||Gradual Adjustment and Equilibrium Uniqueness under Noisy Monitoring
Kasahara, AkitadaIijima, Ryota
Institute of Social and Economic Research Discussion Papers
54 , 2016-03 , The Institute of Social and Economic Research, Osaka University
We study the implications of ﬂexible adjustment in strategic interactions using a class of ﬁnite-horizon models in continuous time. Players take costly actions to aﬀect the evolution of state variables that are commonly observable and perturbed by Brownian noise. The values of these state variables inﬂuence players’ terminal payoﬀs at the deadline, as well as their ﬂow payoﬀs. In contrast to the static case, the equilibrium is unique under a general class of terminal payoﬀ functions. Our characterization of the equilibrium builds on recent developments in the theory of backward stochastic diﬀerential equations (BSDEs). We use this tool to analyze applications, including team production, hold-up problems, and dynamic contests. In a team production model, the unique equilibrium selects an eﬃcient outcome when frictions vanish.