Takuo Sugaya

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 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.

Characterizing the limit set of perfect and public equilibrium payoffs with unequal discounting

We study repeated games with imperfect public monitoring and unequal dis- counting. We characterize the limit set of perfect and public equilibrium payoffs as discount factors converge to 1 with the relative patience between players fixed. We show that the pairwise and individual full rank conditions are sufficient for the folk theorem. In this paper, we characterize the equilibrium payoffs in repeated games with imperfect public monitoring and unequal discounting as discount factors converge to 1 with rel- ative patience fixed. In particular, we show that the pairwise and individual full rank conditions are sufficient for the folk theorem. Lehrer and Pauzner (1999) (henceforth LP) analyze two-player repeated games with perfect monitoring and unequal discounting. They define the set of feasible and sequen- tially individually rational (henceforth SIR) payoffs and show that in two-player games with perfect monitoring, the limit set of subgame perfect equilibrium payoffs coincides with that of SIR payoffs as discount factors converges to 1 with the relative patience fixed (the folk theorem). Recently, Chen and Takahashi (2012) extend the result to n-player games with perfect monitoring. This paper extends their results to imperfect public monitoring. While the proofs of both Lehrer and Pauzner (1999 )a ndChen and Takahashi (2012) are constructive, we em- ploy a nonconstructive approach using the recursive structure of the perfect and public equilibrium (henceforth PPE). Specifically, we attain a characterization of the set of PPE payoffs as discount factors converge to1. In addition, we characterize SIR payoffs. Given these characterizations, we show that if the pairwise and individual full rank conditions are satisfied, these two sets coincide, that is, the folk theorem holds.

Bounding equilibrium payoffs in repeated games with private monitoring: Bounding equilibrium payoffs

We provide a simple sufficient condition for the existence of a recursive upper bound on (the Pareto frontier of) the sequential equilibrium payoff set at a fixed discount factor in two-player repeated games with imperfect private monitoring. The bounding set is the sequential equilibrium payoff set with perfect monitoring and a mediator. We show that this bounding set admits a simple recursive characterization, which nonetheless necessarily involves the use of private strategies. Under our condition, this set describes precisely those payoff vectors that arise in equilibrium for some private monitoring structure, if either non-stationary monitoring or communication is allowed.

Making the Right Assignment: Optimal Contracting for Post-Hire Selection

Contracts that compensate workers if they choose to leave an organization —or Pay to Quit programs —are becoming increasingly prevalent in both established and new companies. In this paper, we address the puzzle of why such employment contracts are offered. We propose a model to study the optimal employment contract when firms face both an adverse selection problem —they need to find a good fit for the project — and a moral hazard problem — they need to incentize employee effort. Moreover, hiring the bad fit is costly for the firm because taking on a worker requires the firm to relinquish an outside option, coming for instance form being able to search for a new candidate. We fully characterize the optimal employment contract in this environment and derive the conditions under which offering a payment for quitting is optimal. ∗Foarta: Stanford Graduate School of Business, 655 Knight Way, Stanford, CA, 94305, tel: (650) 723-4058, email: ofoarta@stanford.edu. Sugaya: Stanford Graduate School of Business, 655 Knight Way, Stanford, CA, 94305, tel: (650) 724-3739, email: tsugaya@stanford.edu.Optimally reallocating human capital to tasks is key for an organization to successfully navigate a transition. We study how to design employment contracts to allocate employees to different valuable projects within an organization given two simultaneous challenges: The employees have private information about their own cost of effort, and they exert unobservable effort. The organization has two types of valuable projects, high and low impact, only the former of which requires effort. It would like to assign only an employee with low effort cost to the high-impact project. We characterize the optimal contract and show how it separates the employee types. The optimal contract menu pairs a higher probability of assignment to the high-impact project with a lower bonus in case of success. A fixed salary may also be used for the employees with high cost of effort, but only in limited cases. We link our results to job design features encountered in practice.

Maintaining Privacy in Cartels

It is conventional wisdom that transparency in cartels—monitoring of competitors’ prices, sales, and profits—facilitates collusion. However, in several recent cases cartels have instead worked to preserve the privacy of their participants’ actions and outcomes. Toward explaining this behavior, we show that cartels can sometimes sustain higher profits when actions and outcomes are observed only privately, because better information can hinder collusion by helping firms devise more profitable deviations from the collusive agreement. We provide conditions under which maintaining privacy is optimal for cartels that follow a market-segmentation strategy.