- Research Papers by Topics
- Paper Abstracts

**1. Research Papers by Topics**

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

- The Existence of Universal Qualitative Belief Spaces (Dec. 23, 2019)

A previous version was circulated as The Existence of Universal Knowledge Spaces (Oct. 28, 2016) - Formalizing Common Belief with No Underlying Assumption on Individual Beliefs Forthcoming at
*Games and Economic Behavior* - On the Consistency among Prior, Posteriors, and Information Sets

A previous version (Sept. 23, 2018), An extended abstract (*Electronic Proceedings in Theoretical Computer Science*297 (2019), 189–205) - A Qualitative Type Space Approach to Hierarchies of Beliefs, Preferences, and Expectations
- Topology-free Bottom-up Constructions of a Universal Type Space
- On the Sense in which an Interactive Belief Model is (Meta-)Known by the Players Within the Model Itself
- Epistemic Foundations for Set-algebraic Representations of Knowledge
*Journal of Mathematical Economics*84 (2019): 73-82 - Can the Crowd be Introspective? Modeling Distributed Knowledge from Collective Information through Inference (Jan. 19, 2019)
- An Information Correspondence Approach to Bridging Knowledge-Belief Representations in Economics and Mathematical Psychology (Sept. 10, 2018)
- Representing Unawareness on State Spaces (Dec. 12, 2018)
- Axiomatizations of Unawareness Structures by Underlying Properties of Knowledge

**Information Economics/Mechanism Design**

- From Equals to Despots: The Dynamics of Repeated Decision Making in Partnerships with Private Information, with Vinicius Carrasco and William Fuchs,
*Journal of Economic Theory*182 (2019): 402-432

**Bargaining, Negotiation, and Communication
**

- Negotiations with Limited Specifiability (Online Appendix), with Yuichiro Kamada (Dec. 21, 2019)

**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

**2. 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.

**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.

**Representing Unawareness on State Spaces**

*Abstract:* I study unawareness by the lack of knowledge on a generalized state space. In order to understand and contrast properties of unawareness in a non-partitional standard state space model and a partitional generalized state space model, I provide a generalized framework that accommodates both models. I ask: when and how a generalized (in particular, standard) state space model has a sensible form of unawareness; and how unawareness relates to ignorance and possibility. First, unawareness can only take two forms: an agent is ignorant of knowing that she does not know an event; and the agent is ignorant of knowing an event. In either case, unawareness is also associated with the ignorance of the possibility of knowing an event. Second, the agent, who is unaware of an event, is ignorant (but not necessarily unaware) of being unaware of it. Third, the agent, facing infinitely many objects of knowledge, may know that there is an event of which she is unaware, while she cannot know that she is unaware of any particular event. Fourth, getting more information can cause the agent to become unaware of some event.