Some thoughts on saddle-point conditions and information structures in zero-sum differential games

Research output: Contribution to journalArticlepeer-review

Abstract

For a very simple two-stage, linear-quadratic, zero-sum difference game with dynamic information structure, we show that (i) there exist nonlinear saddle-point strategies which require the same existence conditions as the well-known linear, closed-loop, no-memory solution and (ii) there exist both linear and nonlinear saddle-point strategies which require more stringent conditions than the unique open-loop solution. We then discuss the implication of this result with respect to the existence of saddle points in zero-sum differential games for different information patterns.

Original languageEnglish (US)
Pages (from-to)165-170
Number of pages6
JournalJournal of Optimization Theory and Applications
Volume18
Issue number1
DOIs
StatePublished - Jan 1 1976
Externally publishedYes

Keywords

  • Game theory
  • information patterns
  • linear-quadratic games
  • saddle-point solutions
  • zero-sum differential games

ASJC Scopus subject areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

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