. 2008 Dec 12;364(1518):807–819. doi: 10.1098/rstb.2008.0257

Table 2.

Evolutionary stability criteria for pure strategies of either target type.

strategy of type 1 individuals	strategy of type 2 individuals	stability criteria	biological effect
play always ω_low (p_low=1)	play always ω_low (q_low=1)	never stable
play always ω_low (p_low=1)	play always ω_medium (q_medium=1)	never stable
play always ω_low (p_low=1)	play always ω_high (q_high=1)	ESS, if $B_{2}^{'}$ (type 1)< $B_{3}^{'}$ (type 1) and $B_{3}^{'} (type 1) > 1 + (1.2 t / (1 + t)) \cdot B_{2}^{'} (type 1)$	type 2 leads; mixed groups move cohesively to target 2
play always ω_medium (p_medium=1)	play always ω_low (q_low=1)	never stable
play always ω_medium (p_medium=1)	play always ω_medium (q_medium=1)	ESS, if $B_{3}^{'}$ (type 1)>5 and $B_{3}^{'}$ (type2)>5	equally shared decision; majority leads cohesive group
play always ω_medium (p_medium=1)	play always ω_high (q_high=1)	ESS, if $B_{2}^{'}$ (type 1)> $B_{3}^{'}$ (type 1); $B_{3}^{'} (type 1) > ((1 + t + 1.6 t B_{2}^{'} (type 1)) / (1 + 0.6 t))$ and $B_{3}^{'}$ (type 2)<5	type 2 leads mixed groups towards target 2; some group fragmentation, thus, partial segregation
play always ω_high (p_high=1)	play always ω_low (q_low=1)	ESS, if $B_{2}^{'}$ (type 2)< $B_{3}^{'}$ (type 2) and $B_{3}^{'} (type 2) > 1 + (1.2 (1 - t) / (1 + (1 - t))) \cdot B_{2}^{'} (type 2)$	type 1 leads; mixed groups move cohesively to target 1
play always ω_high (p_high=1)	play always ω_medium (q_medium=1)	ESS, if $B_{2}^{'}$ (type 2)> $B_{3}^{'}$ (type 2); $B_{3}^{'} (type 2) > ((2 - t + 1.6 (1 - t) B_{2}^{'} (type 2)) / (1.6 - 0.6 t))$ and $B_{3}^{'}$ (type 1)<5	type 1 leads mixed groups towards target 1; some group fragmentation, thus, partial segregation
play always ω_high (p_high=1)	play always ω_high (q_high=1)	ESS, if $B_{3}^{'}$ (type1)<1 and $B_{3}^{'}$ (type 2)<1	complete segregation of the two types