1-convex extensions of incomplete cooperative games and the average value

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F23%3A10468920" target="_blank" >RIV/00216208:11320/23:10468920 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=5mbnLLeirx" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=5mbnLLeirx</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11238-023-09946-8" target="_blank" >10.1007/s11238-023-09946-8</a>

Jazyk výsledku

angličtina

Název v původním jazyce

1-convex extensions of incomplete cooperative games and the average value

Popis výsledku v původním jazyce

The model of incomplete cooperative games incorporates uncer7tainty into the classical model of cooperative games by considering a partial8 characteristic function. Thus the values for some of the coalitions are not9 known. The main focus of this paper is 1-convexity under this framework.10 We are interested in two heavily intertwined questions. First, given an11 incomplete game, how can we ll in the missing values to obtain a complete12 1-convex game? Second, how to determine in a rational, fair, and ecient way13 the payos of players based only on the known values of coalitions?14 We illustrate the analysis with two classes of incomplete games - minimal15 incomplete games and incomplete games with dened upper vector. To answer16 the rst question, for both classes, we provide a description of the set of 1-17 convex extensions in terms of its extreme points and extreme rays. Based on18 the description of the set of 1-convex extensions, we introduce generalisations19 of three solution concepts for complete games, namely the -value, the Shapley20 value and the nucleolus. For minimal incomplete games, we show that all21 of the generalised values coincide. We call it the average value and provide22 dierent axiomatisations. For incomplete games with dened upper vector, we23 show that the generalised values do not coincide in general. This highlights24 the importance and also the diculty of considering more general classes of25 incomplete games.

Název v anglickém jazyce

1-convex extensions of incomplete cooperative games and the average value

Popis výsledku anglicky

The model of incomplete cooperative games incorporates uncer7tainty into the classical model of cooperative games by considering a partial8 characteristic function. Thus the values for some of the coalitions are not9 known. The main focus of this paper is 1-convexity under this framework.10 We are interested in two heavily intertwined questions. First, given an11 incomplete game, how can we ll in the missing values to obtain a complete12 1-convex game? Second, how to determine in a rational, fair, and ecient way13 the payos of players based only on the known values of coalitions?14 We illustrate the analysis with two classes of incomplete games - minimal15 incomplete games and incomplete games with dened upper vector. To answer16 the rst question, for both classes, we provide a description of the set of 1-17 convex extensions in terms of its extreme points and extreme rays. Based on18 the description of the set of 1-convex extensions, we introduce generalisations19 of three solution concepts for complete games, namely the -value, the Shapley20 value and the nucleolus. For minimal incomplete games, we show that all21 of the generalised values coincide. We call it the average value and provide22 dierent axiomatisations. For incomplete games with dened upper vector, we23 show that the generalised values do not coincide in general. This highlights24 the importance and also the diculty of considering more general classes of25 incomplete games.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

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OECD FORD obor

50201 - Economic Theory

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

Theory and Decision

ISSN

0040-5833

e-ISSN

1573-7187

Svazek periodika

Neudeven

Číslo periodika v rámci svazku

2023

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

29

Strana od-do

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Kód UT WoS článku

001026595300001

EID výsledku v databázi Scopus

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