The Vector-valued Maximin

The Vector-valued Maximin

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This work is devoted to the investigation and solution of differential games with a vector-valued pay-off function. Slater-, Pareto- and Geoffrion-optimal strategies are defined for such a game, and their positive and negative properties are examined. A new class of solutions called vector-valued guarantees is proposed and their properties examined. According to the authors, this new approach is superior primarily because it has the properties of equivalence and interchangeability - antagonistic players should be able to achieve guaranteed results simultaneously. The approach is tested in a competition problem, as well as a pursuit game with noise. This book should be useful for students, postgraduates and specialists who are investigating the different fields of applied mathematics, control theory, economics and near-by directions of scientific knowledge.
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Product details

  • Hardback | 312 pages
  • 165.1 x 230 x 25.4mm | 730g
  • Academic Press Inc
  • San Diego, United States
  • English
  • references
  • 0127799508
  • 9780127799506

Table of contents

Quasimotions and their properties; Slater optimality; Pareto optimality; Geoffrion optimality; vector saddle points; vector-valued guarantees; competition problem; a pursuit game with noise. Appendices: some notions of topology; multivalued mappings semicontinuous above; additional propositions from theory of multicultural problems; vector-valued maximins in "static" problems.
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