dc.contributor.author | Mavronicolas, Marios | en |
dc.contributor.author | Monien, Burkhard | en |
dc.contributor.editor | Böckenhauer, Hans-Joachim | en |
dc.contributor.editor | Komm, Dennis | en |
dc.contributor.editor | Unger, Walter | en |
dc.coverage.spatial | Cham | en |
dc.creator | Mavronicolas, Marios | en |
dc.creator | Monien, Burkhard | en |
dc.date.accessioned | 2021-01-22T10:47:33Z | |
dc.date.available | 2021-01-22T10:47:33Z | |
dc.date.issued | 2018 | |
dc.identifier.isbn | 978-3-319-98355-4 | |
dc.identifier.uri | http://gnosis.library.ucy.ac.cy/handle/7/62333 | |
dc.description.abstract | 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 V=E+RV=E+R{\mathsf {V}} = {\mathsf {E}} + {\mathsf {R}} of expectation EE{\mathsf {E}} and a risk valuation RR{\mathsf {R}} of their costs | en |
dc.description.abstract | RR{\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 VV{\mathsf {V}}-equilibrium, no player can unilaterally reduce her cost.The results presented in this paper show that the question whether a 2-player game with such risk-modeling valuations VV{\mathsf {V}} has a VV{\mathsf {V}}-equilibrium is strongly NPNP{\mathcal {NP}}-hard under very mild assumptions. We only have to ask that the valuation functions are strictly quasiconcave or that they fulfill the Weak-Equilibrium-for-Expectation property and that additionally some 2-strategy game has no VV{\mathsf {V}}-equilibrium. These conditions are fulfilled for the functions from Markowitz’s Mean-Variance approach like E+Var,E+SDE+Var,E+SD{\mathsf {E}} + {\mathsf {Var}}, {\mathsf {E}} + {\mathsf {SD}} and the Sharpe Ration, and also for Conditional Value-at-Risk, recently very popular for modeling volatile economic circumstances. | en |
dc.language.iso | en | en |
dc.publisher | Springer International Publishing | en |
dc.source | Adventures Between Lower Bounds and Higher Altitudes: Essays Dedicated to Juraj Hromkovič on the Occasion of His 60th Birthday | en |
dc.source.uri | https://doi.org/10.1007/978-3-319-98355-4_23 | |
dc.title | NP-hardness of equilibria in case of risk-averse players | en |
dc.type | info:eu-repo/semantics/bookChapter | |
dc.description.startingpage | 409 | |
dc.description.endingpage | 422 | |
dc.author.faculty | 002 Σχολή Θετικών και Εφαρμοσμένων Επιστημών / Faculty of Pure and Applied Sciences | |
dc.author.department | Τμήμα Πληροφορικής / Department of Computer Science | |
dc.type.uhtype | Book Chapter | en |