# Game Theory

Submitted By rwatson
Words 2875
Pages 12
Rachel Dillie
SOS-360
Final Project
March 25, 2014

Game Theory

“Game theory is the study of strategic interaction among rational players in an interactive setting” (Stevens, Lecture 1). Elements of a game consist of common knowledge, the players, strategies and payoffs. Every other Friday night my wife and I play cards at our friend’s house and it generally gets more intense as the game and the drinks progress. We mainly play a card game called spades and we play as partners. Common knowledge in this game is every player knows that in order to win you have to bid the correct number of books, meaning you have to guess how many rounds you and your partner can win based off what cards you are holding and what you think the other players are holding in their hands. Each player also is assumed to be an experienced player unless otherwise stated and even if they are it’s easier to guess how the hand will play out. In this card game there is not strictly a pure strategy at play, meaning it doesn’t not involve an act of randomness but a game of mixed strategy. Mixed strategy means using a pure strategy with acts of randomness. I have an idea what the other players will do when it is their turn in the card game but sometimes to force their hand, it is necessary to randomly sacrifice one of your cards to make them display their higher ranked cards. The payoff to a player reflects what that player cares about, not what another player thinks they should care about. Being rational means I make my decisions in a way that will lead to my best expected payoff and in the card game my best payoff is to allow my partner and I to make the required books that we bid and cause the other players to lose, as well as setting the match for the next round. The game of spades is a finite game, meaning the game is sure to end, there is not an infinite number of choices and the...

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