• CUBIC RISK-DOMINANCE INCREASES RECESSIVE CO-OPERATOR EXPLOITATION

PAUL F. SLADE*

Abstract


Frequency-dependent selection between two non-mutating strategies, co-operate or defect, under random genetic drift yields a well-known rule of biological evolutionary game dynamics. When the quotient of singleton type fixation probability functions, that being co-operate upon defect, exceeds unity the relative frequency of the risk-dominant strategy in the population equilibrates to less than ½. Maclaurin series of this quotient of singleton type fixation probability functions calculated at second and third orders enable the convergent domain of the payoff matrix to be obtained exactly. Novel corollaries identify a reduced domain of convergence in which this evolutionary rule holds. Finite population size convergence quantifies the applicability of the asymptotic inequality from which this rule derives. Violation of this evolutionary rule depends on the normalized payoff matrix entries and selection differential. Quantitative analysis illustrates non-negligibility of the quadratic and cubic coefficients in Maclaurin series with selection with selection being inversely proportional to population size.   


Keywords


Co-operation; Fixation probability; Frequency-dependent selection; Maclaurin series; Moran model.

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