  This paper presents a new variant of fictitious play (FP) called
team-fictitious-play (Team-FP) that can reach equilibrium in multi-team
competition, different from the other variants of FP. We specifically focus on
zero-sum potential team games with network separable interactions (ZSPTGs),
unifying potential games (if there is a single team) and zero-sum polymatrix
games (if each team has a single member) due to their wide range of
applications from robotics to financial markets beyond two-team games. Similar
to the FP dynamics, in Team-FP, agents follow a simple behavioral rule where
they respond (with some inertia and exploration in the update of actions) to
the last actions of the neighboring team members and the beliefs formed about
the other neighbors' strategies as if the opponents are playing according to
some stationary strategy. We show the almost sure convergence of the empirical
averages of teams' action profiles to near team-Nash equilibrium in ZSPTGs
under standard assumptions on the step sizes used. We formulate a bound on the
approximation error, decaying with the exploration in the agents' responses. We
further examine the performance of the Team-FP dynamics numerically.
