Pareto Optimality in Finite Horizon Cooperative Difference Games

Yaning Lin () and Weihai Zhang ()
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Yaning Lin: Shandong University of Technology, School of Mathematics and Statistics
Weihai Zhang: Shandong University of Science and Technology, College of Electrical Engineering and Automation

Chapter Chapter 7 in Essays on Pareto Optimality in Cooperative Games, 2022, pp 115-138 from Springer

Abstract: Abstract This chapter investigates Pareto optimality for the discrete-time systems in finite horizon. Utilizing the necessary and sufficient characterization of Pareto optimality, necessary conditions for the existence of Pareto solutions are derived. Then, some convex assumptions are proposed to ensure that the solution of necessary conditions is Pareto efficient. Next, the LQ case is discussed. In addition to the existence conditions, the characterization of Pareto solutions is also studied. It is shown that the solvability of the related difference Riccati equation (DRE) provides a sufficient condition under which Pareto-efficient strategies are equivalent to the weighted sum optimal controls and all Pareto solutions are derived based on the solutions of a set of difference equations. Two examples show the effectiveness of the proposed results.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-19-5049-0_7

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DOI: 10.1007/978-981-19-5049-0_7

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