One-sided adaptation for infinite-horizon linear quadratic N-person non-zero-sum dynamic games and sensitivity analysis

To cite this Article Tan, Xiaohuan and Cruz Jr, Jose B.(2008)'One-sided adaptation for infinite-horizon linear quadratic N-person non-zero-sum dynamic games and sensitivity analysis' This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution , reselling , loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. In this paper, we consider a class of infinite-horizon discrete-time linear quadratic N-person games, in which one of the players lacks complete information about the game. With the assumptions of a perfect state information pattern and steady state feedback strategies, we convert the original game problem into a multivariable adaptive control problem by making use of the concept of fictitious play and the scheme of adaptive control. For the proposed adjustment procedure, we prove that each element of the estimates converges to its corresponding true value under the condition of persistent excitation. We also carry out a sensitivity analysis of performance indices with respect to the embedded unknowns by using multiple models. 1. Introduction Most research in game theory has been devoted to the class of games with complete information, in which all decision makers have knowledge of the mathematical structures as well as the exact values of the parameters of games. Motivated by strategic bidding problems (David 1993) in the deregulated electricity spot market, in this paper we study a class of games with incomplete information. In the electricity spot market, power suppliers have to bid against others to be scheduled to supply power and thus make profits. The interactive decision making behaviours and the conflict of interest embedded in the situation make game theory an appropriate framework to study the bidding process. and Lawarree 2002) apply game theory to the strategic bidding problem, modelling the auctions as games with complete information. However, since the power generation cost functions of competing power suppliers are usually private information, it is not reasonable …