Game theory had always been a frequently-discussed topic no matter in Economics or in Mathematics. For a long perios of time, it showed its influences in the areas, helping people to make decisions in order to reach optimum results adn profit maximization. This blog will introduce this famous theory along with some examples.
Introduction to Game Theory
Game Theory is a model of interative situations between different rational members, each member’s payoff is related to the other members. This concept is first developed by mathematician John von Neumann and economist Oskar Morgenstern in their book named “The Theory of Games and Economic Behavior” in 1944.It is used to analyze the interactions between different parties when the individuual decisions affected others’ benefit. This theory aimmed at producing an optimal solution for every decision-maker under strategic conditions.
Nash Equilibrium
Nash equilibrium is an essential concept in Game Theory which states an ideal outcome reached with all competitiors and no player can increase their payoff by switching to different choices.
Pure-Strategy Nash Equilibrium
In pure-strategy nash equilibrium, we only know the personal optimum situations but has no idea of the strategies of others. Also In these cases, the optimum outcomes will be harder to be reached due to the uncertainties.
Prisoner’s Dilemma is a famous example of the pure-strategy nash equilibrium. Consider the example of two criminals being arrested for a crime. Due to the lack of evidences, officials put criminals in two separate chambers meaning that they can’t communicate with each other about the strategy to cope with the situation. The four possibile outcomes are presented in the following table.
It is easy to see that when both of them are denying, nash equilibrium will be reached. However, when considering the personal best outcomes, accepting will be the best choice. The crash between personal interest and group interest led to the non-optimum result.
Mixed-Strategy Nash Equilibrium
In mixed-strategy nash equilibrium, all possible outcomes can be figured out by considering the probability and can reaches optimum result to profit maximization.