Essays in Information Economics

Author:

Basu, Pathikrit

Graduate Program:

Economics

Degree:

Doctor of Philosophy

Document Type:

Dissertation

Date of Defense:

June 07, 2017

Committee Members:

Kalyan Chatterjee, Dissertation Advisor/Co-Advisor
Kalyan Chatterjee, Committee Chair/Co-Chair
Vijay Krishna, Committee Member
Neil Wallace, Committee Member
Chloe Jeanne Tergiman, Outside Member

Keywords:

Information Economics
Bayesian Persuasion
Learning
Bounded Rationality
Decision Theory
Applied Game Theory
Belief Revision

Abstract:

This dissertation consists of three chapters. The chapters study issues pertaining to optimal use of information under memory constraints, boundedly rational learning, belief updating after events of surprise (zero-probability) and scenarios of persuasion involving strategic design of information In Chapter 1, we study the process of decision-making and inference by a single, boundedly rational, economic agent. The agent chooses either a safe or a risky alternative in each period after receiving a signal about the state of the world in that period. The state of the world is changing according to a Markov process with some degree of persistence across time. The agent's decision rule is expressed as a finite-state automaton with a fixed number of memory states. Updating on the basis of the received signal is, for such an agent, making a transition from one state to another. The finiteness of the number of automaton states automatically suggests that beliefs are classified into categories and a signal causes a (possible) change in the category on the basis of which the next action is taken. The problem is one in partially-observable Markov decision processes (POMDP). We characterise the structure of the optimal decision rule in this setting and show how its properties pin down the categories of beliefs and explain some observed, seemingly irrational behaviour. We then specialise to a fixed state of the world, weaken the optimality requirement to admissibility and derive the staircase structure of the admissible automaton. Finally we examine the question of randomisation in the design of an automaton, propose a measure of the extent of such randomisation and show that there exists a minimal degree of randomisation for the set of automata implementing a given strategy. We show that if the number of signals is large, virtually no randomisation is required. In Chapter 2, we study the problem of updating beliefs by interpreting it as a choice problem (selecting a posterior from a set of admissible posteriors) with a reference point (prior). We use AGM belief revision to define the support of admissible posteriors after observing zero probability events and investigate two classes of updating rules for probabilities : 1) "minimum distance" updating rules which select the posterior closest to the prior by some metric. 2) "lexicographic" updating rules where posteriors are given by a lexicographic probability system. For the former, we show bayesian updating as a special case and for specific AGM belief revisions, provide necessary and sufficient conditions for a minimum distance representation. For the latter, we show that an updating rule is lexicographic if and only if it is bayesian, AGM-consistent and satisfies a weak form of path independence. Lastly, we study a sub-class of lexicographic updating rules, which we call "support-dependent" rules. We show that such updating rules have a minimum distance representation. In Chapter 3, we study a dynamic Bayesian persuasion framework in a finite horizon setting consisting of a Seller and a Buyer. The Seller wishes to persuade the Buyer to buy a durable good at a given price by providing information about its relevance (match quality). The Buyer has private information about his valuation for a good match and we study optimal dynamic information policies employed by the Seller in equilibrium. For a fixed horizon, we show that the Seller always provides signals which truthfully convey a good match but may garble a bad one. Moreover, if the good is not bought in the first stage, the Seller provides information which improves over time. The agents always interact for a fixed amount of time within which a purchase decision is made. The length of this interaction remains fixed even for long horizons and depends only on the prior on the Buyer's valuation. As the horizon goes to infinity, the bulk of the information about match quality is provided in the first period. This allows the Buyer to extract a large amount of information from the Seller at the beginning of their interaction. Even a slight probability of the Buyer being difficult to convince facilitates close to full disclosure immediately.