Seeking Optimal Equilibria for Coverage Games

Abstract

In this paper, we investigate the game theoretic coverage control whose objective is to lead agents to optimal configurations over a mission space. In particular, the objective of this paper is to achieve the control objective (i) in the absense of the perfect prior knowledge on importance of each point and (ii) in the presence of the action constraints. For this purpose, we first formulate coverage problems with two different global objective functions as so-called potential games. Then, we present a payoff-based learning algorithm determining actions based only on the past actual outcomes. The feature of the present algorithm is to allow an agent to take an irrational action. We also clarify a relation between a design parameter of the algorithm and the probability which agents take the optimal actions and prove that the probability can be arbitrarily increased. Then, we demonstrate the effectiveness of the present algorithm through experiments on a testbed.

Application of Irrational Decisions to Simple Experimentation to Guarantee Welfare Maximization

“…Assumption 1 is generally satisfied in a lot of scenarios, e.g. robotic networks and visual sensor networks [3], [7], [11]. Let us now introduce the following terminologies.…”

“…In this paper, the authors present a distributed computation procedure of the utility function U i (a) satisfying the objectives (i)-(iv) after a joint action a is determined. For potential games, a variety of learning algorithms determining agents' action selection rules have been presented in the literature [3], [6], [7], [11]- [13] and some of them compute an equilibrium a * or similar solutions by running the algorithm for a one-shot repeated game associated with strategic game Γ.…”

“…In particular, the authors show in [11] that adding the possibility of taking irrational decisions to the algorithm in [7] leads agents' actions to the potential function maximizers while [7] Algorithm 1 Simple Experimentation with Irrational Decisions Initialization: Joint action a is chosen randomly from A and executed. Then, resulting utility U i (a) is feedbacked and set a b…”

“…In the learning algorithm design, there is a practical challenge: (i) to guarantee social welfare maximization in the presence of (ii) physical constraints and (iii) limitations of communication (iv) without assuming fictitious future payoffs. A solution to such a problem is provided by so-called payoff-based learning [6], [7], [11]- [13] where each agent chooses his action based only on the prior payoffs. In particular, the authors' algorithm [11] takes irrational decisions to the algorithm in [7] and proved convergence to the potential function maximizers.…”

“…Similarly to [3], [7], [11], the above strategic-form game is also generalized to the constrained strategic-form game…”