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Categorical Approach to Conflict Resolution: Integrating Category Theory into the Graph Model for Conflict Resolution

Yukiko Kato

TL;DR

The basic concepts, methods, and application of the C-GMCR framework to the well-known Prisoner's Dilemma and other representative cases suggest that the categorical approach offers new perspectives on stability concepts and can potentially lead to the development of more effective conflict resolution strategies.

Abstract

This paper introduces the Categorical Graph Model for Conflict Resolution (C-GMCR), a novel framework that integrates category theory into the traditional Graph Model for Conflict Resolution (GMCR). The C-GMCR framework provides a more abstract and general way to model and analyze conflict resolution, enabling researchers to uncover deeper insights and connections. We present the basic concepts, methods, and application of the C-GMCR framework to the well-known Prisoner's Dilemma and other representative cases. The findings suggest that the categorical approach offers new perspectives on stability concepts and can potentially lead to the development of more effective conflict resolution strategies.

Categorical Approach to Conflict Resolution: Integrating Category Theory into the Graph Model for Conflict Resolution

TL;DR

The basic concepts, methods, and application of the C-GMCR framework to the well-known Prisoner's Dilemma and other representative cases suggest that the categorical approach offers new perspectives on stability concepts and can potentially lead to the development of more effective conflict resolution strategies.

Abstract

This paper introduces the Categorical Graph Model for Conflict Resolution (C-GMCR), a novel framework that integrates category theory into the traditional Graph Model for Conflict Resolution (GMCR). The C-GMCR framework provides a more abstract and general way to model and analyze conflict resolution, enabling researchers to uncover deeper insights and connections. We present the basic concepts, methods, and application of the C-GMCR framework to the well-known Prisoner's Dilemma and other representative cases. The findings suggest that the categorical approach offers new perspectives on stability concepts and can potentially lead to the development of more effective conflict resolution strategies.
Paper Structure (17 sections, 3 theorems, 4 figures)

This paper contains 17 sections, 3 theorems, 4 figures.

Table of Contents

  1. Introduction
  2. Concepts and Methods
  3. Category Theory
  4. Category
  5. Morphisms
  6. Functors
  7. GMCR
  8. C-GMCR
  9. Correspondence of Elements
  10. C-GMCR
  11. Application and Analysis
  12. Prisoner's Dilemma
  13. Elmira Conflict
  14. International Trade Conflict
  15. Base case
  16. ...and 2 more sections

Key Result

Proposition 1

If a state transition $f:s_1 \to s_2$ exists such that $P_i(s_1) \prec P_i(s_2)$ for DM $i$, then there exists no state transition $g: s_2 \to s1$ with $P_i(s_2) \succ P_i(s_1)$ for the same DM.

Figures (4)

  • Figure 1: Elmira Conflict : C-GMCR
  • Figure 2: International Traded Conflict-Base Case : C-GMCR
  • Figure 3: International Traded Conflict-Intricate Case : C-GMCR
  • Figure 4: New Reachability Model of Prisoners' Dilemma

Theorems & Definitions (6)

  • Proposition 1
  • proof
  • Proposition 2
  • proof
  • Proposition 3
  • proof