Insights on the Theory of Robust Games

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Tác giả: Giovanni Paolo Crespi, Davide Radi, Matteo Rocca

Ngôn ngữ: eng

Ký hiệu phân loại: 519.3 Game theory

Thông tin xuất bản: 2020

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Bộ sưu tập: Metadata

ID: 163898

A robust game is a distribution-free model to handle ambiguity generated by a bounded set of possible realizations of the values of players' payoff functions. The players are worst-case optimizers and a solution, called robust-optimization equilibrium, is guaranteed by standard regularity conditions. The paper investigates the sensitivity to the level of uncertainty of this equilibrium. Specifically, we prove that it is an epsilon-Nash equilibrium of the nominal counterpart game, where the epsilon-approximation measures the extra profit that a player would obtain by reducing his level of uncertainty. Moreover, given an epsilon-Nash equilibrium of a nominal game, we prove that it is always possible to introduce uncertainty such that the epsilon-Nash equilibrium is a robust-optimization equilibrium. An example shows that a robust Cournot duopoly model can admit multiple and asymmetric robust-optimization equilibria despite only a symmetric Nash equilibrium exists for the nominal counterpart game.Comment: 28 pages. 3 figures. Paper presented at the INFORMS Annual Meeting in Houston~(2017), at the 14th Viennese Conference on Optimal Control and Dynamic Games, Vienna~(2019), at the XLII AMASES Annual Meeting in Naples~(2018), at the 10th Workshop Dynamic Models in Economics and Finance -- MDEF in Urbino~(2018), at the 19th Annual SAET Conference in Ischia~(2019)
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