Robust Multiple Objective Game Theory

H. Yu () and H. M. Liu ()
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H. Yu: Chongqing University
H. M. Liu: Chongqing University

Journal of Optimization Theory and Applications, 2013, vol. 159, issue 1, No 15, 272-280

Abstract: Abstract In this paper, we propose a distribution-free model instead of considering a particular distribution for multiple objective games with incomplete information. We assume that each player does not know the exact value of the uncertain payoff parameters, but only knows that they belong to an uncertainty set. In our model, the players use a robust optimization approach for each of their objective to contend with payoff uncertainty. To formulate such a game, named “robust multiple objective games” here, we introduce three kinds of robust equilibrium under different preference structures. Then, by using a scalarization method and an existing result on the solutions for the generalized quasi-vector equilibrium problems, we obtain the existence of these robust equilibria. Finally, we give an example to illustrate our model and the existence theorems. Our results are new and fill the gap in the game theory literature.

Keywords: Robust multiple objective game; Robust optimization; Robust equilibrium; Weakly robust equilibrium (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (8)

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DOI: 10.1007/s10957-012-0234-z

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