Garay József, Varga Zoltán
Research Group of Theoretical Biology and Ecology, Hungarian Academy of Sciences, Department of Plant Taxonomy and Ecology, L. Eötvös University, Pázmány P. sétány 1/C, H-1117 Budapest, Hungary.
Theor Popul Biol. 2011 Nov;80(3):217-25. doi: 10.1016/j.tpb.2011.08.003. Epub 2011 Aug 23.
We consider a survival game of gregarious individuals, in which the aim of the players is survival to reproductive age under predator attacks. The survivor's dilemma (shortly: SVD) game consists in the following: a group member either surely survives alone by fleeing, while its defensive mate may be killed; or tries to save its mate's life, risking to get killed. The dilemma is that, in every single attack, fleeing ensures maximal survival probability, but if its mate survives by fighting both, and they remain together, its risk to be killed at the next attack will be lower. We show that, if defense is successful enough, then the one-attack game is a prisoner's dilemma (PD), where fleeing is the strict ESS. We have additively decomposed the SVD game, according to the survival of the group mate of the focal prey, into two games: the aim of the "collective game" is survival of the group of prey. Counter-wise, the aim of the "hostile game" is survival alone (focal prey survives and its mate is killed by the predator). We obtain the following results: if the attack number is large enough, the multi-attack SVD game is dominated by the "collective game" in the sense that each individual can ensure its own maximal survival probability by maximizing the group survival probability in each attack. In the hostile game, the only strict ESS is the fleeing strategy. In the collective game there are two different cases: either defense is a unique strict ESS, or the collective game is bistable, i.e. fleeing and defense are local strict ESS's. If defense is the only strict ESS in the collective game, and the attack number is large enough, defense replaces fleeing strategy in the multi-attack SVD game. However, in the bistable case, defense cannot invade into the fleeing population. It is shown that, if the interaction between relatives is frequent enough, than defense can replace fleeing strategy, in spite of the fact that in the well-mixed population the collective game is bistable.
我们考虑一个群居个体的生存博弈，其中玩家的目标是在捕食者攻击下存活至繁殖年龄。幸存者困境（简称：SVD）博弈如下：群体中的一员要么独自逃离从而确保存活，但其防御同伴可能会被杀死；要么试图拯救同伴的生命，却要冒着被杀的风险。困境在于，在每一次攻击中，逃离能确保最大的生存概率，但如果其同伴通过战斗存活下来，并且它们继续在一起，那么在下一次攻击中其被杀的风险将会降低。我们表明，如果防御足够成功，那么单次攻击博弈就是囚徒困境（PD），其中逃离是严格的进化稳定策略（ESS）。我们根据焦点猎物的群体同伴的存活情况，将SVD博弈加性分解为两个博弈：“集体博弈”的目标是猎物群体的存活。相反，“敌对博弈”的目标是独自存活（焦点猎物存活而其同伴被捕食者杀死）。我们得到以下结果：如果攻击次数足够多，多轮攻击的SVD博弈由“集体博弈”主导，即每个个体可以通过在每次攻击中最大化群体生存概率来确保自身的最大生存概率。在敌对博弈中，唯一的严格ESS是逃离策略。在集体博弈中有两种不同情况：要么防御是唯一的严格ESS，要么集体博弈是双稳态的，即逃离和防御是局部严格ESS。如果防御是集体博弈中唯一的严格ESS，并且攻击次数足够多，那么在多轮攻击的SVD博弈中防御会取代逃离策略。然而，在双稳态情况下，防御无法侵入逃离群体。结果表明，如果亲属之间的互动足够频繁，那么尽管在充分混合的群体中集体博弈是双稳态的，防御仍可以取代逃离策略。
