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Accuracy Functions and Robustness Tolerances Under the Game Theoretic Framework

Yury Nikulin, Marko M. Mäkelä, Olga Karelkina, Accuracy Functions and Robustness Tolerances Under the Game Theoretic Framework. TUCS Technical Reports 1013, Turku Centre for Computer Science, 2011.

Abstract:

A strategic game with a finite number of players where initial coefficients
(costs) of linear payoff functions are subject to perturbations is considered.
We define robust solution as a feasible solution which for a given set of realizations of uncertain parameters guarantees the minimum value of the worst-case relative regret among all feasible solutions. For different (either Pareto or Nash) equilibria principles considered, appropriate definitions of
the worst-case relative regret are specified. It is shown that these definitions are closely related to the concept of accuracy function being recently intensively studied in the literature. We also present the concept of robustness tolerances of a single cost vector associated with a strategy choice of a player. The tolerance is defined as the maximum level of perturbation of the cost
vector which does not destroy the game solution robustness. We present formulae allowing the calculation of the robustness tolerance with respect to a chosen equilibrium obtained for some initial costs. The results are illustrated with several numerical examples.

Files:

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BibTeX entry:

@TECHREPORT{tNiMaKa11a,
  title = {Accuracy Functions and Robustness Tolerances Under the Game Theoretic Framework},
  author = {Nikulin, Yury and Mäkelä, Marko M. and Karelkina, Olga},
  number = {1013},
  series = {TUCS Technical Reports},
  publisher = {Turku Centre for Computer Science},
  year = {2011},
  ISBN = {978-952-12-2611-3},
}

Belongs to TUCS Research Unit(s): Other

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