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# GAME THEORY (Chapter 13 Summary).docx

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School
McGill University
Department
Economics (Arts)
Course
ECON 230D2
Professor
John C Kurien
Semester
Winter

Description
GAME THEORY Strategic decisions result in payoffs for the players Cooperative game: game in which participants can negotiate binding contracts that allow them to plan joint strategies. Noncooperative game: contracts and negotiations not possible We focus on non-cooperative games, where it is essential to understand your opponents point of view and to deduce his likely response to your actions Dominant Strategy: strategy that is optimal no matter what an opponent does. Firm A does better if it does a certain move than it would in both options of the other move, so it must do the first move. When both players have a dominant strategy, we call it equilibrium in dominant strategies If there is no dominant strategy, the firm without the strategy must put themselves in the other firms shoes and see if they have a dominant strategy, and what they would do, to decide what we would do General equilibrium concept to ensure strategies are stable: Nash Equilibrium (each player is doing the best it can given the actions of its opponents. Since players have no reason to deviate from Nash eq, it is stable. I’m doing the best I can given what you’re doing, you’re doing the best you can given what I’m doing. (as opposed to dominant, we’re both doing the best we can no matter what, which is a special case of Nash equilibrium). There could be no Nash equilibrium, or several. If there are two Nash equilibriums (crispy/sweet example), firms might be able to signal each other in order for them both to come off better. Pure strategy: player makes a specific choice or takes a specific action Mixed strategy: No Nash equilibrium in pure strategy, but there is for mixed strategies(matching pennies). No combo leaves both players satisfied. Mixed strategy is strategy in which players make random choices among two or more possible actions, based on a set of chosen probabilities (they would keep changing their choices) If a random strategy wasn’t used, the other player would eventually discern the pattern of choice the first player makes, and screw them over. Once we allow for mixed strategies, EVERY game has at least one Nash equilibrium. Some games have Nash equilibrium in both pure and mixed strategies. They can provide other solutions, but not necessarily realistic ones (battle of the sexes). THEREFORE, THIS CHAPTER FOCUSES ON PURE STRATEGIES. Difference between prisoner’s dilemma and firms: in firms, choice is repeated and payoffs are received over and over again. With each repetition each firm can develop a reputation about its own behaviour and can study the behavior of its competitors. Tit-for-tat strategy: start out with high price, maintain as long as other firm cooperates and charges high price. As soon as competitor lowers price, follow suit and charge lower price. If
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