Structured Equilibria for Dynamic Games with Asymmetric Information and Dependent Types

Nasimeh Heydaribeni () and Achilleas Anastasopoulos
Additional contact information
Nasimeh Heydaribeni: Department of Electrical and Computer Engineering, University of California San Diego, La Jolla, CA 92093, USA
Achilleas Anastasopoulos: Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI 48109, USA

Games, 2025, vol. 16, issue 2, 1-37

Abstract: We consider a dynamic game with asymmetric information where each player privately observes a noisy version of a (hidden) state of the world V , resulting in dependent private observations. We study the structured perfect Bayesian equilibria (PBEs) that use private beliefs in their strategies as sufficient statistics for summarizing their observation history. The main difficulty in finding the appropriate sufficient statistic (state) for the structured strategies arises from the fact that players need to construct (private) beliefs on other players’ private beliefs on V , which, in turn, would imply that one needs to construct an infinite hierarchy of beliefs, thus rendering the problem unsolvable. We show that this is not the case: each player’s belief on other players’ beliefs on V can be characterized by her own belief on V and some appropriately defined public belief. We then specialize this setting to the case of a Linear Quadratic Gaussian (LQG) non-zero-sum game, and we characterize structured PBEs with linear strategies that can be found through a backward/forward algorithm akin to dynamic programming for the standard LQG control problem. Unlike the standard LQG problem, however, some of the required quantities for the Kalman filter are observation-dependent and, thus, cannot be evaluated offline through a forward recursion.

Keywords: dynamic games with asymmetric information; perfect Bayesian equilibrium (PBE); structured equilibria; Linear Quadratic Gaussian (LQG) games (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2025
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2073-4336/16/2/12/pdf (application/pdf)
https://www.mdpi.com/2073-4336/16/2/12/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jgames:v:16:y:2025:i:2:p:12-:d:1604023

Access Statistics for this article

Games is currently edited by Ms. Susie Huang

More articles in Games from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().