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1648. A Coopetition Index for Coalitions in Simple Monotone Games.

Invited abstract in session MC-36: Game Theory, Solutions and Structures III, stream Game Theory, Solutions and Structures.

Monday, 12:30-14:00
Room: 32 (building: 306)

Authors (first author is the speaker)

1. Michele Aleandri
Economics and Finance, Luiss University
2. Marco Dall'Aglio
Dept of Economics and Finance, LUISS University

Abstract


The measurement of power for players in cooperative games traditionally focuses on the effort that single players exert on every coalition of other players. A more recent stream of works focuses on the evaluation of the power of groups (see Flores R., Molina E., Tejada J. (2019), Evaluating groups with the generalized Shapley value 4OR, 17 (2), 141-172) together with an estimation of their interactions, defined in Grabisch M., Roubens M. (1999), An axiomatic approach to the concept of interaction among players in cooperative games. International Journal of Game Theory 28: 547-565, as the average of finite order differences for the players in the coalition.

We examine the use of such indexes in the context of monotone simple games and we verify that the original interaction index captures the group’s relationship in terms of collaboration and competition for two players, but fails to do so for larger groups.

We therefore define a collaboration-competition index that is based on the notion of essential criticality and coincides with Grabisch and Rouben’s interaction index for two players. We analyze its properties and we put the index at work with some applications.

Keywords

Status: accepted

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