Working papers : 1) Learnability and Models of Decision Making under Uncertainty (with Federico Echenique)
Abstract : We study whether some of the most important models of decision-making under uncertainty are uniformly learnable, in the sense of PAC learnability. Our setting involves an analyst whose task is to estimate or learn an agent's preference based on data available on the agent's choices. A model of preferences is learnable if the analyst can construct a learning rule to precisely learn the agent's preference with enough data. We consider the Expected Utility, Choquet Expected Utility and Max-min Expected Utility model: arguably the most important models of decision-making under uncertainty. We show that the models of Expected Utility and Choquet Expected Utility are learnable. Morever, the sample complexity of the former is linear and of the latter, is exponential, in the number of states of uncertainty. The Max-min Expected Utility model is learnable when there are two states but is not learnable when there are three states or more.
2) Repeated Coordination with Private Learning (with Kalyan Chatterjee, Tetsuya Hoshino and Omer Tamuz)
Abstract : We study a repeated game with payoff externalities and observable actions where two players receive information over time about an underlying payoff-relevant state, and strategically coordinate their actions. Players learn about the true state from private signals, as well as the actions of others. They commonly learn the true state (Cripps et. al., 2008) but do not coordinate in every equilibrium. We show that it is possible to construct equilibria in which players eventually coordinate on the correct action, for any discount factor. For high discount factors we show that in addition players can also achieve efficient payoffs.
3) On interim rationality, belief formation and learning in decision problems with bounded memory (with Kalyan Chatterjee)
Economics Working Paper No.110, Institute for Advanced Study, School of Social Science, Princeton, NJ :
Abstract : 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-observed 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.
4) Bayesian Updating Rules and AGM Belief Revision
Abstract : We interpret the problem of updating beliefs 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 up- dating rules, which we call ”support-dependent” rules. We show that such updating rules have a minimum distance representation.
5) Dynamic Bayesian Persuasion with a Privately Informed Receiver
Abstract : 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.
6) Ethnic conflicts, Rumours and an Informed Agent (with Souvik Dutta and Suraj Shekhar)
Abstract: Rumours often precipitate ethnic conflicts and cause immense damage to life and property. There may exist an agent who knows if the rumour is true or false. We analyze a cheap talk game with multiple audiences (ethnicities) to see how this informed agent (b) may influence the outcome of rumours by sending strategic signals. Since b is biased towards her own ethnicity, she finds it difficult to convince the other ethnicity that she is giving them correct information. We show that even if b is known to be biased towards her own ethnicity, peace is possible in equilibrium. Additionally, we prove that there are only three equilibrium outcomes possible in symmetric strategies. Conflict is inevitable in one. The other outcomes have the following features. One, there may be peace whenever b deems it possible. Two, while b gives more informative signals to her own ethnicity, she may misinform a segment of her own ethnicity in equilibrium.