\(\mathcal {NP}\)-Hardness of Equilibria in Case of Risk-Averse Players
2018
We study the complexity of deciding the existence of mixed equilibria for minimization games where players use valuations other than expectation to evaluate their costs. We consider risk-averse players seeking to minimize the sum \({\mathsf {V}} = {\mathsf {E}} + {\mathsf {R}}\) of expectation \({\mathsf {E}}\) and a risk valuation \({\mathsf {R}}\) of their costs; \({\mathsf {R}}\) is non-negative and vanishes exactly when the cost incurred to a player is constant over all choices of strategies by the other players. In a \({\mathsf {V}}\)-equilibrium, no player can unilaterally reduce her cost.
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