2019/09/10 by Nasimeh Heydaribeni, Heydaribeni, Nasimeh, Achilleas Anastasopoulos +1
Computer Science · Economics, Econometrics and Finance · Engineering · Mathematics · #Bayesian Modeling and Causal Inference #Economic theories and models #FOS: Economics and business #FOS: Electrical engineering #General Economics (econ.GN) #Markov Chains and Monte Carlo Methods #Systems and Control (eess.SY) #cs.SY #econ.GN #eess.SY #electronic engineering #information engineering #q-fin.EC
paper · pdf · doi:10.48550/arxiv.1909.04834
openalex publication_date 2019/09/10 · arxiv created 2019/09/11 · arxiv updated 2019/09/12 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28
We consider a non-zero-sum linear quadratic Gaussian (LQG) dynamic game with asymmetric information. Each player observes privately a noisy version of a (hidden) state of the world V, resulting in dependent private observations. We study perfect Bayesian equilibria (PBE) for this game with equilibrium strategies that are linear in players' private estimates of V. The main difficulty arises from the fact that players need to construct estimates on other players' estimate on V, which in turn would imply that an infinite hierarchy of estimates on estimates needs to be constructed, rendering the problem unsolvable. We show that this is not the case: each player's estimate on other players' estimates on V can be summarized into her own estimate on V and some appropriately defined public information. Based on this finding we characterize the PBE through a backward/forward algorithm akin to dynamic programming for the standard LQG control problem. Unlike the standard LQG problem, however, Kalman filter covariance matrices, as well as some other required quantities, are observation-dependent and thus cannot be evaluated off-line through a forward recursion.