Rene Saran

Menu-dependent preferences and revelation principle

We extend the set of preferences to include menu-dependent preferences and characterize the domain in which the revelation principle holds. A weakening of the well-known contraction consistency is shown to define a subset of this domain. However, we show that minimax-regret preference can be outside the domain.

Mechanism Design with Bounded Depth of Reasoning and Small Modeling Mistakes

We consider mechanism design in contexts in which agents exhibit bounded depth of reasoning (level k) instead of rational expectations. We use simple direct mechanisms, in which agents report only rst-order beliefs. While level 0 agents are assumed to be truth tellers, level k agents best-respond to their belief that other agents have at most k 1 levels of reasoning. We nd that incentive compatibility is necessary for implementation in this framework, while its strict version alone is sucient. Adding continuity to both directions, the same results are obtained for continuous implementation with respect to small modeling mistakes. We present examples to illustrate the permissiveness of our ndings in contrast to earlier related results under the assumption of rational expectations.

Bilateral trading with naive traders

We introduce naive traders in bilateral trading. These traders report their true types in direct mechanisms and bid/ask their values/costs in auctions. We show that by expropriating naive traders in direct mechanisms, the mechanism designer can subsidize additional trades by strategic traders and improve efficiency. In fact, complete expropriation of naive traders is a necessary condition for constrained efficiency. A significant implication is that in the presence of naive traders, ex-post individually rational mechanisms are not constrained efficient. In contrast, if the traders must use a given mechanism, then the introduction of naive traders has an ambiguous effect on efficiency.

Ex-Post Regret Learning in Games with Fixed and Random Matching: The Case of Private Values

In contexts in which players have no priors, we analyze a learning process based on ex-post regret as a guide to understand how to play games of incomplete information under private values. The conclusions depend on whether players interact within a fixed set (fixed matching) or they are randomly matched to play the game (random matching). The relevant long run predictions are minimal sets that are closed under “the same or better reply” operations. Under additional assumptions in each case, the prediction boils down to pure Nash equilibria, pure ex-post equilibria or pure minimax regret equilibria. These three paradigms exhibit nice robustness properties in the sense that they are independent of beliefs about the exogenous uncertainty of type spaces. The results are illustrated in second-price auctions, first-price auctions and Bertrand duopolies.

Regret Matching with Finite Memory

We consider the regret matching process with finite memory. For general games in normal form, it is shown that any recurrent class of the dynamics must be such that the action profiles that appear in it constitute a closed set under the “same or better reply�? correspondence (CUSOBR set) that does not contain a smaller product set that is closed under “same or better replies,�? i.e., a smaller PCUSOBR set. Two characterizations of the recurrent classes are offered. First, for the class of weakly acyclic games under better replies, each recurrent class is monomorphic and corresponds to each pure Nash equilibrium. Second, for a modified process with random sampling, if the sample size is sufficiently small with respect to the memory bound, the recurrent classes consist of action profiles that are minimal PCUSOBR sets. Our results are used in a robust example that shows that the limiting empirical distribution of play can be arbitrarily far from correlated equilibria for any large but finite choice of the memory bound.

Implementation by Sortition in Nonexclusive Information Economies

We study the Bayesian implementation problem in economies that are divided into groups consisting of two or more individuals with the same information. Our results cover problems like that of allocating public funds among states, regulating activities causing externalities among firms, locating public facilities in neighborhoods, electing candidates from multiple districts etc. Instead of the standard communication protocol of direct democracy whereby the planner consults all individuals, we analyze sortition schemes whereby the planner consults only a subset of the individuals, called senators, who are selected via some kleroterion (i.e., a lottery machine) p. In general environments, under mild economic assumptions on preferences, we show that every social choice function (SCF) that is implementable by direct democracy is also p-implementable if p always selects two or more individuals from each group and the selection process does not partition any group into disconnected subgroups (in the sense that individuals belonging to different subgroups are never selected together). In quasilinear environments satisfying a generic condition on individuals beliefs, every SCF can be implemented by a simple and economically meaningful mechanism in which the kleroterion selects a predesignated group leader and one other randomly chosen individual from each group.