Orthogonal elementary interactions for bimatrix games

György Szabó and Balázs Király

Physica A: Statistical Mechanics and its Applications, 2025, vol. 677, issue C

Abstract: In symmetric matrix games, the interaction is defined through a single payoff matrix that can be decomposed into elementary interactions of four types representing games with self- and cross-dependent payoffs, coordination-type interactions, and rock–paper–scissors-like cyclic dominance. Here, this analysis is extended to a similar anatomy of bimatrix games given by two matrices. The respective self- and cross-dependent components describe extended versions of donation games expanding the range of social dilemmas. The most attractive classification utilizes the fact that games can be separated into the sum of a fraternal and a zero-sum part whose payoff matrices can then be further divided into symmetric and antisymmetric terms. This approach revealed two types of interaction not present in symmetric games: directed anticoordination components share some features with both partnership games and rock–paper–scissors-like cyclic dominance; the combinations of matching pennies components prevent the existence of a potential, which precludes detailed balance with the Boltzmann distribution under Glauber-type dynamics. In another departure from symmetric games, bimatrix games may admit a non-Hermitian potential matrix, which could possibly give rise to thermodynamic behaviors not found in classical spin models. Some curiosities of the directed anticoordination interaction are illustrated by simulations when the players are located on a square lattice.

Keywords: Matrix decomposition; Non-reciprocal interaction; Non-hermitian potential; Lattice spin model; Evolutionary game theory; Social dilemma (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437125005722
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:677:y:2025:i:c:s0378437125005722

DOI: 10.1016/j.physa.2025.130920

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().