Stochastic Discrete-Time Nash Games with Constrained State Estimators

A.R. Kian, J.B. Cruz and M. A. Simaan
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A.R. Kian: Genscape
J.B. Cruz: Ohio State University
M. A. Simaan: University of Pittsburgh

Journal of Optimization Theory and Applications, 2002, vol. 114, issue 1, No 7, 188 pages

Abstract: Abstract In this paper, we consider stochastic linear-quadratic discrete-time Nash games in which two players have access only to noise-corrupted output measurements. We assume that each player is constrained to use a linear Kalman filter-like state estimator to implement his optimal strategies. Two information structures available to the players in their state estimators are investigated. The first has access to one-step delayed output and a one-step delayed control input of the player. The second has access to the current output and a one-step delayed control input of the player. In both cases, statistics of the process and statistics of the measurements of each player are known to both players. A simple example of a two-zone energy trading system is considered to illustrate the developed Nash strategies. In this example, the Nash strategies are calculated for the two cases of unlimited and limited transmission capacity constraints.

Keywords: stochastic linear-quadratic systems; nonzero-sum discrete-time Nash games; optimal Nash strategies; estimator-controller; stochastic dynamic programming; Nash equilibrium (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1023/A:1015468205980

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