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Table 1 The pay-off matrix for the cooperation/competition game

From: Environmental adversity and uncertainty favour cooperation

X ¯ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGacaGaaiaabeqaaeqabiWaaaGcbaWaa0aaaeaacqWGybawaaaaaa@2D1D@ Cooperate Compete
Cooperate f ( R 1 ) + Δ 2 , f ( R 2 ) + Δ 2 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacPC6xNi=xH8viVGI8Gi=hEeeu0xXdbba9frFj0xb9qqpG0dXdb9aspeI8k8fiI+fsY=rqGqVepae9pg0db9vqaiVgFr0xfr=xfr=xc9adbaqaaeGacaGaaiaabeqaaeqabiWaaaGcbaGaemOzay2aaeWaaeaacqWGsbGudaWgaaWcbaGaeGymaedabeaaaOGaayjkaiaawMcaaiabgUcaRKqbaoaalaaabaGaeuiLdqeabaGaeGOmaidaaOGaeiilaWIaemOzay2aaeWaaeaacqWGsbGudaWgaaWcbaGaeGOmaidabeaaaOGaayjkaiaawMcaaiabgUcaRKqbaoaalaaabaGaeuiLdqeabaGaeGOmaidaaaaa@3ED1@ α · f(R1), f(R2) + Δ
Compete f(R1) + Δ, α · f(R2) f(R1), f(R2)
  1. Entries indicate the mean of the payoff distribution to the row player followed by the column player. R1 and R2 are the amount of resources owned by the row and column player respectively, and Δ = [f(R1 + R2) - f(R1) - f(R2)]+ (i.e., it takes only the positive values of the expression in brackets and it is zero if the value of the expression is negative). The function f is a diminishing return function, and R1 and R2 are typically in the range where 2f(x) ≤ f(2x), and 0 <α < 1.