Evolution of cooperation without iterations and without relatedness: strategic behaviour in public goods games and 2-person games

自然界中的许多相互作用是对立的，因为达尔文的自然选择导致适者生存，而一个人的优势通常是另一个人的劣势。然而，利他主义和合作的例子很多：从不能繁殖、只为蚁群工作的蚂蚁体内的不育士兵，到猫鼬的哨兵，一旦捕食者接近，它们就会发出警报。利他主义者为帮助他人付出代价，而这是自私的人不会付出的代价。因为利他主义者和自私的个体最终会为了繁殖而竞争，自私的个体应该具有优势。那么，我们如何解释合作的存在呢？一种解决方案是，利他主义者通常是家庭成员：例如，蚂蚁和其他群居昆虫通过帮助巢穴来帮助它们的姐妹。通过这种方式，他们有利于自己基因的传播，因为他们利他主义的目标很有可能携带相同的基因。另一种解决方案是，利他主义可以针对在连续相遇中处于回报地位的个人。因此，作为利他主义者可能会得到回报，因为利他主义者从他们帮助过的人那里获得了好处。然而，这两种解释并不完全令人满意，因为有许多共生与合作的情况下，个人没有亲缘关系，永远不会再见面，但在这些情况下，合作是存在的。我的工作旨在了解这些情况是如何发生的。我通过开发博弈论的模型来做到这一点，博弈论是从约翰·纳什(著名电影《美丽的心灵》中的作品)发展而来的数学分支。在数学中，游戏描述的是两个玩家发生冲突，每个人都试图获得最大回报的情况。数学是必要的，因为结果并不总是直观的。例如，考虑一群人目击犯罪的情况。如果其中一人报了警，罪犯就会被逮捕。逮捕罪犯是一项公益事业。然而，对个人来说，报警的成本很小，而且当有很多目击者时，每个人都更愿意报警的人是其他人。如果罪犯被逮捕，所有人都会更好，但每个人都更愿意让其他人承担风险和付出代价。人们会认为，当有更多的人可以志愿服务时，有人报警的可能性就会增加；事实上，当太多人目睹犯罪时，通常没有人自愿帮助。这就是战略行为的效果--每个人都以一定的概率依赖于其他人，随着可能的志愿者数量的增加，这种可能性也会增加，当证人数量更多时，这种可能性会增加得更多。事实上，当一个人是唯一的(或少数几个)可能的志愿者时，他通常更有可能提供帮助。这不是直观的，但已经有很多例子被记录下来，并且可以用博弈论来证明。数学也是有用的，因为它可以提出精确和实用的预测。在合作的情况下，这些预测可以帮助我们制定战略，加强自私的个人之间的合作。例如，如何才能诱使人们更频繁地报警？一种解决方案是减少(而不是增加！)一部分证人报警的能力，例如通过削弱他们打电话的能力，并向每个人证明这一点。当只有几个目击者能够真正提供帮助时，这些人会更愿意自愿。在我的工作中，我分析了类似的、更复杂的案例，在这些案例中，可能是自私的个人行动可以提供集体利益，我建议在这些情况下加强合作的战略解决方案。

Many interactions in nature are antagonistic because Darwinian natural selection leads to the survival of the fittest, and one's advantage is usually someone else's disadvantage. Yet, many cases of altruism and cooperation exist: from sterile soldiers in ants that do not reproduce and only work for the colony, to sentinels in meerkats that give the alarm in case of predators approaching. Altruists pay a cost for helping other individuals, a cost that selfish individuals do not pay. Because altruist and selfish individuals ultimately compete for reproduction, the selfish individuals should have an advantage. How can we explain the existence of cooperation then? One solution is that altruists are usually family members: ants and other social insects for example help their sisters by helping the nest. In this way they favour the spread of their own genes, because the targets of their altruism bear the same genes with high probability. Another solution in that altruism can be directed towards individuals that are in a position to reciprocate in successive encounters. Being altruist, therefore, may pay back because altruists receive a benefit from those whom they have helped. These two explanations, however, are not fully satisfactory, because there are many cases of symbiosis and cooperation in which individuals are not related and will never meet again, and yet cooperation exists in these cases. My work aims at understanding how these cases are possible. I do this by developing models of game theory, the branch of mathematics developed from the work of John Nash (the 'Beautiful Mind' of the famous movie). A game, in mathematics, is the description of a situation in which two players are in conflict and each tries to get the maximum payoff. Mathematics is necessary because the results are not always intuitive. Consider for example the case of a group of people witnessing a crime. If one of them called the police the criminal could be arrested. Arresting the criminal is a public good. Calling the police, however, has a small cost for an individual, and when there are many witnesses everybody prefers that it is someone else that calls the police. Everybody is better off if the criminal is arrested, but everybody prefers that it is somebody else that takes the risk and pays the cost. One would think that, when more people are available to volunteer, the probability that someone calls the police increases; in fact when too many people witness a crime, usually nobody volunteers to help. This is the effect of strategic behaviour - everybody relies on someone else with a certain probability, and as the number of possible volunteers increases, this probability increases, and it increases more when the number of witnesses is larger. In fact when one is the only (or one of few) possible volunteer, he is usually more likely to help. This is not intuitive, but many example have been documented, and it can be demonstrated by game theory. Mathematics is useful also because it can suggest precise and practical predictions. In the case of cooperation these predictions can help us devise strategies to increase cooperation among selfish individuals. For example, how is it possible to induce people to call the police more often? One solution is to reduce (not to increase!) the ability of a part of the witnesses to call the police, for example by impairing their ability to make a phone call, and to make this evident to everybody. When only a few witnesses can actually help, these ones will be more willing to volunteer. In my work I analyse similar, more complicated cases in which individual actions, that can be selfish, can provide a collective good, and I suggest strategic solutions to increase cooperation in these situations.