Mapping Power Relations: A Geometric Framework for Game-Theoretic Analysis

This paper introduces a geometric framework for analyzing power relations in games, independent of their strategic form. We define a canonical preference space where each player's relational stance is a normalized vector. This model eliminates the arbitrariness of selecting utility functions, a limitation of recent approaches. We show how classical concepts-bargaining power, dependence, reciprocity-are recovered and generalized within this space. The analysis proceeds in two steps: projecting a game's payoffs and outcomes onto the space, and then reducing the resulting landscape using key metrics. These include a Center of Mass (CoM) and structural indices for Hierarchy (H) and Reciprocity (R). Applications to canonical games (Prisoner's Dilemma, Battle of the Sexes) and economic models (Cournot duopoly) demonstrate that the framework reveals underlying structural similarities across different strategic settings and provides a quantitative characterization of relational dynamics. It thus bridges cooperative and non-cooperative game theory by conceptualizing power as a structural property of the mapping from preferences to equilibria.

• Publication year

  2025

• Venue

  Unknown venue

• Publication date

  2025-11-10

• Fields of study

  Mathematics, Economics

• Identifiers
  arXiv 2511.07287
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• A General Measure of Bargaining Power for Non-Cooperative Games

  2024influential reference
• Bayesian Persuasion

  2024cited by this paper
• Giving according to GARP: An experimental test of the consistency of preferences for altruism (by James Andreoni and John Miller)

  2021cited by this paper
• ECONOMICS AND POWER

  2020cited by this paper
• Anti-Dühring

  2020cited by this paper
• Models of Other-Regarding Preferences, Inequality, and Redistribution

  2018cited by this paper
• Dependence in games and dependence games

  2011cited by this paper
• A within-subject analysis of other-regarding preferences

  2011cited by this paper
• Interdependent preferences

  2010cited by this paper
• The concept of power

  2007cited by this paper
• Individual Preferences for Giving

  2005cited by this paper
• Efficient Rent Seeking

  2001cited by this paper
• UNDERSTANDING SOCIAL PREFERENCES WITH SIMPLE TESTS

  2001cited by this paper
• ERC: A Theory of Equity, Reciprocity, and Competition

  2000cited by this paper
• Systems of Benevolent Utility Functions

  1999cited by this paper
• A Theory of Fairness, Competition and Cooperation

  1998cited by this paper
• Power in competitive exchange

  1998cited by this paper
• Contest success functions

  1996cited by this paper
• ON THE CONCEPT OF POWER IN ECONOMICS

  1991cited by this paper
• Bargaining in Legislatures

  1989cited by this paper
• Love and Spaghetti, The Opportunity Cost of Virtue

  1989cited by this paper
• Community, anarchy, and liberty

  1982cited by this paper
• Perfect Equilibrium in a Bargaining Model

  1982cited by this paper
• Dizionario di politica

  1976cited by this paper
• Unequal Exchange: A Study of the Imperialism of Trade

  1972cited by this paper
• Manuale di economia politica

  1965cited by this paper
• The Strategy of Conflict.

  1961cited by this paper
• A Method for Evaluating the Distribution of Power in a Committee System

  1954cited by this paper
• Imperialism : The Highest Stage of Capitalism

  1934cited by this paper

• No citing papers are available for this paper.