  Decentralized team problems where players have asymmetric information about
the state of the underlying stochastic system have been actively studied, but
games between such teams are less understood. We consider a general model of
zero-sum stochastic games between two competing teams. This model subsumes many
previously considered team and zero-sum game models. For this general model, we
provide bounds on the upper (min-max) and lower (max-min) values of the game.
Furthermore, if the upper and lower values of the game are identical (i.e., if
the game has a value), our bounds coincide with the value of the game. Our
bounds are obtained using two dynamic programs based on a sufficient statistic
known as the common information belief (CIB). We also identify certain
information structures in which only the minimizing team controls the evolution
of the CIB. In these cases, we show that one of our CIB based dynamic programs
can be used to find the min-max strategy (in addition to the min-max value). We
propose an approximate dynamic programming approach for computing the values
(and the strategy when applicable) and illustrate our results with the help of
an example.
