Week 9 Notes
Week 9 Notes PAM 2000
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This 3 page Class Notes was uploaded by Eunice on Monday April 4, 2016. The Class Notes belongs to PAM 2000 at Cornell University taught by McDermott, E in Fall 2015. Since its upload, it has received 19 views. For similar materials see Intermediate Microeconomics in Political Science at Cornell University.
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Date Created: 04/04/16
PAM 2000 McDermott Spring 2016 March 22, 2016 Game theory o John Nash o Prisoners’ Dilemma a game in which all players have dominant strategies that result in profits (or other payoffs) that are inferior to what they could achieve if they use cooperative strategies Best response: the strategy that maximizes a player’s payoff given its beliefs about its rivals’ strategies Nash equilibrium: a set of strategies such that, when all other players use the best response strategy, no player can obtain a higher payoff by choosing a different strategy Pure strategy: each player chooses one strategy 100% of the time assigning a probability of 1 to a single action action with certainty no nash equilibrium guaranteed Mixed strategy: players can choose multiple nash equilibrium guaranteed dominant strategy: the choice preferred by a player regardless of what the other player decides game is used to talk about cartels and in determining whether players will stick to a collusive agreement economists argue that self-interested firms will undercut a cartel for a repeated game this may not be true o Battle of the Sexes: pure strategy multiple nash equilibria o Dynamic Games prior games discussed occur where the players move/make a decision simultaneously (no previous certain knowledge about the other players’ actions) Dynamic Games: players move sequentially or move simultaneously repeatedly over time, so a player has perfect information about the other players’ previous moves for our purposes, only consider sequentially moving players extensive form: specifies the n players, the sequence in which they make their moves, the actions they can take at each move, the information that each player has about players’ previous moves, and the payoff function over the possible strategies the charts used for prior games are called normal form a subgame: any node and all the nodes that follow it usually several subgames subgame perfect nash equilibrium: players’ strategies are a nash equilibrium in every sub game backward induction: first determine the best response by the last player to move next determine the best response for the player who made the next to last move repeat the process back to the at the beginning of the game the equilibrium found is technically composed of steps (and so technically not a nash equilibrium) credible threat: an announcement that a firm will use a strategy harmful to its rival and that the rival believes because the firm’s strategy is ration in the sense that it is in the firm’s best interest to use it making a commitment makes a threat more credible a commitment mechanism: through one, a player is locked into a course of action that one might not otherwise choose but that produces a desired result reputation matters The Stackelberg Model different types of competition exists in imperfect competition: duopoly, oligopoly sequential with a first mover/first entrant and the other firm(s) following/responding March 24, 2016 Review: Game Theory o how to solve simultaneous move (normal form) game how to find a nash equilibrium/equilibria (assuming one exists) o what is a dominant strategy and how to tell if it exists for a player o solve a sequential move game by Backward Induction this yields a subgame perfect nash equilibrium Auction o imperfect information in the games we discussed earlier, we assumed players knew the payoff functions of the other player(s) we usually think of these “functions” as values with an auction players devise bidding strategies without knowing the payoff functions of the other players o auction: a sale in which property or a service is solf to the highest bidder three key components: the number of units being sold (typically 1) the format of the bidding the value that potential bidders place on the good (privately known) types of auctions English o auctioneer starts the bidding at the lowest price that is acceptable to the seller and then repeatedly encourages potential buyers to bid more than the previous highest bidder dutch o ends dramatically with the first “bid” o seller starts by asking if anyone wants to buy at a relatively high price o seller reduces the price by given increments until someone accepts the offered price and buys at that price sealed bid o everyone submits a bid simultaneously without seeing anyone else’s bid and the highest bidder wins first price auction: the winner pays its own highest bid second price auction: the winner pays the amount bid by the second-highest bidder people will reveal the true value that they are willing to pay for the item useful for firms trying to extract maximum profit from bidders o objectives of bidder maximize consumer surplus the difference between the price they pay and the price they would have been willing to pay o Private vs. Common private value: how much the good is worth to the bidder no one else knows this common value: something like a commodity has a value that is the same for any buyer although the value may not be known in common value auctions: the winner’s curse o winning bid will often exceed the common value of the good
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