# Research

• My research fields are microeconomic theory, game theory and information economics.
• In particular, I am interested in epistemic game theory, mechanism design and dynamic games.
• Broadly, my research agenda is to model and elucidate the role that information plays in strategic situations.

### Research Papers by Topics

Epistemic Game Theory/Reasoning about Belief, Knowledge, and Unawareness

Information Economics/Mechanism Design

Bargaining, Negotiation, and Communication

Other(s)

• ASEAN Financial Integration, with Geert Almekinders, Alex Mourmouras, Jianping Zhou, and Yong Sarah Zhou, IMF Working Paper No. 15/34, Feb. 23, 2015

### Paper Abstracts

The Existence of Universal Qualitative Belief Spaces

Abstract: This paper establishes the existence of a canonical representation of players’ interactive beliefs with a number of desirable features. Players’ beliefs can be qualitative, truthful (i.e., knowledge), or probabilistic (e.g., countably-additive, finitely-additive, or non-additive). Players’ logical and introspective properties can be specified one by one. The canonical model is the \textquotedblleft largest” interactive belief model to which any particular model can be mapped in a unique belief-preserving way. The canonical model incorporates all possible ways in which players’ interactive beliefs are described. Each state of the canonical model encodes players’ interactive beliefs at that state within itself in a coherent manner.

Are the Players in an Interactive Belief Model Meta-certain of the Model Itself?

Abstract: In an interactive belief model, are the players “commonly meta-certain” of the model itself? This paper explicitly formalizes such implicit “common meta-certainty” assumption. To that end, the paper expands the objects of players’ beliefs from events to functions defined on the underlying states. Then, the paper defines a player’s belief-generating map: it associates, with each state, whether a player believes each event at that state. The paper formalizes what it means by: “a player is (meta-)certain of her own belief-generating map” or “the players are (meta-)certain of the profile of belief-generating maps (i.e., the model).” The paper shows: a player is (meta-)certain of her own belief-generating map if and only if her beliefs are introspective. The players are commonly (meta-)certain of the model if and only if, for any event which some player i believes, it is common belief that player i believes the event. This paper then asks whether the “common meta-certainty” assumption is needed for an epistemic characterization of game-theoretic solution concepts. The paper shows: if each player is logical and (meta-)certain of her own strategy and belief-generating map, then each player correctly believes her own rationality. Consequently, common belief in rationality alone leads to actions that survive iterated elimination of strictly dominated actions.

From Equals to Despots: The Dynamics of Repeated Decision Making in Partnerships with Private Information, with Vinicius Carrasco and William Fuchs

Abstract: This paper considers an optimal renegotiation-proof dynamic Bayesian mechanism in which two privately informed players repeatedly have to take a joint action without resorting to side-payments. We provide a general framework which accommodates as special cases committee decision and collective insurance problems. Thus, we formally connect these separate strands of literature. We show: (i) first-best values can be arbitrarily approximated (but not achieved) when the players are sufficiently patient; (ii) our main result, the provision of intertemporal incentives necessarily leads to a dictatorial mechanism: in the long run the optimal scheme converges to the adoption of one player’s favorite action. This can entail one agent becoming a permanent dictator or a possibility of having sporadic ”regime shifts.”

Negotiations with Limited Specifiability, with Yuichiro Kamada

Abstract: We study negotiations with limited specifiability—each party may not be able to fully specify a negotiation outcome. We construct a class of negotiation protocols to conduct comparative statics on specifiability as well as move structures. We find that asynchronicity of proposal announcements narrows down the equilibrium payoff set, in particular leading to a unique prediction in negotiations with a ”common interest” alternative. The equilibrium payoff set is not a singleton in general, and depends on the fine details of how limitation on specifiability is imposed. The equilibrium payoff set is weakly larger under limited specifiability than under unlimited specifiability.

Epistemic Foundations for Set-algebraic Representations of Knowledge

Abstract: This paper formalizes an informal idea that an agent’s knowledge is characterized by a collection of sets such as a σ-algebra within the framework of a state space model. The paper fully characterizes why the agent’s knowledge takes (or does not take) such a set algebra as a σ-algebra or a topology, depending on logical and introspective properties of knowledge and on the underlying structure of the state space. The agent’s knowledge is summarized by a collection of events if and only if she can only know what is true, she knows any logical implication of what she knows, and she is introspective about what she knows. In this case, for any event, the collection that represents knowledge has the maximal event included in the original event. When the underlying space is a measurable space, the collection becomes a $\sigma$-algebra if and only if the agent is additionally introspective about what she does not know.

