  We introduce a new class of context dependent, incomplete information games
to serve as structured prediction models for settings with significant
strategic interactions. Our games map the input context to outcomes by first
condensing the input into private player types that specify the utilities,
weighted interactions, as well as the initial strategies for the players. The
game is played over multiple rounds where players respond to weighted
aggregates of their neighbors' strategies. The predicted output from the model
is a mixed strategy profile (a near-Nash equilibrium) and each observation is
thought of as a sample from this strategy profile. We introduce two new
aggregator paradigms with provably convergent game dynamics, and characterize
the conditions under which our games are identifiable from data. Our games can
be parameterized in a transferable manner so that the sets of players can
change from one game to another. We demonstrate empirically that our games as
models can recover meaningful strategic interactions from real voting data.
