Competitive experimentation with private information: The survivor's curse

We study a winner-take-all R&D race between two firms that are privately informed about the arrival rate of an invention. Over time, each firm only observes whether the opponent left the race or not. The equilibrium displays a strong herding effect, that we call a ‘survivor's curse.’ Unlike in the case of symmetric information, the two firms may quit the race (nearly) simultaneously even when their costs and benefits for research differ significantly.     

The Nash-threats folk theorem with communication and approximate common knowledge in two player games

We show that the use of communications to coordinate equilibria generates a Nash-threats folk theorem in two-player games with “almost public” information. The results generalize to the n-person case. However, the two-person case is more difficult because it is not possible to sustain equilibria by comparing the reports of different players, and using these “third parties” to effectively enforce contracts.     

Iterated potential and robustness of equilibria

For any given set-valued solution concept, it is possible to consider iterative elimination of actions outside the solution set. This paper applies such a procedure to define the concept of iterated monotone potential maximizer (iterated MP-maximizer). It is shown that under some monotonicity conditions, an iterated MP-maximizer is robust to incomplete information [A. Kajii, S. Morris, The robustness of equilibria to incomplete information, Econometrica 65 (1997) 1283-1309] and absorbing and globally accessible under perfect foresight dynamics for a small friction [A. Matsui, K. Matsuyama, An approach to equilibrium selection, J. Econ. Theory 65 (1995) 415-434]. Several simple sufficient conditions under which a game has an iterated MP-maximizer are also provided.     

Dynamic signaling and market breakdown

We consider the effects a public revelation of information (e.g. rating, grade) has on trading in a dynamic signaling model. Competing buyers offer prices to a privately informed seller who can reject them and delay trade. Delay is costly and the seller has no commitment to its duration. The external public information allows for signaling in equilibrium. More interestingly, we characterize the dynamics of trade and prices. If signals are noisy, no trade takes place just before the revelation of external information. If signals are fully revealing, then trade occurs even close to revelation, however, transaction prices are discontinuous.     

A belief-based approach to the repeated prisoners' dilemma with asymmetric private monitoring

This paper extends the belief-based approach to the repeated prisoners' dilemma with asymmetric private monitoring. We first find that the previous belief-based techniques [T. Sekiguchi, Efficiency in repeated prisoners' dilemma with private monitoring, J. Econ. Theory 76 (1997) 345-361; V. Bhaskar, I. Obara, Belief-based equilibria in the repeated prisoners' dilemma with private monitoring, J. Econ. Theory 102 (2002) 40-69] cannot succeed when players' private monitoring technologies are sufficiently different. We then modify the previous belief-based approach by letting the player with smaller observation errors always randomize between cooperate and defect along the cooperative path of the play. We show that with vanishing observation errors, efficiency and a folk theorem can be approximated using our modified belief-based strategies.     

Investment timing and learning externalities

We study a duopoly model of investment, in which each player learns about the quality of a common value project by observing some public background information, and possibly the experience of his rival. Investment costs are private information, and the background signal takes the form of a Poisson process conditional on the quality of the project being low. The resulting attrition game has a unique, symmetric equilibrium, which depends on initial public beliefs. We determine the impact of changes in the cost and signal distributions on investment timing, and how equilibrium is affected when a first-mover advantage is introduced.     

Reputation and exogenous private learning

Short-run competitors in the chain store game receive noisy signals of the long-run incumbent firm's type. The history of signals, which in the limit is fully revealing, is observable to the competitors but possibly not to the incumbent. As long as there is sufficient noise in the signals, then in any equilibrium a patient weak incumbent obtains a payoff strictly higher than her minmax payoff.     

Delay and information aggregation in stopping games with private information

We consider equilibrium timing decisions in a model with a large number of players and informational externalities. The players have private information about a common payoff parameter that determines the optimal time to invest. They learn from each other in real time by observing past investment decisions. We develop new methods of analysis for such large games, and we give a full characterization of symmetric equilibria. We show that the equilibrium statistical inferences are based on an exponential learning model. Although the beliefs converge to truth, learning takes place too late. Ex-ante welfare is strictly between that without observational learning and that with full information.     

Dynamic mechanism design with hidden income and hidden actions

We develop general recursive methods to solve for optimal contracts in dynamic principal-agent environments with hidden states and hidden actions. Starting from a general mechanism with arbitrary communication, randomization, full history dependence, and without restrictions on preferences or technology, we show that the optimal contract can be implemented as a recursive direct mechanism. A curse of dimensionality which arises from the interaction of hidden income and hidden actions can be overcome by introducing utility bounds for behavior off the equilibrium path. Environments with multiple actions are implemented using multiple layers of such off-path utility bounds.     

Do new brooms sweep clean? When and why dismissing a manager increases the subordinates’ performance

If a manager stays in office for a long time he will have learned much about his subordinates. Thus competition among them will be weak as the manager has made up his mind who is suited best for which position. With a new manager the “race” for favorable tasks is restarted leading subordinates to exert higher effort. But for the firm-owner the trade-off arises that with a new manager effort is larger but the quality of task allocation is worse since information is lost. The optimal dismissal policy will be nonmonotonic in the expected heterogeneity of the subordinates’ abilities.     

