Skyrms’ book, Evolution of the Social Contract, offers a compelling explanation as to why individuals, when placed with one-shot prisoner’s dilemmas, will often cooperate, or choose the equilibrium that will benefit both parties equally. He uses examples to outline how individuals of certain environments frequently engage in activities that benefit the group at their own personal expense. Using both game theory and decision theory, Skyrms explores problems with the social contract when it is applied to evolutionary dynamics. In the chapters of the book, he offers new insights into concepts such as sex and justice, commitment, and mutual aid.
Skyrms’ writing goes beyond traditional game theory, and exposes some weaknesses in its application. He rejects the theory’s traditional interpretation of rational actors and actions by discovering some glaring inconsistencies. Skyrms conducted a number of experiments using one-shot prisoners’ dilemmas. The ultimatum the author introduces in the first chapter serves as a simple example of a one-shot prisoners’ dilemma. In the initial form of the example, Skyrms proposes there is a cake that must be divided between two individuals. Each individual is looking to maximize his or her utility, and therefore, wants as much of the cake as possible. However, there is a third party, or what Skryms labels a “referee.” The two individuals must determine the percentage or portion of the cake they want and summit these requests to the referee. The percentages must not exceed 100%, or the referee will consume all the cake. It is therefore not in either parties’ best interest to request a significantly large portion. Additionally, if the total of the two requests is below 100% of the cake, the referee will take the left-over portion. The two parties will then aim to maximize their portion, however the best claim that an individual submits is dependent upon the other party’s claim. There are two interacting optimization problems (Skyrms 3, 4).
An answer to the puzzle will be found in solutions that are in equilibrium. An equilibrium in informed rational self-interest, or a Nash equilibrium, is any solution to the problem whereby neither party could do better by altering its position. However, this is a general and broad definition. Further stipulations may be added. It could be further requisite that should a party alter its position, not only would it not do better, it would do worse than it would have at equilibrium. The inclusion of this additional provision is considered a strict Nash equilibrium. To arrive at such an outcome, given Skyrms example, each individual will request half of the cake (Skyrms 4, 5).
Such a result is frequent in laboratory experiments. The behaviors can be a bit puzzling when approaching the situation from the view of traditional game theory. One could argue that such a...