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The graph structure of two-player games.

Oliver Biggar1, Iman Shames2

  • 1CIICADA Lab, Australian National University, Canberra, 2601, Australia. oliver.biggar@anu.edu.au.

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|February 1, 2023
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Summary

This study introduces response graphs for analyzing two-player games, revealing their structure is key to understanding game properties like zero-sum and potential games. These graphs are crucial for evolutionary game theory and multi-agent learning.

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Area of Science:

  • Game Theory
  • Computational Game Theory
  • Multi-Agent Systems

Background:

  • Response graphs model strategic interactions in two-player games.
  • Sink strongly connected components are vital in evolutionary game theory and multi-agent learning.
  • Understanding game properties without cardinal payoffs is crucial.

Purpose of the Study:

  • To analyze two-player games using response graphs.
  • To characterize games sharing response graphs with zero-sum or potential games.
  • To investigate the role of specific response graph structures (Matching Pennies, Coordination) in general games.

Main Methods:

  • Analysis of game strategy profiles and player preferences.
  • Characterization of games based on response graph properties.
  • Demonstration of duality between zero-sum and potential game response graphs.
  • Examination of non-iteratively-dominated strategies within subgames.

Main Results:

  • Response graphs capture non-trivial game properties independent of cardinal payoffs.
  • A duality exists between games sharing response graphs with zero-sum and potential games.
  • Response graphs of Matching Pennies and Coordination are fundamental to all two-player games.
  • Games sharing response graphs with both zero-sum and potential games are dominance-solvable.

Conclusions:

  • Response graphs offer a simple yet powerful model for strategic interaction.
  • The structure of response graphs reveals fundamental game characteristics.
  • The findings have implications for evolutionary game theory and multi-agent learning research.