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.

Ensuring sufficient liquidity is one of the key challenges for designers of prediction markets. Various market making algorithms have been proposed in the literature and deployed in practice, but there has been little effort to evaluate their benefits and disadvantages in a systematic manner. We introduce a novel experimental design for comparing market structures in live trading that ensures fair comparison between two different microstructures with the same trading population. Participants trade on outcomes related to a two-dimensional random walk that they observe on their computer screens. They can simultaneously trade in two markets, corresponding to the independent horizontal and vertical random walks. We use this experimental design to compare the popular inventory-based logarithmic market scoring rule (LMSR) market maker and a new information based Bayesian market maker (BMM). Our experiments reveal that BMM can offer significant benefits in terms of price stability and expected loss when controlling for liquidity; the caveat is that, unlike LMSR, BMM does not guarantee bounded loss. Our investigation also elucidates some general properties of market makers in prediction markets. In particular, there is an inherent tradeoff between adaptability to market shocks and convergence during market equilibrium. 1

We propose a general framework for the design of securities markets over combinatorial or infinite state or outcome spaces. The framework enables the design of computationally efficient markets tailored to an arbitrary, yet relatively small, space of securities with bounded payoff. We prove that any market satisfying a set of intuitive conditions must price securities via a convex cost function, which is constructed via conjugate duality. Rather than deal with an exponentially large or infinite outcome space directly, our framework only requires optimization over a convex hull. By reducing the problem of automated market making to convex optimization, where many efficient algorithms exist, we arrive at a range of new polynomial-time pricing mechanisms for various problems. We demonstrate the advantages of this framework with the design of some particular markets. We also show that by relaxing the convex hull we can gain computational tractability without compromising the market institution’s bounded budget.

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

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

Summary I am interested in (1) the design of intelligent agents and systems, primarily guided by machine learning; (2) modeling and understanding collective dynamics that result from intelligent individual behavior; and (3) using this understanding to inform the design of venues where people and automated agents come together to interact. A central focus of my research is on understanding how information flows through systems, how it can be best used by intelligent agents, and how its presence, absence, or the form in which it is available impacts decisions at the individual and systemic levels. My work can be categorized into four broad themes. 1: Collective intelligence I am interested in both modeling and understanding the dynamics of collective intelligence, and in designing algorithms that allow us to use the power of collective wisdom to make better decisions. I have been working on the foundations of a rigorous theory of how information grows in novel social media like Wikipedia and the blogosphere, and on information aggregation and dissemination in prediction markets. In recent work, we have documented some remarkable regularities in the life cycles of average Wikipedia pages and blog posts [26, 27]. They exhibit a concave rise to an editing / commenting peak, followed by decay at a 1/t rate over time. We have proposed a simple model of information creation that matches the data

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 risk-neutral (expected utility maximizing) and Kelly criterion (expected log-utility maximizing) market makers. Computing the optimal policy for a risk-neutral 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 risk-neutral market maker never offers a myopically irrational bet.