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The strategy of conflict and cooperation (1808.06750v7)

Published 21 Aug 2018 in econ.TH, cs.MA, and q-bio.PE

Abstract: This paper introduces a unified framework called cooperative extensive form games, which (i) generalizes standard non-cooperative games, and (ii) allows for more complex coalition formation dynamics than previous concepts like coalition-proof Nash equilibrium. Central to this framework is a novel solution concept called cooperative equilibrium system (CES). CES differs from Nash equilibrium in two important respects. First, a CES is immune to both unilateral and multilateral `credible' deviations. Second, unlike Nash equilibrium, whose stability relies on the assumption that the strategies of non-deviating players are held fixed, CES allows for the possibility that players may regroup and adjust their strategies in response to a deviation. The main result establishes that every cooperative extensive form game, possibly with imperfect information, possesses a CES. For games with perfect information, the proof is constructive. This framework is broadly applicable in contexts such as oligopolistic markets and dynamic political bargaining.

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Authors (1)
  1. Mehmet S. Ismail (19 papers)
Citations (1)
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Summary

  • The paper introduces Cooperative Extensive Form Games (CEFGs) and the Cooperative Equilibrium System (CES) to integrate coalition formation with extensive form strategy modeling.
  • The paper shows that CES remains robust against both unilateral and multilateral deviations by allowing players to adjust strategies dynamically.
  • The paper applies the framework to real-world scenarios like oligopolistic markets and political bargaining, offering insights into strategic coalition dynamics.

An Overview of Cooperative Extensive Form Games and the Cooperative Equilibrium System

The paper "The Strategy of Conflict and Cooperation" introduces a novel framework in game theory called Cooperative Extensive Form Games (CEFGs). This framework is designed to expand the scope of standard non-cooperative games, managing the intricacies of coalition formation and strategic interactions beyond previous concepts like coalition-proof Nash equilibrium. At the center of this framework is the innovative solution concept referred to as the Cooperative Equilibrium System (CES).

Key Contributions

  1. Unified Framework of Cooperative Games:
    • CEFGs generalize non-cooperative games by integrating a mechanism for strategic coalition formation, considering both the externalities and synergies that arise.
    • The framework accommodates potentially dynamic coalitional arrangements, aspects often neglected in traditional cooperative game theory.
  2. Cooperative Equilibrium System (CES):
    • Unlike Nash Equilibrium, which is susceptible to unilateral deviations, a CES withstands both unilateral and multilateral 'credible' deviations.
    • Distinctly, CES does not assume the strategies of non-deviating players are fixed, acknowledging that these players may adjust their strategies in response to deviations, allowing for regrouping and renegotiations.
  3. Existence of CES:
    • The paper establishes that every cooperative extensive form game possesses a CES, with constructive proofs provided for games with perfect information.
    • This result holds broadly across strategic contexts like oligopolistic markets and political bargaining, enhancing its universality and applicability.

Insights and Implications

  • Theoretical Implications: The robustness of CES against credible deviations provides a more refined understanding of equilibrium stability in the presence of complex strategic interactions and coalition dynamics.
  • Practical Implications: In real-world applications, such as oligopolistic competition or international negotiations, the framework can model and predict outcomes where firms or countries strategize not only based on individual interests but also on potential alliances or coalitions. For instance, in oligopolistic markets, firms may form cartels without binding agreements, yet remain stable in the competitive strategy landscape.
  • Future Research Directions:
    • Computational Challenges: The complexity of calculating CES increases exponentially with the number of players due to the multitude of possible coalition structures, suggesting a need for efficient algorithms and computational methods.
    • Extensions of Framework: The exploration of more generalized scenarios, including games with incomplete information, wealth transfers, and dynamic contract writing, can enrich the modeling capabilities of CEFGs.

Conclusion

The paper presents valuable progress in understanding cooperation and conflict in games with multiple participants. By embedding coalition dynamics into the extensive form structure, the framework and its accompanying solution concept, CES, open fresh avenues for examining strategic interactions and game-theoretic modeling. This contribution is poised to enhance both the theoretical richness and practical application of game theory in understanding complex strategic environments.

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