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.
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When there is zero or negative payoff then the modifier is a dictator.
Using the above idea, we can distinguish leaders from dictators. A dictators may be a leader to a group of followers which represent a subset of entire population. This subset of population, (i.e. follower of the leader-dictator) benefit from the dictatorship at the expense of the rest. To the rest of the population, the dictator is not a leader as he does not result in a Pareto improvement for them. A dictators may have power over the entire population but the entire population are not his followers. A person can chose to be the follower of a leader but cannot chose to leave a dictatorship.
Having established that the leader have to result in a Pareto improvement. We propose that there are two games which represent the possibilities of Pareto improvement the leader can result in.
In the former case, the leader can change the payoff such that Pareto equilibrium can be reached. In the later case, the leader act as coordinator who coordinate the followers to move from a bad Nash equilibrium to a better Nash equilibrium resulting in a Pareto improvement or coordinate the follower to a Nash equilibrium that benefits all. In the former case, the power given by the followers to...