Modelling macro behavior is an important goal of a lot of applied mathematical and statistical fields. In Game Theory it is in fact the micro behavior that is modelled so that the macro behavior can be observed. This is an important subject that extends to applications not only in Mathematics but Economics, Biology, Ecology and Military Sciences.
In this talk I will present an important building block of the field: the Normal Form Game. This is a model of interactive behavior of a finite number of agents who all act within their self-interest. An important mathematical question that arises from the concept of a Normal Form Game is whether there exists a particular behavior at which all agents will be at an equilibrium with no incentive to change.
The answer to this is yes: and it is called a Nash Equilibrium. This is named after the incredible work of John Nash, who won the Nobel prize in economics for his 25-page thesis in which he proved the equilibrium exists.
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