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An Interpretation of Function of Leadership Using Game Theory.

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An interpretation of function of leadership using game theory.

This paper seek to provide a generalisation of the function of leadership using game theory. Assuming there are 2 ends of spectrum of people- extreme rational and extreme irrational people. Most people will lies within the spectrum with only a handful of them representing extreme rational or extreme irrational. Dixit (2004) define rationality as having 'two essential ingredient: complete knowledge of one's own interests, and flawless calculation of what actions will best serve those interest.' Game theory interpretation of the function leadership assumes the follower lies towards the rational end of the spectrum.

Given the follower are mostly rational, we can assume that there are 2 ends of spectrum of people- altruistic people and home economicus. Most people will lies within the 2 ends of spectrum with only a handful of them representing totally altruistic people or homo economicus. The proposed interpretation of the function of leadership assumes the followers lies towards the home economicus end of the spectrum. A brief treatment of the altruistic followers are given at the end of the paper.

When followers are given the choice of doing a particular action A. There are two possibilities, either the action result in a positive payoff to the followers or a negative payoff.
1)If action A result in a positive payoff and the assumption that the follower are rational, we can assume that rational followers would engage in action A regardless whether there is a leader or not.
2)If action A result in a zero or negative payoff and the assumption that the follower are rational homo economicus, we can assume that rational followers would not engage in action A without any modifier of the situation payoff.
We assume a possible modifier of the situation represent a leader or a dictator. If the

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