Cooperative Control via Congestion Game Approach

Abstract

The optimization of facility-based systems is considered. First, the congestion game is converted into a matrix form, so that the matrix approach is applicable. Then, a facilitybased system with a system performance criterion is considered. A necessary and sufficient condition is given to assure that the system is convertible into a congestion game with the given system performance criterion as its potential function by designing proper facility-cost functions. Using this technology, for a dynamic facility-based system the global optimization may be reached when each agent optimizes its payoff functions. Finally, the approach is extended to those systems which are partly or nearly convertible.

Optimization via game theoretic control

“…Using STP technique, Han et al. [ 11 ] obtained necessary and sufficient conditions for the solvability. Moreover, a design method is also proposed.…”

From STP to game-based control

“…Based on the potential equation and STP approach, some elementary studies have been done for this [79,80]. As for the game theoretic control of networked games, Bayesian game may provide a nice framework, because in a networked game a player can hardly get complete information [81].…”

Matrix Expression of Shapley Value in Graphical Cooperative Games

“…In our recent work [10], a simple matrix formula is obtained to calculate the Shapley value and the basic mathematical method is the semitensor product of matrices (STP), which is a generalization of the traditional matrix product [11]. is method has been successfully applied in the analysis and control problems of logical networks [12][13][14][15][16][17][18][19][20][21][22][23][24][25], and then it has been used in finite game theory [26][27][28][29][30], evolutionary games [31][32][33][34][35][36][37][38], finite automata [39,40], graph theory [41], etc. Unlike the canonical cooperative games being considered in [10], this paper studies a new class of cooperative games, called graphical cooperative games.…”