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 decision is quite irrational. If utility is measured in terms of material resources, the individuals are acting irrationally. However, it is not necessarily irrational for individuals to cooperate in situations where the individual's gain is so dependent upon the other individual. It seems Skyrms is not attempting to explain this irrationality, but rather, is exploring how people can interpret utility in a broader context than personal self-interest. As he states in the text, "Equilibrium in informed rational self-interest, even when strictly construed, does not explain our conception of justice" (Skyrms 5).
Skyrms incorporates evolution and the theory of survival of the fittest' into his exploration of game theory and choice. Skyrms presupposes that our behavioral dispositions are inherited, and have evolved over time. He relates our sense of justice in certain situations to our set of behavioral dispositions. Given that behaviors are inherited, Skyrms proposes that certain notions of justice have come into existence by evolving over many years. Certain behaviors,...