We explore the striking mathematical connections that exist between market scoring rules, cost function based prediction markets, and no-regret learning. We first show that any cost function based prediction market can be interpreted as an algorithm for the commonly studied problem of learning from expert advice by equating the set of outcomes on which bets are placed in the market with the set of experts in the learning setting, and equating trades made in the market with losses observed by the learning algorithm. If the loss of the market organizer is bounded, this bound can be used to derive an O ( √ T) regret bound for the corresponding learning algorithm. We then show that the class of markets with convex cost functions exactly corresponds to the class of Follow the Regularized Leader learning algorithms, with the choice of a cost function in the market corresponding to the choice of a regularizer in the learning problem. Finally, we show an equivalence between market scoring rules and prediction markets with convex cost functions. This implies both that any market scoring rule can be implemented as a cost function based market maker, and that market scoring rules can be interpreted naturally as Follow the Regularized Leader algorithms. These connections provide new insight into how it is that commonly studied markets, such as the Logarithmic Market Scoring Rule, can aggregate opinions into accurate estimates of the likelihood of future events.

Abstract. We introduce the concept of a trust network—a decentralized payment infrastructure in which payments are routed as IOUs between trusted entities. The trust network has directed links between pairs of agents, with capacities that are related to the credit an agent is willing to extend another; payments may be routed between any two agents that are connected by a path in the network. The network structure introduces group budget constraints on the payments from a subset of agents to another on the trust network: this generalizes the notion of individually budget constrained bidders. We consider a multi-unit auction of identical items among bidders with unit demand, when the auctioneer and bidders are all nodes on a trust network. We define a generalized notion of social welfare for such budgetconstrained bidders, and show that the winner determination problem under this notion of social welfare is NP-hard; however the flow structure in a trust network can be exploited to approximate the solution with a factor of 1 − 1/e. We then present a pricing scheme that leads to an incentive compatible, individually rational mechanism with feasible payments that respect the trust network’s payment constraints and that maximizes the modified social welfare to within a factor 1 − 1/e. 1

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

Recently, there has been an increase in the usage of centrally managed markets which are run by some form of pari-mutuel mechanism. A parimutuel mechanism is characterized by the ability to shield the market organizer from financial risk by paying the winners from the stakes of the losers. The recent introduction of new, modified pari-mutuel methods has spurred the growth of prediction markets as well as new financial derivative markets. Coinciding with this increased usage, there has been much work on the research front which has produced several mechanisms and a slew of interesting results. We will introduce a new pari-mutuel market-maker mechanism with many positive qualities including convexity, truthfulness and strong performance. Additionally, we will provide the first quantitative performance comparison of some of the existing pari-mutuel market-maker mechanisms. 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

Prediction markets are designed to elicit information from multiple agents in order to predict (obtain probabilities for) future events. A good prediction market incentivizes agents to reveal their information truthfully; such incentive compatibility considerations are commonly studied in mechanism design. While this relation between prediction markets and mechanism design is well understood at a high level, the models used in prediction markets tend to be somewhat different from those used in mechanism design. This paper considers a model for prediction markets that fits more straightforwardly into the mechanism design framework. We consider a number of mechanisms within this model, all based on proper scoring rules. We discuss basic properties of these mechanisms, such as incentive compatibility. We also draw connections between some of these mechanisms and cooperative game theory. Finally, we speculate how one might build a practical prediction market based on some of these ideas. 1

Summary. Automated market makers are algorithmic agents that provide liquidity in electronic markets. We construct two new automated market makers that each solve an open problem of theoretical and practical interest. First, we formulate a market maker that has bounded loss over separable measure spaces. This opens up an exciting new set of domains for prediction markets, including markets on locations and markets where events correspond to the natural numbers. Second, by shifting profits into liquidity, we create a market maker that has bounded loss in addition to a bid/ask spread that gets arbitrarily small with trading volume. This market maker matches important attributes of real human market makers and suggests a path forward for integrating automated market making agents into markets with real money. 1.1