An Information Correspondence Approach to Bridging Knowledge-Belief Representations in Economics and Mathematical Psychology

Abstract: This paper develops a model of interactive beliefs and knowledge which I call an information correspondence. The information correspondence assigns multiple information sets at each state. It reduces to a standard possibility correspondence when it assigns a unique information set at each state. This generalization allows one to analyze an agent who fails to believe the conjunction of her own beliefs or a tautology. While a possibility correspondence may not be able to represent probabilistic beliefs, this generalization enables one to study qualitative and probabilistic beliefs in a unified manner. The model also generalizes, in a mathematical sense, a knowledge representation in mathematical psychology known as a surmise function. The paper bridges seemingly different knowledge and belief representations in economics and mathematical psychology. The paper also connects the information correspondence model to knowledge and belief representations in computer science, logic, and philosophy.

Can the Crowd be Introspective? Modeling Distributed Knowledge from Collective Information through Inference
Abstract: This paper studies distributed knowledge among agents who possibly have contradictory beliefs with each other. The paper formalizes distributed knowledge as knowledge logically deduced from agents’ collective information, consisting of events that some agent believes whenever they are true. As a result, distributed knowledge is true, monotonic, and positively introspective, even though agents’ beliefs are not. Agents’ false beliefs do not lead to distributed knowledge. Distributed knowledge can fail negative introspection even if agents’ beliefs satisfy it. Agents cannot necessarily have distributed knowledge of the lack of distributed knowledge of an event. Thus, agents can be collectively unaware of events. If agents’ beliefs are true, monotonic, positively introspective, and conjunctive, then distributed knowledge coincides with knowledge possessed by the least knowledgeable ”wise man” who knows everything each agent knows.

Formalizing Common Belief with No Underlying Assumption on Individual Beliefs

Abstract: This paper formalizes common belief among players with no underlying assumption on their individual beliefs. Especially, players may not be logically omniscient, i.e., they may not believe logical consequences of their beliefs. The key idea is to use a novel concept of a common basis: it is an event such that, whenever it is true, every player believes its logical consequences. The common belief in an event obtains when a common basis implies the mutual belief in that event. If players’ beliefs are assumed to be true, then common belief reduces to common knowledge. The formalization nests previous axiomatizations of common belief and common knowledge which have assumed players’ logical monotonic reasoning. Under this formalization, unlike others, if players have common belief in rationality then their actions survive iterated elimination of strictly dominated actions even if their beliefs are not monotonic.

On the Consistency among Prior, Posteriors, and Information Sets

Abstract: This paper studies implications of the consistency conditions among prior, posteriors, and information sets on introspective properties of qualitative belief induced from information sets. The main result reformulates the consistency conditions as: (i) the information sets, without any assumption, almost surely form a partition; and (ii) the posterior at a state is equal to the Bayes conditional probability given the corresponding information set. Implications are as follows. First, each posterior is uniquely determined. Second, qualitative belief reduces to fully introspective knowledge in a ”standard” environment. Thus, a care must be taken when one studies non-veridical belief or non-introspective knowledge. Third, an information partition compatible with the consistency conditions is uniquely determined by the posteriors. Fourth, qualitative and probability-one beliefs satisfy truth axiom almost surely. The paper also sheds light on how the additivity of the posteriors yields negative introspective properties of beliefs.

Unawareness without AU Introspection

Abstract: This paper studies unawareness in terms of the lack of knowledge in a model that generalizes both a non-partitional standard-state-space model and a stationary generalized-state-space model. The resulting model may not necessarily satisfy AU Introspection: an agent, who is unaware of an event, is unaware of being unaware of it. Yet, the paper shows that such agent does not know whether she is unaware of it, i.e., she is ignorant of being unaware of it. First, the paper asks when and how the generalized model (in particular, a standard-state-space model) has a non-trivial form of unawareness and sensible properties of unawareness. Second, the paper studies the implications of the violation of AU Introspection. An agent, when facing infinitely many objects of knowledge, may know that there is an event of which she is unaware. Treating new information only at face value can cause an agent to become unaware of some event.