  In this paper, we present a model of a game among teams. Each team consists
of a homogeneous population of agents. Agents within a team are cooperative
while the teams compete with other teams. The dynamics and the costs are
coupled through the empirical distribution (or the mean field) of the state of
agents in each team. This mean-field is assumed to be observed by all agents.
Agents have asymmetric information (also called a non-classical information
structure). We propose a mean-field based refinement of the Team-Nash
equilibrium of the game, which we call mean-field Markov perfect equilibrium
(MF-MPE). We identify a dynamic programming decomposition to characterize
MF-MPE. We then consider the case where each team has a large number of players
and present a mean-field approximation which approximates the game among
large-population teams as a game among infinite-population teams. We show that
MF-MPE of the game among teams of infinite population is easier to compute and
is an $\varepsilon$-approximate MF-MPE of the game among teams of finite
population.
