Topic12_Game Theory

Topic12_Game Theory - Topic 12 12 Game Theory Ratna k....

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Topic 12 Game Theory Ratna k. Shrestha
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Gaming and Strategic Decisions ame a situation in which layers he Game is a situation in which players (the participants) make strategic decisions. Examples : ap e s firms competing with each other by setting prices group of consumers bidding against each other in an auction Strategic decisions result in payoffs (rewards or benefits) to the players. 2
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Gaming and Strategic Decisions Game theory tries to determine optimal strategy for each player. Optimal strategy for a player is the one that maximizes his/her expected payoff. We consider players are rational (that means they maximize their own profits/payoffs). 3
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Non-cooperative v. Cooperative Games ooperative Game Cooperative Game Players negotiate binding contracts that llow them to plan joint strategies. allow them to plan joint strategies. Example: Buyer and seller negotiating the price of a good or service or a joint pg j venture by two firms. Non-cooperative Game Negotiation or enforcement of binding contracts between players is not possible. 4
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Static vs. Dynamic Games Static Game Each player acts only once and simultaneously (or without knowing rival’s action). Players have perfect information about the payoffs but not the rival’s move. Dynamic Game Players move either sequentially (Stackelberg model) or repeatedly (play 5 Cournot game many times).
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tatic Game Static Game ormal form f A normal form of a static game pecifies High Low AA specifies players’ possible strategies, their High 4, 4 5, 4 payoffs for each combination of strategies. Low 4.5, 4.5 4, 5 6
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Dominant Strategies ominant Strategy the one that is optimal Dominant Strategy is the one that is optimal no matter what an opponent does. dominant strategy is table the sense A dominant strategy is stable, in the sense that players will choose this strategy and will not deviate from it. In the next game, Firm A always chooses Advertise (no matter what Firm B does). Therefore, “Advertise” is Firm A’s dominant strategy. 7
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Dominant Strategies y the same token, “Advertise” is also Firm By the same token, Advertise is also Firm B’s dominant Strategy. Since both firms choose “Advertise”, , (Advertise, Advertise) is the Nash equilibrium of this game. In the modified advertising game, Firm B has “Advertise” as the dominant strategy. Given that Firm B chooses “Advertise”, Firm A will choose “Don’t”. So (Ad, Don’t Ad) is the 8 Nash equilibrium.
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Payoff Matrix for Advertising Game on’t Firm B Advertise Don’t Advertise Advertise 10, 5 15, 0 on’t Don t Advertise 10, 2 6, 8 9
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on’t Firm B Modified Advertising Game Advertise Don t Advertise 10, 5 15, 0 Advertise on’t 10, 2 12, 8 Don t Advertise 10
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This note was uploaded on 05/11/2011 for the course COMM 295 taught by Professor Ratna during the Winter '09 term at UBC.

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Topic12_Game Theory - Topic 12 12 Game Theory Ratna k....

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