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

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.