Insights on the Theory of Robust Games
Abstract
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.
Keywords
Cite
@article{arxiv.2002.00225,
title = {Insights on the Theory of Robust Games},
author = {Giovanni Paolo Crespi and Davide Radi and Matteo Rocca},
journal= {arXiv preprint arXiv:2002.00225},
year = {2020}
}
Comments
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)