A limit characterization of belief-free equilibrium payoffs in repeated games

The present paper studies repeated games with private monitoring, and characterizes the set of belief-free equilibrium payoffs in the limit as the discount factor approaches one and the noise on private information vanishes. Contrary to the conjecture by Ely et al. [J.C. Ely, J. Hörner, W. Olszewski, Belief-free equilibria in repeated games, Econometrica 73 (2005) 377-415], the equilibrium payoff set is computed by the same formula, no matter how many players there are. As an application of this result, a version of the folk theorem is established for N-player prisoner's dilemma games.     

Efficiency results in N player games with imperfect private monitoring

We demonstrate that efficiency is achievable in a certain class of N player repeated games with private, almost perfect monitoring. Our equilibrium requires only one period memory and can be implemented by two state automata. Furthermore, we show that this efficiency result holds with any degree of accuracy of monitoring if private signals are hemiindependent. Whereas most existing research focuses on two player cases or only a special example of N player games, our results are applicable to a wide range of N player games of economic relevance, such as trading goods games and price-setting oligopolies.     

Folk theorem with communication

This paper proves a new folk theorem for repeated games with private monitoring and communication, extending the idea of delayed communication in Compte [O. Compte, Communication in repeated games with imperfect private monitoring, Econometrica 66 (1998) 597-626] to the case where private signals are correlated.The sufficient condition for the folk theorem is generically satisfied with more than two players, even when other well-known conditions are not. The folk theorem also applies to some two-players repeated games.     

UNIQUENESS OF EQUILIBRIUM PAYOFFS IN FINITELY REPEATED GAMES WITH IMPERFECT MONITORING*

This paper examines when a finitely repeated game with imperfect monitoring has a unique equilibrium payoff vector. This problem is nontrivial under imperfect monitoring, because uniqueness of equilibrium (outcome) in the stage game does not extend to finitely repeated games. A (correlated) equilibrium is equilibrium minimaxing if any player's equilibrium payoff is her minimax value when the other players choose a correlated action profile from the actions played in the equilibrium. The uniqueness result holds if all stage game correlated equilibria are equilibrium minimaxing and have the same payoffs. The uniqueness result does not hold under weaker conditions.     

Coordination failure in repeated games with private monitoring

Players coordinate continuation play in repeated games with public monitoring. We investigate the robustness of such equilibrium behavior with respect to ex-ante small private-monitoring perturbations. We show that with full support of public signals, no perfect public equilibrium is robust if it induces a “regular” 2×2$2\times 2$ coordination game in the continuation play. This regularity condition is violated in all belief-free equilibria. Indeed, with an individual full rank condition, every interior belief-free equilibrium is robust. We also analyze block belief-free equilibria and point out that the notion of robustness is sensitive to whether we allow for uninterpretable signals.     

Mechanism design with side payments: Individual rationality and iterative dominance

We investigate the collective decision with incomplete information and side payments. We show that a direct mechanism associated with the social choice function that satisfies budget balancing, incentive compatibility, and interim individual rationality exists for generic prior distributions. We consider the possibility that a risk-averse principal extracts full surplus in agency problems with adverse selection. With regard to generic prior distributions, we show that there exists a modified direct mechanism associated with the virtual social choice function, which satisfies budget balancing and interim individual rationality, such that truth telling is the unique three times iteratively undominated message rule profile.     

Interlinkage and Generous Tit‐for‐Tat Strategy

We investigate an infinitely‐repeated prisoners' dilemma with imperfect monitoring and consider the possibility that the interlinkage of the players' distinct activities enhances implicit collusion. We show a necessary and sufficient condition for the existence of a generous tit‐for‐tat Nash equilibrium. Such an equilibrium, if it exists, is unique. This equilibrium achieves approximate efficiency when monitoring is almost perfect, where the discount factors are fixed.     

Incentive compatibility and differentiability: New results and classic applications

We provide several generalizations of Mailath?s (1987) [9] result that in games of asymmetric information with a continuum of types incentive compatibility plus separation implies differentiability of the informed agent?s strategy. The new results extend the theory to classic models in finance such as Leland and Pyle (1977) [8], Glosten (1989) [4], and DeMarzo and Duffie (1999) [3], that were not previously covered.     

Endogenous supply of fiat money

We consider whether reputation concerns can discipline the behavior of a long-lived self-interested agent who has a monopoly over the provision of fiat money. We obtain that when this agent can commit to a choice of money supply, there is a monetary equilibrium where it never overissues. We show, however, that monetary equilibria with no overissue do not exist when there is no commitment. This happens because the incentives this agent has to maintain a reputation for providing valuable currency disappear once its reputation is high enough. More generally, we prove that in the absence of commitment overissue happens infinitely often in any monetary equilibrium. We conclude by showing that imperfect memory can restore the positive result obtained with commitment.     

Pigouvian pricing and stochastic evolutionary implementation

We study the implementation of efficient behavior in settings with externalities. A planner would like to ensure that a group of agents make socially optimal choices, but he only has limited information about the agents’ preferences, and can only distinguish individual agents through the actions they choose. We describe the agents’ behavior using a stochastic evolutionary model, assuming that their choice probabilities are given by the logit choice rule. We prove that there is a simple price scheme with the following property: regardless of the realization of preferences, a group of agents subjected to the price scheme will spend the vast majority of time in the long run behaving efficiently. The price scheme defines a game that may possess multiple equilibria, but we are able to obtain a unique and efficient selection from this set because of the stochastic nature of the agents’ choice rule. We conclude by comparing the performance of our price scheme with that of VCG mechanisms.