- Research Papers by Topics
- Paper Abstracts

**1. Research Papers by Topics**

**Epistemic Game Theory**

- The Existence of Universal Knowledge Spaces (Previous version, Oct 28, 2016)
- On the Sense in which a Model of Interactive Knowledge is (Meta-)Known by the Players Within the Model Itself
- Epistemic Foundations for Set-algebraic Representations of Knowledge (Sep 10, 2018)
- An Information Correspondence Approach to Bridging Knowledge-Belief Representations in Economics and Mathematical Psychology (Sep 10, 2018)
- Can the Crowd be Introspective? Modeling Distributed Knowledge from Collective Information through Inference
- Formalizing Common Belief with No Underlying Assumption on Individual Beliefs (August 10, 2018)
- On the Consistency among Prior, Posteriors, and Information Sets (May 5, 2018)
- Representing Unawareness on State Spaces (Sep 10, 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

**Bargaining, Negotiation, and Communication
**

- Negotiations with Limited Specifiability (Online Appendix), with Yuichiro Kamada (July 10, 2018)

**Other(s)**

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

**2. Paper Abstracts**

**The Existence of Universal Knowledge Spaces**

*Abstract:* We provide a formal framework capable of capturing players’ interactive knowledge in a strategic context with a number of desirable features. First, we can specify players’ logical and introspective abilities as well as the language that they can use in their reasoning. Second, our framework admits tractable representations of players’ knowledge and common knowledge and nests previous interactive knowledge models. The main result of the paper is that the framework admits a canonical representation of players’ knowledge. The canonical model is a ”largest” model of knowledge to which any particular knowledge space can be mapped in a unique knowledge-preserving way.

**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.

**Negotiations with Limited Specifiability, with Yuichiro Kamada**

*Abstract:* This paper studies negotiations with *limited specifiability*—each party may not be able to fully specify a negotiation outcome. We construct a class of negotiation protocols under which we can 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, contains any payoff profile that gives each player no less than her individually-rational and worst Pareto-efficient payoff, and is weakly larger under limited specifiability than under unlimited specifiability. The degree to which limitation on specifiability affects the prediction of a negotiation depends on the fine details of how such limitation is imposed.

**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 of knowledge. The formalization is based on the agent’s logical and introspective abilities and on the underlying structure of the state space. The agent is logical and introspective about what she knows if and only if her knowledge is summarized by a collection of events with the property that, for any event, the collection has the maximal event included in the original event. When the underlying space is a measurable space, the collection becomes a σ-algebra if and only if the agent is additionally introspective about what she does not know. The paper characterizes why the agent’s knowledge takes (or does not take) such a set algebra as a σ-algebra or a topology, depending on the agent’s logical and introspective abilities and on the underlying environment.

**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 the distributed knowledge of the lack of the distributed knowledge of an event. Thus, agents can be collectively unaware of events. If agents’ beliefs are true, monotonic, and positively introspective, then distributed knowledge coincides with knowledge possessed by the least knowledgeable \textquotedblleft 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 in that they do not believe logical consequences of their beliefs. The key idea is to use a novel concept of common bases: a common basis 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. In the paper, individual beliefs are represented as operators on a general set algebra so that they can be qualitative or probabilistic. 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. The paper also studies how common belief inherits properties of individual beliefs.

**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. I ask: when and how a 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 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.