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<p>Many solution concepts have been proposed within the Graph Model for Conflict Resolution to represent many behaviors that decision makers (DMs) can have in strategic settings. Among these solution concepts, the limited move stability stands out because it allows analyzing the conflict a variable number of steps forward, taking into account the preferences of all DMs involved in the conflict. However, for conflicts involving more than two DMs, there are two definitions of limited move stability that we argue to have undesired properties. For that reason, we present two alternative definitions for limited move stability for conflicts with multiple DMs, called: Alternative Limited-Move stability with Cooperative Coalition (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(L_h^{CC}\)</EquationSource> </InlineEquation>) and Alternative Limited-Move stability with Individualistic Coalition (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(L_h^{CI}\)</EquationSource> </InlineEquation>). Moreover, we obtained results relating these concepts to classical GMCR stability concepts. Furthermore, we provide results that establish the equivalence among the stability notions <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(L_h^{CC}\)</EquationSource> </InlineEquation>, <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(L_h^{CI}\)</EquationSource> </InlineEquation> and <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\text {Maximin}_h\)</EquationSource> </InlineEquation>, for conflicts in which the DMs belonging to the opposing coalition have equal and completely opposite preferences to those of the focal DM. An application to the Elmira conflict illustrates the usefulness of the proposed concepts in a real conflict situation.</p>

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Alternative Limited Move Stabilities in the Graph Model for Conflict Resolution with Multiple Decision Makers

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  • 发表日期：

    2026年2月24日

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  • Alecio Soares,
  • Giannini I. A. Vieira,
  • Leandro C. Rêgo

摘要

Many solution concepts have been proposed within the Graph Model for Conflict Resolution to represent many behaviors that decision makers (DMs) can have in strategic settings. Among these solution concepts, the limited move stability stands out because it allows analyzing the conflict a variable number of steps forward, taking into account the preferences of all DMs involved in the conflict. However, for conflicts involving more than two DMs, there are two definitions of limited move stability that we argue to have undesired properties. For that reason, we present two alternative definitions for limited move stability for conflicts with multiple DMs, called: Alternative Limited-Move stability with Cooperative Coalition ( \(L_h^{CC}\) ) and Alternative Limited-Move stability with Individualistic Coalition ( \(L_h^{CI}\) ). Moreover, we obtained results relating these concepts to classical GMCR stability concepts. Furthermore, we provide results that establish the equivalence among the stability notions \(L_h^{CC}\) , \(L_h^{CI}\) and \(\text {Maximin}_h\) , for conflicts in which the DMs belonging to the opposing coalition have equal and completely opposite preferences to those of the focal DM. An application to the Elmira conflict illustrates the usefulness of the proposed concepts in a real conflict situation.