Published papers

We formulate a new model of strategic group formation by farsighted players in a seller–buyer setting. In each period, sellers are partitioned into groups/brands. At the end of each period, one seller may fail and exit the market by exogenous shock. When there is a vacant slot in the market, an entrant seller comes and chooses which existing group to join or to create a new group. There is a trade-off: larger groups enjoy more-than-proportional benefits of group size thanks to, for example, their visibility to attract customers and their negotiation power in factor markets. However, larger groups are more likely to experience member failure, which is a reputation loss. We find that when the rate of reputation loss is small, clustering is inevitable, but as the rate of reputation loss increases, the largest group with a bad reputation does not attract an entrant, dissolving a cluster. With a limited group-size benefit and a high rate of reputation loss, all entrants create a new group; that is, no clustering occurs. A mathematically interesting result is that, even though the model itself is stationary and symmetric, depending on the parameters, there may be multiple pure-strategy, symmetric stationary equilibria, or there may be no such equilibrium. The economic implications include that group reputation may prevent clustering and that similar markets can have different cluster structures.

Repetition is a classic mechanism for the evolution of cooperation. The standard way to study repeated games is to assume that there is an exogenous probability with which every interaction is repeated. If it is sufficiently likely that interactions are repeated, then reciprocity and cooperation can evolve together in repeated prisoner’s dilemmas. Who individuals interact with can however also be under their control, or at least to some degree. If we change the standard model so that it allows for individuals to terminate the interaction with their current partner, and find someone else to play their prisoner’s dilemmas with, then this limits the effectiveness of disciplining each other within the partnership, as one can always leave to escape punishment. The option to leave can however also be used to get away from someone who is not cooperating, which also has a disciplining effect. We find that the net effect of introducing the option to leave on cooperation is positive; with the option to leave, the average amount of cooperation that evolves in simulations is substantially higher than without. One of the reasons for this increase in cooperation is that partner choice creates endogenous phenotypic assortment. Compared to the standard models for the co-evolution of reciprocity and cooperation, and models of kin selection, our model thereby produces a better match with many forms of human cooperation in repeated settings. Individuals in our model end up interacting, not with random others that they cannot separate from, once matched, or with others that they are genetically related to, but with partners that they choose to stay with, and that are similarly dependable not to play defect as they are themselves.

There is a widespread hope that, in the near future, algorithms become so sophisticated that “solutions” to most problems are found by machines. In this note, we throw some doubts on this expectation by showing the following impossibility result: given a set of finite-memory, finite-iteration algorithms, a continuum of games exist, whose unique and strict Nash equilibrium cannot be reached from a large set of initial states. A Nash equilibrium is a social solution to conflicts of interest, and hence finite algorithms should not be always relied upon for social problems. Our result also shows how to construct games to deceive a given set of algorithms to be trapped in a cycle without a Nash equilibrium.

This article is inspired by real-world phenomena that firms lose customers based on imprecise information and take a long time to recover. If consumers are playing an ordinary repeated game with fixed partners, there is no clear reason why recovery happens slowly. However, if consumers are playing an endogenously repeated game, a class of simple efficient equilibria exhibits the asymmetry of fast loss and slow recovery of customers after a bad signal. Exit is systematic, but formation of a new partnership is random. We also give empirical evidence of our equilibria at an individual-firm level.

