Lect05_Slides

Lect05_Slides - CoordinationGamesand...

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Coordination Games and Continuous Strategy Spaces More Complicated Simultaneous Move Games
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ther Coordination Games Other Coordination Games Suppose you and a partner are asked to choose one element om the following sets of choices If you both make the same from the following sets of choices. If you both make the same choice, you earn $1, otherwise nothing. { Red , Green , Blue } {Heads, Tails} {7, 100, 13, 261, 555} rite down an answer to the following questions If your Write down an answer to the following questions. If your partner writes the same answer you win $1, otherwise nothing. A positive number A month of the year A woman’s name
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nti oordination Games Anti Coordination Games ot the same dress! (Fashion) Not the same dress! (Fashion) Not the same words/ideas (Writing) LUPI, a Swedish lottery game designed in 2007: Choose a positive integer from 1 to 99 inclusive. The winner is the one person who chooses the lowest unique positive integer (LUPI). If no unique integer choice, no winner.
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nother Example of Multiple Equilibria in Pure Another Example of Multiple Equilibria in Pure Strategies: The Alpha Beta game. Strategies for Alpha (Row) are Up (U), Middle (M) or Down (D). Strategies for Beta (Column) are Left (L) or Right (R).
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Finding Equilibria by Eliminating Dominated Strategies. ... Strategies U and M are weakly dominated for Player Alpha by t D strategy D. Suppose we eliminate strategy U first. The resulting game is: I f eliminate L and then M, the solution is D,R.
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Can Lead to the Wrong Conclusion ...Can Lead to the Wrong Conclusion. Suppose instead we eliminated Alpha’s M strategy first. The resulting me is: game is: Now if we eliminate R and then U, the solution is D,L. Lesson: If there are weakly dominated strategies, consider all possible orders for removing these strategies when searching for the Nash quilibria of the game equilibria of the game.
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nding Equilibria via est Response Finding Equilibria via Best Response Analysis Always Works: There are two mutual best responses: (D,L) and (D,R).These are the two Nash equilibria of the (, ) q game.
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Cournot Competition p A game where two firms (duopoly) compete in terms of the quantity sold (market share) of a homogeneous good is referred to as a Cournot game after the French economist who first studied it. Let q 1 and q 2 be the number of units of the good that are brought to market by firm 1 and firm 2. Assume the market price, P, is determined by market demand: P=a b(q 1 +q 2 ) if a>b(q 1 +q 2 ), P=0 otherwise. P q 1 +q 2 a Slope = b Firm 1’s profits are (P c)q 1 and firm 2’s profits are (P c)q 2 , where c is the marginal cost of producing each unit of the good. Assume both firms seek to maximize profits.
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Numerical Example, Discrete Choices Suppose P = 130 (q 1 +q 2 ), so a=130, b=1 The marginal cost per unit, c=$10 for both firms.
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Lect05_Slides - CoordinationGamesand...

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