interval of their choice. Both the call market mechanism and two automated market maker mechanisms, logarithmic market scoring rule (LMSR) and dynamic parimutuel markets (DPM), are generalized to handle interval bets on continuous or countably infinite outcomes. We examine problems associated with operating these markets. We show that the auctioneer’s order matching problem for interval bets can be solved in polynomial time for call markets. DPM can be generalized to deal with interval bets on both countably infinite and continuous outcomes and remains to have bounded loss. However, in a continuous-outcome DPM, a trader may incur loss even if the true outcome is within her betting interval. The LMSR market maker suffers from unbounded loss for both countably infinite and continuous outcomes.

Abstract. A potential downside of prediction markets is that they may incentivize agents to take undesirable actions in the real world. For example, a prediction market for whether a terrorist attack will happen may incentivize terrorism, and an in-house prediction market for whether a product will be successfully released may incentivize sabotage. In this paper, we study principal-aligned prediction mechanisms– mechanisms that do not incentivize undesirable actions. We characterize all principal-aligned proper scoring rules, and we show an “overpayment” result, which roughly states that with n agents, any prediction mechanism that is principal-aligned will, in the worst case, require the principal to pay Θ(n) times as much as a mechanism that is not. We extend our model to allow uncertainties about the principal’s utility and restrictions on agents ’ actions, showing a richer characterization and a similar “overpayment ” result.

Abstract. A dynamic pari-mutuel market (DPM) is a hybrid between a continuous double auction (CDA) and a pari-mutuel market. Like a CDA, a DPM incentivizes traders to reveal their information early. Like a pari-mutuel market, a DPM has infinite liquidity, allowing trades at any time. In this paper, we examine empirical questions related to DPMs: Do prices in DPMs predict events of interests? How do traders behave in DPMs? Leveraging a data set from the Yahoo!/O’Reilly Tech Buzz Game, a live system using the DPM, we show that prices offer informative forecasts of future event trends. At the agent level, we find that on average human traders outperform robot traders who randomly place trades. Those human traders who are seemingly more rational, buying when the implied market probability is low and selling when it is high, obtain higher profit on average than those who appear less rational. We examine other aspects of the game, including incentives to manipulate the market. 1

I consider the design of policy-making institutions to aggregate preferences and information. A pervasive incentive problem hinders the creation of desirable deliberative institutions; participants that expect to have minority interests have an incentive to misrepresent their information. Moreover, contrary to conventional wisdom, diversity of preferences or information sources amplifies this incentive problem. It is only when all types of participants expect to have the majority interests or no individual’s private information can be decisive that full aggregation is possible.The addition of external incentives enables efficient aggregation of preferences and information. The external incentives need only depend on agent actions and, interestingly, the magnitude of these external incentives can be vanishingly small for large groups. These external incentives can be created by augmenting deliberation with concerns about ex-poste monitoring or ex-interum perceptions of competence, the opportunity to trade in information markets, or the opportunity to join clubs with network externalities.

This paper presents a framework for applying prediction markets to corporate decision making. The analysis is motivated by the recent surge of interest in markets as information aggregation devices and their potential use within firms. We characterize the amount of outcome manipulation that results in equilibrium and the impact of this manipulation on market prices. (JEL: D71, D82, D83, D84)