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<p>In this paper, we consider a class of strategy-form games, where the agents play a noncooperative game and a cooperative game concurrently. In this model, we introduce the notion of equilibria, and prove the equilibrium existence theorem with finitely many agents and finite dimensional strategy spaces by the result of Bonnisseau and Iehl<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10957_2025_2774_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="10" /> </InlineMediaObject> <EquationSource Format="TEX">\(\acute{\hbox {e}}\)</EquationSource> <EquationSource Format="MATHML"><math> <mover accent="true"> <mtext>e</mtext> <mo>´</mo> </mover> </math></EquationSource> </InlineEquation> (2007). Furthermore, we provide a generalization to strategy-form games with infinite dimensional strategy spaces. Finally, we define the weak equilibrium concept for strategy-form games with infinitely many agents, noncooperative and cooperative frameworks, and prove the weak equilibrium existence theorem.</p>

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Equilibria in Strategy-Form Games with Both Noncooperative and Cooperative Frameworks

  • 期刊论文

  • 发表日期：

    2025年7月15日

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  • Zhe Yang

摘要

In this paper, we consider a class of strategy-form games, where the agents play a noncooperative game and a cooperative game concurrently. In this model, we introduce the notion of equilibria, and prove the equilibrium existence theorem with finitely many agents and finite dimensional strategy spaces by the result of Bonnisseau and Iehl \(\acute{\hbox {e}}\) e ´ (2007). Furthermore, we provide a generalization to strategy-form games with infinite dimensional strategy spaces. Finally, we define the weak equilibrium concept for strategy-form games with infinitely many agents, noncooperative and cooperative frameworks, and prove the weak equilibrium existence theorem.