  In dynamic games with asymmetric information structure, the widely used
concept of equilibrium is perfect Bayesian equilibrium (PBE). This is expressed
as a strategy and belief pair that simultaneously satisfy sequential
rationality and belief consistency. Unlike symmetric information dynamic games,
where subgame perfect equilibrium (SPE) is the natural equilibrium concept, to
date there does not exist a universal algorithm that decouples the
interdependence of strategies and beliefs over time in calculating PBE. In this
paper we find a subset of PBE for an infinite horizon discounted reward
asymmetric information dynamic game. We refer to it as Structured PBE or SPBE;
in SPBE, any agents' strategy depends on the public history only through a
common public belief and on private history only through the respective agents'
latest private information (his private type). The public belief acts as a
summary of all the relevant past information and it's dimension does not
increase with time. The motivation for this comes the common information
approach proposed in Nayyar et al. (2013) for solving decentralized team
(non-strategic) resource allocation problems with asymmetric information. We
calculate SPBE by solving a single-shot fixed-point equation and a
corresponding forward recursive algorithm. We demonstrate our methodology by
means of a public goods example.
