Computing Superdifferentials of Lovász Extension with Application to Coalitional Game

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F16%3A00467447" target="_blank" >RIV/67985556:_____/16:00467447 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1007/978-3-319-40596-4_4" target="_blank" >http://dx.doi.org/10.1007/978-3-319-40596-4_4</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-319-40596-4_4" target="_blank" >10.1007/978-3-319-40596-4_4</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Computing Superdifferentials of Lovász Extension with Application to Coalitional Game

Popis výsledku v původním jazyce

Every coalitional game can be extended from the powerset onto the real unit cube. One of possible approaches is the Lovász extension, which is the same as the discrete Choquet integral with respect to the coalitional game. We will study some solution concepts for coalitional games (core, Weber set) using superdifferentials developed in non-smooth analysis. It has been shown that the core coincides with Fréchet superdifferential and the Weber set with Clarke superdifferential for the Lovász extension, respectively. We introduce the intermediate set as the limiting superdifferential and show that it always lies between the core and the Weber set. From the game-theoretic point of view, the intermediate set is a non-convex solution containing the Pareto optimal payoff vectors, which depend on some ordered partition of the players and the marginal coalitional contributions with respect to the order.

Název v anglickém jazyce

Computing Superdifferentials of Lovász Extension with Application to Coalitional Game

Popis výsledku anglicky

Every coalitional game can be extended from the powerset onto the real unit cube. One of possible approaches is the Lovász extension, which is the same as the discrete Choquet integral with respect to the coalitional game. We will study some solution concepts for coalitional games (core, Weber set) using superdifferentials developed in non-smooth analysis. It has been shown that the core coincides with Fréchet superdifferential and the Weber set with Clarke superdifferential for the Lovász extension, respectively. We introduce the intermediate set as the limiting superdifferential and show that it always lies between the core and the Weber set. From the game-theoretic point of view, the intermediate set is a non-convex solution containing the Pareto optimal payoff vectors, which depend on some ordered partition of the players and the marginal coalitional contributions with respect to the order.

Druh

D - Stať ve sborníku

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/GA15-00735S" target="_blank" >GA15-00735S: Analýza stability optim a ekvilibrií v ekonomii</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2016

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 2016)

ISBN

978-3-319-40595-7

ISSN

—

e-ISSN

—

Počet stran výsledku

11

Strana od-do

35-45

Název nakladatele

Springer International

Místo vydání

Cham

Místo konání akce

Eindhoven

Datum konání akce

20. 6. 2016

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

000389515800004