Friday, 28 December 2012

Game Theory- The Rock-Paper-Scissors Algorithm

From the roll of a die and the shift of a pawn to the spin of a cue and the flip of a card, its principles come into action through the players, their strategies and their payoffs. A premise that entails the methodology, skill and technique behind even the most primitive forms of human leisure and makes something serious out of the business of games. One where equilibria are sought, risk and choice are evaluated and conflicting interests are observed in a manner of critique; a platform where competition and completeness are deduced and location, segregation and randomisation are considered. A formulation of not only the players but the games themselves in a means that quantifies the tricks and flicks to winning and the shortcomings to losing. Game theory is to games as calculus is to change, for games offer a wealth of profundity regarding the mechanics of human skill and strategy as well as the strategic basis to decision making; extending well into frontiers such as economics and evolutionary biology where the flux of mutation and competition play themselves out like a well choreographed game. Consider the prisoner's dilemma, where two suspects are apprehended on the suspicion of thievery, if a bargain is offered to each suspect with the promise of mitigated jail time in return for cooperation the end result will be unfold with defection by both parties due to the notion of strict dominance despite the seemingly logical outcome of cooperation by both parties. Furthermore, the classic battle of the sexes takes form in game theory whereby a man and woman desire boxing and ballet respectively however they simultaneously desire to be together. In order to go about such a game, one necessitates the utility of the Nash equilibrium in its mixed strategy form; an equilibrium in which there exists a set of strategies, one for the man and one for the woman such that no player has an incentive or advantage to change his or her strategy given what the other players are doing. Analogous to a law that no one would break despite the absence of law enforcement or capital punishment. A more familiar circumstance would be that of rock-paper-scissors, whereby Nash equilibrium may be reached via mixed strategy given the zero sum nature of the game. An overall nexus of balance and conformity driven towards the satisfaction of both parties and the achievement of a realistic and level headed outcome, comparable to an algorithm that plays the game over and over until scissors and paper fit hand in hand.

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