Yuichiro Kamada

Hierarchical cheap talk

We investigate situations in which agents can communicate to each other only through a chain of intermediators, for example because they have to obey institutionalized communication protocols. We assume that all involved in the communication are strategic, and might want to influence the action taken by the final receiver. The set of pure strategy equilibrium outcomes is simple to characterize, monotonic in each intermediators bias, does not depend on the order of intermediators, and intermediation in these equilibria cannot improve information transmission. However, none of these conclusions hold for mixed equilibria. We provide a partial characterization of mixed equilibria, and offer an economically relevant sufficient condition for every equilibrium to be outcome-equivalent to a pure equilibrium and hence the simple characterization and comparative statics results to hold for the set of all equilibria.

Stability concepts in matching under distributional constraints

Many real matching markets are subject to distributional constraints. To guide market designers faced with constraints, we propose new stability concepts. A matching is strongly stable if satisfying blocking pairs inevitably violates a constraint. We show that a strongly stable matching may not exist, and that existence is guaranteed if and only if all distributional constraints are trivial. To overcome this difficulty, we propose a more permissive concept, weak stability. We demonstrate a weakly stable matching always exists, implies efficiency, and is characterized by standard normative axioms. These results are obtained in a more general environment than those in existing studies, accommodating a wide variety of applications.

Rationalizable Partition-Confirmed Equilibrium

Rationalizable partition-confirmed equilibrium (RPCE) describes the steady-state outcomes of rational learning in extensive-form games when rationality is common knowledge and players observe a partition of the terminal nodes. RPCE allows players to make inferences about unobserved play by others. We discuss the implications of this using numerous examples, and discuss the relationship of RPCE to other solution concepts in the literature.

The Equivalence Between Costly and Probabilistic Voting Models

In costly voting models, voters abstain when a stochastic cost of voting exceeds the benefit from voting. In probabilistic voting models, they always vote for a candidate who generates the highest utility, which is subject to random shocks. We prove an equivalence result: In two-candidate elections, given any costly voting model, there exists a probabilistic voting model that generates winning probabilities identical to those in the former model for any policy announcements, and vice versa. Thus many predictions of interest established in one of the models hold in the other as well, providing robustness of the conclusions to model specifications.

Strongly Consistent Self-Confirming Equilibrium

Fudenberg and Levine (1993a) introduced the notion of self-confirming equilibrium, which is generally less restrictive than Nash equilibrium. Fudenberg and Levine also defined a concept of consistency, and claimed in their Theorem 4 that with consistency and other conditions on beliefs, a self-confirming equilibrium has a Nash equilibrium outcome. We provide a counterexample that disproves Theorem 4 and prove an alternative by replacing consistency with a more restrictive concept, which we call strong consistency. In games with observed deviators, self-confirming equilibria are strongly consistent self-confirming equilibria. Hence, our alternative theorem ensures that despite the counterexample, the corollary of Theorem 4 is still valid. Copyright 2010 The Econometric Society.

Stability and strategy-proofness for matching with constraints: A necessary and sufficient condition: Matching with constraints

Distributional constraints are common features in many real matching markets, such as medical residency matching, school admissions, and teacher assignment. We develop a general theory of matching mechanisms under distributional constraints. We identify the necessary and sufficient condition on the constraint structure for the existence of a mechanism that is stable and strategy-proof for the individuals. Our proof exploits a connection between a matching problem under distributional constraints and a matching problem with contracts.

Contracting with Word-of-Mouth Management

We incorporate word of mouth (WoM) in a classic Maskin-Riley contracting problem, allowing for referral rewards to senders of WoM. Current customers’ incentives to engage in WoM can affect the contracting problem of a firm in the presence of positive externalities of users. We fully characterize the optimal contract scheme and provide other comparative statics. In particular, we show that offering a free contract is optimal only if the fraction of premium users in the population is small. The reason is that by offering a free product, the firm can incentivize senders to talk by increasing expected externalities that they receive and this can (partly) substitute for paying referral rewards only if there are few premium customers. This result is consistent with the observation that companies that successfully offer freemium contracts oftentimes have a high percentage of free users.