In repeated Prisoner’s Dilemma, the C-trigger strategy played by all players is well known to achieve symmetric efficiency when players are sufficiently patient. By contrast, if players are free to quit a repeated Prisoner’s Dilemma without information flow to new partners, cooperation from the outset of new partnerships cannot be a part of any symmetric equilibrium. Fujiwara-Greve and Okuno-Fujiwara (Rev Econ Stud 76:993–1021, 2009) showed that symmetric trust-building strategies can constitute an equilibrium for sufficiently long initial (D, D) (trust-building) periods. However, trust-building periods create social loss of payoffs, and there is a possibility that an asymmetric equilibrium with some players cooperating immediately, while others defect, may be more efficient. We show that there is a “fundamentally asymmetric” locally stable Nash equilibrium consisting of the most cooperative strategy (C-trigger with ending the partnership when betrayed) and the most noncooperative strategy, which plays D and ends the partnership immediately. When the deviation gain is relatively small, the fundamentally asymmetric equilibrium is neutrally stable against equilibrium entrants within trust-building strategies and is more efficient than any Nash equilibrium consisting of non-degenerate trust-building strategies. Our result indicates that behavioral diversity can be stable and beneficial for the society, even if players are free to escape from personalized punishments.

We consider the voluntarily separable repeated Prisoner's Dilemma model in which players randomly meet and form pairs to repeatedly play Prisoner's Dilemma only by mutual agreement. While the literature has dealt with the case of no information flow across partnerships, we consider the case in which players can issue a "reference letter" to verify at least that the partnership entered the cooperation phase. We show that such reference letters can be voluntarily provided by the partners even at some cost, and that the sheer existence of a letter shortens the trust-building periods and thus improves social efficiency. © 2011 Elsevier Inc.

Ordinary repeated games do not apply to real societies where one can cheat and escape from partners. We formulate a model of endogenous relationships that a player can unilaterally end and start with a randomly assigned new partner with no information flow. Focusing on two-person, two-action Prisoner's Dilemma, we show that the endogenous duration of partnerships generates a significantly different evolutionary stability structure from ordinary random matching games. Monomorphic equilibria require initial trust building, while a polymorphic equilibrium includes earlier cooperators than any strategy in monomorphic equilibria and is thus more efficient. This is due to the non-linearity of average payoffs. © 2009 The Review of Economic Studies Limited.

We formulate dynamic games which give a rationale to the firm size-wage effect that the sheer firm size increases wages. We postulate that past wages of large firms are known to new employees, while those of small firms are not. Large firms can credibly induce workers to expect high future wages and reduce turnover, while small firms have no choice but to be myopic and pay low wages. The equilibrium wage differential obtains under the same worker characteristics and production function. We provide empirical evidence that workers' expectations depend on firm size and affect wages as predicted by our model. © Japanese Economic Association 2004.

It is in workers' interest to leave their jobs if better work can be found, but imperfect information on outside opportunities impedes their job search. We describe two theories on workers' search using the organizational size as a proxy for work characteristics and derive hypotheses on how the organizational size distribution in a labor market affects job separations. We test the hypotheses with NLSY 79 data on job separations, finding that diversity in organizational sizes affects worker mobility. Workers are more likely to move within counties with many organizations larger than their current one or many organizations of different sizes and are more likely to leave counties lacking these characteristics.

The outside opportunity structure is important in predicting the likelihood and direction of job change but has received little attention. We view the ecology of organizations as a determinant of worker expectations of outside opportunity and connect characterizations of organizational size diversity and inequality with job matching and firm reputation theory on how worker expectations are affected by organizational characteristics. This leads to the predictions that greater organizational diversity and inequality within a sector of the labor market will cause more intrasector job changes and fewer intersector job changes. We test these predictions on intra- and interindustrial and regional job changes, yielding supportive results on both industrial and geographical job mobility. Comparison of the results suggests stronger evidence in favor of reputation than matching theory.

The outside opportunity structure is important in predicting the likelihood and direction of job change but has received little attention. Using reputation theory and matching theory we show that worker expectations are affected by organizational characteristics and therefore influences mobility.

We characterize the equilibria of grim trigger strategies of repeated games with outside offers. We show a computable bound to the equilibrium payoffs under grim-trigger strategies.

'Unlike usual contractual setting, when a worker can quit at each period, the timing of reward is crutial. We shos that immediate reward before quits is weakly optimal.'

Class assignment rules match multiple students to multiple classes. We show the necessary and sufficient condition for feasible assignments and a sufficient condition for strategy-proofness.