{"year":"2016","status":"public","intvolume":"       634","author":[{"last_name":"Monien","full_name":"Monien, Burkhard","first_name":"Burkhard"},{"first_name":"Marios","full_name":"Mavronicolas, Marios","last_name":"Mavronicolas"}],"publisher":"Elsevier","volume":634,"title":"The complexity of equilibria for risk-modeling valuations","_id":"144","user_id":"42447","citation":{"mla":"Monien, Burkhard, and Marios Mavronicolas. “The Complexity of Equilibria for Risk-Modeling Valuations.” <i>Theoretical Computer Science</i>, vol. 634, Elsevier, 2016, pp. 67–96, doi:<a href=\"https://doi.org/10.1016/j.tcs.2016.04.013\">10.1016/j.tcs.2016.04.013</a>.","ama":"Monien B, Mavronicolas M. The complexity of equilibria for risk-modeling valuations. <i>Theoretical Computer Science</i>. 2016;634:67-96. doi:<a href=\"https://doi.org/10.1016/j.tcs.2016.04.013\">10.1016/j.tcs.2016.04.013</a>","ieee":"B. Monien and M. Mavronicolas, “The complexity of equilibria for risk-modeling valuations,” <i>Theoretical Computer Science</i>, vol. 634, pp. 67–96, 2016.","apa":"Monien, B., &#38; Mavronicolas, M. (2016). The complexity of equilibria for risk-modeling valuations. <i>Theoretical Computer Science</i>, <i>634</i>, 67–96. <a href=\"https://doi.org/10.1016/j.tcs.2016.04.013\">https://doi.org/10.1016/j.tcs.2016.04.013</a>","bibtex":"@article{Monien_Mavronicolas_2016, title={The complexity of equilibria for risk-modeling valuations}, volume={634}, DOI={<a href=\"https://doi.org/10.1016/j.tcs.2016.04.013\">10.1016/j.tcs.2016.04.013</a>}, journal={Theoretical Computer Science}, publisher={Elsevier}, author={Monien, Burkhard and Mavronicolas, Marios}, year={2016}, pages={67–96} }","chicago":"Monien, Burkhard, and Marios Mavronicolas. “The Complexity of Equilibria for Risk-Modeling Valuations.” <i>Theoretical Computer Science</i> 634 (2016): 67–96. <a href=\"https://doi.org/10.1016/j.tcs.2016.04.013\">https://doi.org/10.1016/j.tcs.2016.04.013</a>.","short":"B. Monien, M. Mavronicolas, Theoretical Computer Science 634 (2016) 67–96."},"language":[{"iso":"eng"}],"type":"journal_article","date_updated":"2022-01-06T06:51:59Z","publication":"Theoretical Computer Science","has_accepted_license":"1","project":[{"name":"SFB 901","_id":"1"},{"_id":"7","name":"SFB 901 - Subprojekt A3"},{"name":"SFB 901 - Project Area A","_id":"2"}],"abstract":[{"lang":"eng","text":"Following the direction pioneered by Fiat and Papadimitriou in their 2010 paper [12], 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+R of expectationE and a risk valuationR of their costs; 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 V-equilibrium, no player could unilaterally reduce her cost.Say that V has the Weak-Equilibrium-for-Expectation property if all strategies supported in a player's best-response mixed strategy incur the same conditional expectation of her cost. We introduce E-strict concavity and observe that every E-strictly concave valuation has the Weak-Equilibrium-for-Expectation property. We focus on a broad class of valuations shown to have the Weak-Equilibrium-for-Expectation property, which we exploit to prove two main complexity results, the first of their kind, for the two simplest cases of the problem:• Two strategies: Deciding the existence of a V-equilibrium is strongly NP-hard for the restricted class of player-specific scheduling games on two ordered links [22], when choosing R as (1)Var (variance), or (2)SD (standard deviation), or (3) a concave linear sum of even moments of small order.• Two players: Deciding the existence of a V-equilibrium is strongly NP-hard when choosing R as (1)γ⋅Var, or (2)γ⋅SD, where γ>0 is the risk-coefficient, or choosing V as (3) a convex combination of E+γ⋅Var and the concave ν-valuationν−1(E(ν(⋅))), where ν(x)=xr, with r≥2. This is a concrete consequence of a general strong NP-hardness result that only needs the Weak-Equilibrium-for-Expectation property and a few additional properties for V; its proof involves a reduction with a single parameter, which can be chosen efficiently so that each valuation satisfies the additional properties."}],"file_date_updated":"2018-03-21T12:58:42Z","date_created":"2017-10-17T12:41:20Z","ddc":["040"],"doi":"10.1016/j.tcs.2016.04.013","file":[{"creator":"florida","file_size":633599,"date_created":"2018-03-21T12:58:42Z","date_updated":"2018-03-21T12:58:42Z","relation":"main_file","content_type":"application/pdf","access_level":"closed","file_name":"144-Monien_Mavronicolas-TCS2016_01.pdf","file_id":"1557","success":1}],"page":"67-96"}