Game theory

In game theory, the study of applied mathematics in a strategic situation, a game in which a situation may arise where there is a Nash equilibrium that is Pareto dominated could be the Nash bargaining game. It is a simple game used to measure bargaining interaction between two parties. It works by getting both parties to submit a demand for a share of something, and if the sum of both requests is lower than the total then both parties get their request. If however the sum of both requests exceeds the total value then both parties will receive nothing.

If the requirement of uniqueness is removed from the definition, then we can add infinitely repeated games, as they are not required to be unique and can be repeated indefinitely. Such a solution to the problem of majoritarian cycling in two-dimensional policy space may be designed to imitate an election system, using three potential voters. A stable set of conditions would be that all voters are primarily concerned with themselves and not others, and that there is no political influence on their choice.

The policies and the social science elements of choice are important here, as they will affect the decision making process and provide multi-dimensional policies that the voters will have to deal with. However the conditions, due to social and political elements, are not stable and do not make this case Pareto optimal. The “independence of irrelevant alternatives” requirement is a term for how we go about linking decision making theories and social science.

The key theory behind IIA is that one has two choices, A and B, yet when a third choice, C in added, the choices A and B are not affected by the availability of choice C. The Borda count and simple plurality do not meet this requirement as the two systems cannot stop the addition of choice C from affecting choices A and B. The Borda count system relies on the social choice element, and the plurality system reverses the positions of A and B, whilst adding an irrelevant alternative that will have an effect on the outcome of the choice.

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