16 research outputs found
Algorithms for generalized potential games with mixed-integer variables
We consider generalized potential games, that constitute a fundamental subclass of generalized Nash equilibrium problems. We propose different methods to compute solutions of generalized potential games with mixed-integer variables, i.e., games in which some variables are continuous while the others are discrete. We investigate which types of equilibria of the game can be computed by minimizing a potential function over the common feasible set. In particular, for a wide class of generalized potential games, we characterize those equilibria that can be computed by minimizing potential functions as Pareto solutions of a particular multi-objective problem, and we show how different potential functions can be used to select equilibria. We propose a new Gauss–Southwell algorithm to compute approximate equilibria of any generalized potential game with mixed-integer variables. We show that this method converges in a finite number of steps and we also give an upper bound on this number of steps. Moreover, we make a thorough analysis on the behaviour of approximate equilibria with respect to exact ones. Finally, we make many numerical experiments to show the viability of the proposed approaches
Optimal resource allocation in femtocell networks based on Markov modeling of interferers' activity
Femtocell networks offer a series of advantages with respect to conventional cellular networks. However, a potential massive deployment of femto-access points (FAPs) poses a big challenge in terms of interference management, which requires proper radio resource allocation techniques. In this article, we propose alternative optimal power/bit allocation strategies over a time-frequency frame based on a statistical modeling of the interference activity. Given the lack of knowledge of the interference activity, we assume a Bayesian approach that provides the optimal allocation, conditioned to periodic spectrum sensing, and estimation of the interference activity statistical parameters. We consider first a single FAP accessing the radio channel in the presence of a dynamical interference environment. Then, we extend the formulation to a multi-FAP scenario, where nearby FAP's react to the strategies of the other FAP's, still within a dynamical interference scenario. The multi-user case is first approached using a strategic non-cooperative game formulation. Then, we propose a coordination game based on the introduction of a pricing mechanism that exploits the backhaul link to enable the exchange of parameters (prices) among FAP's
Gap functions for quasi-equilibria
An approach for solving quasi-equilibrium problems (QEPs) is proposed relying on gap functions, which allow reformulating QEPs as global optimization problems. The (generalized) smoothness properties of a gap function are analysed and an upper estimates of its Clarke directional derivative is given.
Monotonicity assumptions on both the equilibrium and constraining bifunctions are a key tool to guarantee that all the stationary points of a gap function actually solve QEP. A few classes of constraints satisfying such assumptions are identified covering a wide range of situations. Relying on these results, a descent method for solving QEP is devised and its convergence proved. Finally, error bounds are given in order to guarantee the boundedness of the sequence generated by the algorithm
Communication-Efficient Distributed Machine Learning over Strategic Networks: A Two-Layer Game Approach
This paper considers a game-theoretic framework for distributed learning
problems over networks where communications between nodes are costly. In the
proposed game, players decide both the learning parameters and the network
structure for communications. The Nash equilibrium characterizes the tradeoff
between the local performance and the global agreement of the learned
classifiers. We introduce a two-layer algorithm to find the equilibrium. The
algorithm features a joint learning process that integrates the iterative
learning at each node and the network formation. We show that our game is
equivalent to a generalized potential game in the setting of symmetric
networks. We study the convergence of the proposed algorithm, analyze the
network structures determined by our game, and show the improvement of the
social welfare in comparison with the distributed learning over non-strategic
networks. In the case study, we deal with streaming data and use telemonitoring
of Parkinson's disease to corroborate the results.Comment: 20 pages, 9 figure