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
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In sequential games, the players must alternate moves and in simultaneous games, the players can act at the same time. To analyze a sequential game, follow the basic strategic rule of looking ahead and reason back. Look ahead to the very last decision, and assume that if it comes to that point, the deciding player will choose their optimal outcome, meaning the highest payoff, or most desirable result. Back up to the second-to-last decision, and assume the next player would choose their best outcome, treating the following decision as fixed, because we have already decided what that player will pick if it should come to that. Continue reasoning back in this way until all decisions have been fixed. There is a company called Albano Cleaner’s in my area that currently dominates the market and makes $300,000 per year, and we are considering starting a competing company. If we enter the market, Albano Cleaners will have two choices, accept the competition or fight a price war. We have done market research from which we expect that if Albano accepts the competition, each firm will make a profit of $100,000 however, if they fight a price war, they will suffer a net loss of $100,000, and we will lose $200,000. Now we can look ahead and reason back. Looking ahead, if Albano faces the last choice, it will be between $100,000 profit and $100,000 loss. Naturally, they will choose the profit and if reasoning back, we now know it will not come to a price war, which means our