Qingmin Liu

Limited records and reputation bubbles

This paper offers a tractable and fully rational model to study the economics of reputation in a dynamic market with limited record-keeping, i.e., a market in which new entrants observe only the last few periods of play of the long-run player instead of the full history of the market. We show that trust is gradually granted to the opportunistic long-run player despite the fact that his type is perfectly observed by the short-run opponents, and the perfectly informed short-run players ride and drive up “reputation bubbles” at the expense of their uninformed successors. We characterize equilibrium payoffs uniformly over time, which is useful for analyzing ongoing repeated relationships where the starting moments have passed.

Ordinal Efficiency, Fairness, and Incentives in Large Markets

Efficiency and symmetric treatment of agents are the primary goals of resource allocation in environments without transfers. Focusing on ordinal mecha- nisms in which no small group of agents can substantially change the allocations of others, we show that all asymptotically efficient, symmetric, and asymptotically strategy-proof mechanisms lead to the same allocations in large markets. In particular, many mechanisms — both well-known and newly developed — are allocationally equivalent. This equivalence is consistent with prior empirical findings that different mechanisms lead to similar allocations in school choice. We also show that uniform randomizations over deterministic efficient mechanisms are asymptotically efficient.

Stable Matching with Incomplete Information

We formulate a notion of stable outcomes in matching problems with one-sided asymmetric information. The key conceptual problem is to formulate a notion of a blocking pair that takes account of the inferences that the uninformed agent might make. We show that the set of stable outcomes is nonempty in incomplete-information environments, and is a superset of the set of complete-information stable outcomes. We then provide sufficient conditions for incomplete-information stable matchings to be efficient. Lastly, we define a notion of price-sustainable allocations and show that the set of incomplete-information stable matchings is a subset of the set of such allocations.

Limited Records and Reputation

We study the impact of limited records on reputation dynamics, that is, how the set of equilibria and equilibrium payoffs changes in a model in which one long-lived player faces a sequence of short-lived players who observe only limited information about past play (the last K periods of the long-lived players actions). We show that limited records dramatically change the equilibrium behavior. Moreover, with limited records, equilibria in games with complete and incomplete information are strikingly different (in contrast to games with complete records). We also obtain a lower bound for equilibrium payoffs at any moment of the game, not only at the beginning, thus providing a stronger long-run prediction.

Contests for Experimentation

We study contests for innovation with learning about the innovation’s feasibility and opponents’ outcomes. We characterize contests that maximize innovation when the designer chooses a prize-sharing scheme and a disclosure policy. A “public winner-takes-all” contest dominates public contests—where any success is immediately disclosed—with any other prize-sharing scheme as well as winner-takes-all contests with any other disclosure policy. Yet, jointly modifying prize sharing and disclosure can increase innovation. In a broad class of mechanisms, it is optimal to share the prize with disclosure following a certain number of successes; under simple conditions, a “hidden equal-sharing” contest is optimal.

Correlation and common priors in games with incomplete information

This paper provides an explicit characterization of correlations that are implicitly captured by partition models for incomplete information games. The main result of this paper shows that every partition model for incomplete information can be decomposed into the conjunctions of a unique non-redundant model and a unique “individually uninformative” correlating device. The separation of the correlating device from the underlying non-redundant model allows us to separate their strategic implications. As an application, we use this correlation device to define correlated equilibria. Separating the common-prior property of the correlating devices from the underlying state space sheds light on the difference between interim independent and correlated rationalizability.

Transparency and price formation

We study the role that price transparency plays in determining the efficiency and surplus division in a sequential bargaining model of price formation with asymmetric information. Under natural assumptions on type distributions and for any discount factor, we show that the unobservability of past negotiations leads to lower prices and faster trading. Unobservability, therefore, enhances the “Coasian effect” by fostering efficiency and diverting more of the surplus to the player who possesses private information. In addition, we show that the equilibrium is unique and is in pure strategies in the nontransparent regime; this stands in sharp contrast to the existing literature and allows for a better understanding of the Coasian effect and price observability.

THE ROLE OF INFORMATION IN INNOVATION AND COMPETITION

Innovation is typically a trial-and-error process. While some research paths lead to the innovation sought, others result in dead ends. Because firms benefit from their competitors working in the wrong direction, they do not reveal their dead-end findings. Time and resources are wasted on projects that other firms have already found to be fruitless. This is a major problem, particularly in industries that rely heavily on trial-and-error research. We offer a simple model with two firms and two research lines to study this prevalent problem. We characterize the equilibrium in a decentralized environment that necessarily entails significant efficiency losses due to wasteful dead-end replication and an information externality that leads to an early abandonment of the risky project. We show that different types of firms follow different innovation strategies and create different kinds of welfare losses. In an extension of the core model, we also study a centralized mechanism whereby firms are incentivized to disclose their actions and share their private information in a timely manner.

The Role of Information Innovation and Competition

Innovation is typically a trial-and-error process. While some research paths lead to the innovation sought, others result in dead ends. Because firms benefit from their competitors working in the wrong direction, they do not reveal their dead-end findings. Time and resources are wasted on projects that other firms have already found to be fruitless. This is a major problem, particularly in industries that rely heavily on trial-and-error research. We offer a simple model with two firms and two research lines to study this prevalent problem. We characterize the equilibrium in a decentralized environment that necessarily entails significant efficiency losses due to wasteful dead-end replication and a flight to safety–an early abandonment of the risky project. We show that different types of firms follow different innovation strategies and create different kinds of welfare losses. In an extension of the core model, we also study a centralized mechanism whereby firms are incentivized to disclose their actions and share their private information in a timely manner. JEL Classification: O31, D92.

Stable Matching with Incomplete Information (Second Version)

We formulate a notion of stable outcomes in matching problems with one-sided asymmetric information. The key conceptual problem is to formulate a notion of a blocking pair that takes account of the inferences that the uninformed agent might make from the hypothesis that the current allocation is stable. We show that the set of stable outcomes is nonempty in incomplete information environments, and is a superset of the set of complete-information stable outcomes. We then provide sufficient conditions for incomplete-information stable matchings to be efficient. Lastly, we define a notion of price sustainable allocations and show that the set of incomplete- information stable matchings is a subset of the set of such allocations.