Aggregative games provide a rich abstraction to model strategic multi-agent interactions. We focus on learning local aggregative games, where the payoff of each player is a function of its own action and the aggregate behavior of its neighbors in a connected digraph. We show the existence of a pure strategy epsilon-Nash equilibrium in such games when the payoff functions are convex or sub-modular. We prove an information theoretic lower bound, in a value oracle model, on approximating the structure of the digraph with non-negative monotone sub-modular cost functions on the edge set cardinality. We also introduce gamma-aggregative games that generalize local aggregative games, and admit epsilon-Nash equilibrium that are stable with respect to small changes in some specified graph property. Moreover, we provide estimation algorithms for the game theoretic model that can meaningfully recover the underlying structure and payoff functions from real voting data.

In contrast, in a game theoretic setting, myopic strategic interactions among players lead to a Nash equilibrium or locally optimal configuration rather than highest scoring global configuration.

Structured prediction methods have been remarkably successful in learning mappings between input observations and output configurations [1; 2; 3]. The central guiding formulation involves learning a scoring function that recovers the configuration as the highest scoring assignment. In contrast, in a game theoretic setting, myopic strategic interactions among players lead to a Nash equilibrium or locally optimal configuration rather than highest scoring global configuration. Learning games therefore involves, at best, enforcement of local consistency constraints as recently advocated [4].

Aggregative games provide a rich abstraction to model strategic multi-agent interactions. We focus on learning local aggregative games, where the payoff of each player is a function of its own action and the aggregate behavior of its neighbors in a connected digraph. We show the existence of a pure strategy epsilon-Nash equilibrium in such games when the payoff functions are convex or sub-modular. We prove an information theoretic lower bound, in a value oracle model, on approximating the structure of the digraph with non-negative monotone sub-modular cost functions on the edge set cardinality. We also introduce gamma-aggregative games that generalize local aggregative games, and admit epsilon-Nash equilibrium that are stable with respect to small changes in some specified graph property.

Aggregative games provide a rich abstraction to model strategic multi-agent interactions. We focus on learning local aggregative games, where the payoff of each player is a function of its own action and the aggregate behavior of its neighbors in a connected digraph. We show the existence of a pure strategy epsilon-Nash equilibrium in such games when the payoff functions are convex or sub-modular. We prove an information theoretic lower bound, in a value oracle model, on approximating the structure of the digraph with non-negative monotone sub-modular cost functions on the edge set cardinality. We also introduce gamma-aggregative games that generalize local aggregative games, and admit epsilon-Nash equilibrium that are stable with respect to small changes in some specified graph property. Moreover, we provide estimation algorithms for the game theoretic model that can meaningfully recover the underlying structure and payoff functions from real voting data.