On Convexity in Games with Externalities

In this paper we study a family of extensions of the Shapley value for games in partition function form with n players. In particular, we provide a complete characterization for all linear, symmetric, efficient and null solutions in these environments. Finally, we relate our characterization result with other ways to extend the Shapley value in the literature.

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An Almost Ideal Sharing Scheme for Coalition Games with Externalities

SSRN Electronic Journal ◽

10.2139/ssrn.643641 ◽

2004 ◽

Cited By ~ 26

Author(s):

Johan Eyckmans ◽

Michael Finus

Keyword(s):

Sharing Scheme ◽

Games With Externalities

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Assignment games with externalities revisited

Economic Theory Bulletin ◽

10.1007/s40505-017-0117-4 ◽

2017 ◽

Vol 5 (2) ◽

pp. 247-257 ◽

Cited By ~ 5

Author(s):

Jens Gudmundsson ◽

Helga Habis

Keyword(s):

Assignment Games ◽

Games With Externalities

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The Stochastic Shapley Value for coalitional games with externalities

Games and Economic Behavior ◽

10.1016/j.geb.2017.04.008 ◽

2018 ◽

Vol 108 ◽

pp. 65-80 ◽

Cited By ~ 7

Author(s):

Oskar Skibski ◽

Tomasz P. Michalak ◽

Michael Wooldridge

Keyword(s):

Shapley Value ◽

Coalitional Games ◽

Games With Externalities

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An Extension of the Solidarity Value for Environments with Externalities

International Game Theory Review ◽

10.1142/s0219198917500074 ◽

2017 ◽

Vol 19 (02) ◽

pp. 1750007

Author(s):

Julio Rodríguez-Segura ◽

Joss Sánchez-Pérez

Keyword(s):

Unique Function ◽

Marginal Contribution ◽

Transferable Utility ◽

Games With Externalities ◽

Transferable Utility Games ◽

Axiomatic Extension

In this paper, we propose an axiomatic extension for the Solidarity value of Nowak and Radzik [1994] A solidarity value for [Formula: see text]-person transferable utility games, Int. J. Game Theor. 23, 43–48] to the class of games with externalities. This value is characterized as the unique function that satisfies linearity, symmetry, efficiency and average nullity. In this context, we discuss a key subject of how to extend the concept of average marginal contribution to settings where externalities are present.

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The Core of Aggregative Cooperative Games with Externalities

The B E Journal of Theoretical Economics ◽

10.1515/bejte-2014-0054 ◽

2016 ◽

Vol 16 (1) ◽

pp. 389-410 ◽

Cited By ~ 4

Author(s):

Giorgos Stamatopoulos

Keyword(s):

Normal Form ◽

Characteristic Function ◽

Coalition Formation ◽

Cooperative Games ◽

Grand Coalition ◽

Normal Form Games ◽

The Core ◽

Aggregative Games ◽

Games With Externalities

AbstractThis paper analyzes cooperative games with externalities generated by aggregative normal form games. We construct the characteristic function of a coalition S for various coalition formation rules and we examine the corresponding cores. We first show that the $$\gamma $$-core is non-empty provided each player’s payoff decreases in the sum of all players’ strategies. We generalize this result by showing that if S believes that the outside players form at least $$l(s) = n - s - (s - 1)$$ coalitions, then S has no incentive to deviate from the grand coalition and the corresponding core is non-empty (where n is the number of players in the game and s the number of members of S). We finally consider the class of linear aggregative games (Martimort and Stole 2010). In this case, if S believes that the outsiders form at least $$\widehat l(s) = {n \over s} - 1$$ coalitions [where $$\widehat l(s) \le l(s)$$] a core non-emptiness result holds again.

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