Local Aggregative Games
نویسندگان
چکیده
Aggregative games provide a rich abstraction to model strategic multi-agent interactions. We introduce 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 pure strategy -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 define a new notion of structural stability, and introduce γ-aggregative games that generalize local aggregative games and admit -Nash equilibrium that are stable with respect to small changes in some specified graph property. Moreover, we provide algorithms for our models that can meaningfully estimate the game structure and the parameters of the aggregator function from real voting data.
منابع مشابه
Continuous-time integral dynamics for Aggregative Game equilibrium seeking
In this paper, we consider continuous-time semidecentralized dynamics for the equilibrium computation in a class of aggregative games. Specifically, we propose a scheme where decentralized projected-gradient dynamics are driven by an integral control law. To prove global exponential convergence of the proposed dynamics to an aggregative equilibrium, we adopt a quadratic Lyapunov function argume...
متن کاملAggregate comparative statics
In aggregative games, each player’s payoff depends on her own actions and an aggregate of the actions of all the players (for example, sum, product or some moment of the distribution of actions). Many common games in industrial organization, political economy, public economics, and macroeconomics can be cast as aggregative games. In most of these situations, the behavior of the aggregate is of ...
متن کاملProjected-gradient algorithms for generalized equilibrium seeking in Aggregative Games are preconditioned Forward-Backward methods
We show that projected-gradient methods for the distributed computation of generalized Nash equilibria in aggregative games are preconditioned forward-backward splitting methods applied to the KKT operator of the game. Specifically, we adopt the preconditioned forward-backward design, recently conceived by Yi and Pavel in the manuscript “A distributed primal-dual algorithm for computation of ge...
متن کاملA distributed algorithm for average aggregative games with coupling constraints
We consider the framework of average aggregative games, where the cost function of each agent depends on his own strategy and on the average population strategy. We focus on the case in which the agents are coupled not only via their cost functions, but also via affine constraints on the average of the agents’ strategies. We propose a distributed algorithm that achieves an almost Nash equilibri...
متن کاملAggregative Games and Best-Reply Potentials
This paper introduces quasi-aggregative games and establishes conditions under which such games admit a best-reply potential. This implies existence of a pure strategy Nash equilibrium without any convexity or quasi-concavity assumptions. It also implies convergence of best-reply dynamics under some additional assumptions. Most of the existing literature’s aggregation concepts are special cases...
متن کامل