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09 February 2025
 
  » arxiv » 1605.0431

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Complex behaviour in cyclic competition bimatrix games
Cezary Olszowiec ;
Date 2 May 2016
AbstractWe consider an example of cyclic competition bimatrix game which is a Rock-Scissors-Paper game with assumption about perfect memory of the playing agents. For the analysis of asymptotic behaviour close to the boundary of state space, we provide the description of naturally appearing heteroclinic network, with discretized dynamics in its neighbourhood. Quotient network is investigated as well and compared to the invalid models already considered in the literature. Parameter space is divided into four regions where we observe either irregular behaviour, or preference to follow itinerary consisting of strategies for which one or the other agent do not lose, or they alternate in winning. These regions are separated by two analytical curves and lines where game is either symmetric (system is not C^1 linearisable) or is zero-sum so the system is Hamiltonian. On each of these curves we observe different bifurcation scenarions.
Source arXiv, 1605.0431
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