Distributed seeking of Nash equilibria in mobile sensor networks

Abstract

Abstract-In this paper we consider the problem of distributed convergence to a Nash equilibrium based on minimal information about the underlying noncooperative game. We assume that the players/agents generate their actions based only on measurements of local cost functions, which are corrupted with additive noise. Structural parameters of their own and other players' costs, as well as the actions of the other players are unknown. Furthermore, we assume that the agents may have dynamics: their actions can not be changed instantaneously. We propose a method based on a stochastic extremum seeking algorithm with sinusoidal perturbations and we prove its convergence, with probability one, to a Nash equilibrium. We discuss how the proposed algorithm can be adopted for solving coordination problems in mobile sensor networks, taking into account specific motion dynamics of the sensors. The local cost functions can be designed such that some specific overall goal is achieved. We give an example in which each agent/sensor needs to fulfill a locally defined goal, while maintaining connectivity with neighboring agents. The proposed algorithms are illustrated through simulations.

Distributed mobility and power control for noncooperative robotic ad hoc and sensor networks

“…There has been a large surge of interest in treating these systems in the game theoretic framework, which is a natural approach to cooperative control problems (e.g., [6], [11], [12]), and has been shown to be effective for dealing with resource allocation problems in networking (e.g., [13], [14]). Specifically, the effectiveness of game theoretic approach to power control in wireless networks has been shown in the existing literature (e.g., [14]- [18] and references therein).…”

Nash equilibrium seeking with infinitely-many players

“…In [4], a synchronous distributed learning algorithm, where players remember their own actions and utility values from the previous two time steps, is shown to converge in probability to the set of restricted Nash equilibria. An approach, which is similar to our Nash seeking method for games with finitely-many players (found in [5], [6], [7]), is studied in [8] to solve coordination problems in mobile sensor networks. A comprehensive treatment of static and dynamic noncooperative game theory can be found in [9].…”

Distributed convergence to Nash equilibria by adversarial networks with directed topologies

“…It is also worth noting that finding the saddle point of function using (sub)gradient dynamics has also been studied in discrete time [11], [13], [14]. The distributed computation of Nash equilibria in noncooperative games has been investigated in different contexts, see for example [15], [16], [17].…”