Partitions as a Model for Numerical Simulation

Pavel Bocharov; Alexander Goryashko; Evgeny Nikulchev

doi:10.15866/iremos.v9i1.7823

Partitions as a Model for Numerical Simulation

Pavel Bocharov⁽¹⁾, Alexander Goryashko⁽²⁾, Evgeny Nikulchev^(3*)

^(*) Corresponding author

Authors' affiliations

DOI: https://doi.org/10.15866/iremos.v9i1.7823

Abstract

We propose a new approach to investigating such non-cooperative games, as tournaments and evolutionary games. Our model of symmetric game is based on partition classes of integers, and the rules are similar to those of well-known Colonel Lotto game. We present detailed model of dynamics of evolutionary game with two populations of matrix strategies. A win (according to Lotto game’s rules) leads to precise replication of the winning strategy, a loss leads to eliminating the losing strategy. We specify efficiently computable properties of partitions allowing to classify the set of partitions according to their winning ability and present detailed simulation results for the evolutionary Lotto game with (100,10)-partitions. The results of the simulations fully support the classification principles we are proposing.
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Keywords

Partition; Composition; Partition Game; Colonel Lotto Game; Population Dynamic; Reproduction; Fitness; Balance; Relative Strength

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