Conflict Resolution Using the Graph Model: Strategic Interactions in Competition and Cooperation by Haiyan Xu Keith W. Hipel D. Marc Kilgour & Liping Fang

Author:Haiyan Xu, Keith W. Hipel, D. Marc Kilgour & Liping Fang
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

5.3.4.1 Matrix Representation of Stabilities Indexed a for Preference with Uncertainty

In the definitions indexed a, DM i has an incentive to move to states with uncertain preferences relative to the status quo, but, when assessing possible sanctions, will not consider states with uncertain preferences (Li et al. 2004).

Theorem 5.21

State is stable for DM i iff .

Theorem 5.21 implies that Nash stability definitions are identical for both 2-DM and n-DM models with preference uncertainty because Nash stability does not consider opponents’ responses.

For GMR, DM i considers the opponents’ responses, which are reachable states of coalition by the legal UM sequences. First, the matrix using Theorem 5.20 can be constructed for . Define the stability matrix as

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