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Higher-order Sequential Stabilities in the Graph Model for Conflict Resolution for Bilateral Conflicts

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Abstract

The Graph Model for Conflict Resolution (GMCR) is a flexible model and has been widely used for describing and analyzing conflicts. Stability analysis is used in the GMCR to determine possible solutions for the conflict. Several solution concepts have been proposed which accommodate different decision makers’ (DMs) behavior. Some of them are: Nash, General Metarationality (GMR) and Sequential Stability (SEQ). For a state to be Nash stable for a DM, such DM cannot move to a more preferred state in a single step. For GMR and SEQ, while considering moving to a more preferred state, the DM foresees whether the opponent can react leading the conflict to a state not preferred to the current one. What differs GMR and SEQ is that, in SEQ the opponent’s move simultaneously sanctions the focal DM and benefits the opponent. We show, by means of an example, that there are situations in which the opponent’s reaction is implausible in the sense that it involves the opponent leaving an SEQ stable state for him. In order to avoid that problem, we propose new solution concepts for the GMCR, called Higher-order Sequential Stabilities, and explore their relation with other solution concepts commonly used in the GMCR.

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Source: Hipel and Obeidi (2005)

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Source: Hipel and Obeidi (2005)

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Notes

  1. Throughout the paper, without loss of generality, we refer to the DM who moves first using feminine pronouns and to the opponent using masculine pronouns.

  2. We should mention that in the original stability analysis of Hipel and Obeidi (2005), they reported state 35 as Nash stable. However, state 35 is not Nash stable for DM SES since from state 35, DM SES has a UI to state 18. Since from state 18, DM GMDE can only sanction DM SES moving to state 17 or state 19 and neither of these moves are UI for DM GMDE, state 35 is GMR, but not SEQ for DM SES. Finally, state 35 is also SMR since DM SES cannot escape the sanction from state 19 to a state better than state 35 for him.

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Funding

Funding was provided by Conselho Nacional de Desenvolvimento Científico e Tecnológico (307556/2017-4, 428325/2018-1) and Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (001).

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Authors and Affiliations

  1. Statistics and Applied Math Department, Universidade Federal do Ceará, Fortaleza, CE, 60455-760, Brazil

    Leandro Chaves Rêgo

  2. Graduate Programs in Statistics and Management Engineering, Universidade Federal de Pernambuco, Recife, PE, 50740-550, Brazil

    Leandro Chaves Rêgo

  3. Graduate Program in Management Engineering, Universidade Federal de Pernambuco, Recife, PE, 50670-901, Brazil

    France E. G. de Oliveira

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  1. Leandro Chaves Rêgo
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  2. France E. G. de Oliveira
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Correspondence to Leandro Chaves Rêgo.

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Rêgo, L.C., de Oliveira, F.E.G. Higher-order Sequential Stabilities in the Graph Model for Conflict Resolution for Bilateral Conflicts. Group Decis Negot 29, 601–626 (2020). https://doi.org/10.1007/s10726-020-09668-0

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