Game+Theory


 * GAME THEORY**

Game Theory elaborates upon Hobbes' theory of the State of Nature.

Game Theory relies on rational behavior for interactive decision making on the assumption that human beings are absolutely rational in their economic choices in order to maximize rewards.

An common example of modern game theory is called the **Prisoner's Dilemma,** which is explained below.

Scenario
Two conspirators are arrested and interrogated separately. If one implicates the other, he may go free while the other receives a life sentence. Yet, if both confess, bad fate befalls them. If both stay silent, insufficient evidence will lead them being charged with and convicted of a lesser crime.

Description
To confess or not confess? __Dominant Strategy:__ Evaluate separately each of the strategic outcomes that leads to the best reward, a dominant strategy. Each player has a dominant strategy, which is the strategy that is the best to choose, regardless of what the other player does. __Dominant Strategy Equilibrium:__ Each player has a dominant strategy, resulting in an equilibrium that is Pareto dominated by an alternate outcome in which each player plays the dominated strategy. To confess is a dominant strategy but when both prisoners confess it is considered a dominant strategy equilibrium.

The Prisoner's Dilemma rests on two assumptions: 1) Players are rational. 2) Players will only play the game once.

Further experiments have shown that when the players participate in iterated (multiple) games, they tend to cooperate. One can apply this finding to the political arena today and the global context in which countries know they will be interacting with each other in the future.

=Robert Axelrod’s Model of the Prisoner’s Dilemma=
 * ||  || **Player 2** ||   ||
 * ||  || Cooperate || Defect ||
 * **Player 1** || Cooperate || R, R || S, T ||
 * || Defect || T, S || P,P ||

Payouts (in descending order): T = Temptation R = Reward P = Punishment S = Sucker

In Hobbes’ State of Natureboth players are motivated by self-preservation and self-gain. In the State of Nature, players would choose the option thatboth can earn the greatest payout (Temptation) and avoid the greatest loss(Sucker). As such, the dominant strategyin a single iteration game would be to defect or attack the other playerinstead of cooperating.

The true question that the prisoner's dilemma asks is about the state of human nature. Will people be willing to cooperate when it is their own self-interest to dissent? Denying would either get a prisoner off free or if both deny lead to a harser sentence. This leads to a significant dilemma, which has been studied for hundreds of years.