Lect05_Slides

Lect05_Slides - 2/13/2012 Coordination Problems and Other...

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2/13/2012 1 Coordination Problems and Other Topics in Simultaneous Move Games More Complicated Simultaneous Move Games Coordination Problems Any time we have multiple Nash equilibrium, we loose predictive power; we cannot say which equilibrium will be chosen. Games with multiple Nash equilibria are known as coordination games. Coordination games can be strategic settings where all players want to do the same thing, e.g. convict the guilty acquit the innocent. Coordination games can also be strategic settings where players want to do different things, e.g. drive through an intersection / yield to the other driver.
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2/13/2012 2 The Pittsburgh Left Turn Game Driver 1 Driver 2 Payoffs are in terms of seconds gained or lost (with minus sign) Driver 2 (Plan: proceed through intersection) Proceed with Plan Yield to Other Driver 1490 1490 5 5 Driver 1 (Plan: make left turn) Proceed with Plan -1490 , -1490 , -5 Yield to Other Driver -5 , 5 -10 , -10 Equilibria in the Pittsburgh Left Turn Game Both equilibria have one driver proceeding, while the other yields. Both equilibria are efficient . In such cases, governments often step in to impose one equilibrium by law. This game is a particular version of the game of “Chicken” Driver 2 (Plan: proceed through intersection) Proceed with Plan Yield to Other Driver 1490 1490 5 5 Driver 1 (Plan: make left turn) Proceed with Plan -1490 , -1490 , -5 Yield to Other Driver -5 , 5 -10 , -10
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2/13/2012 3 “Anti Coordination” Coordination Games 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) lowest unique positive integer (LUPI). If there is no unique integer choice, there is no winner. “Coordination” Coordination Games Suppose you and a partner are asked to choose one element from the following sets of choices. If you both make the same hi $1 th i thi choice, you earn $1, otherwise nothing. { Red , Green , Blue } {Heads, Tails} {7, 100, 13, 261, 555} Write down an answer to the following questions. If your partner writes the same answer you win $1, otherwise nothing nothing. A positive number A month of the year A woman’s name
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2/13/2012 4 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). What are the multiple equilibria in this game? Why? Finding Equilibria by Eliminating Dominated Strategies. ... Strategies U and M are weakly dominated for Player Alpha by strategy D. Suppose we eliminate strategy U first. The resulting game is: It now appears as though there is a unique equilibrium at D,R.
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2/13/2012 5 ...Can Lead to the Wrong Conclusion.
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This note was uploaded on 03/04/2012 for the course ECON 1200 taught by Professor Staff during the Fall '08 term at Pittsburgh.

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Lect05_Slides - 2/13/2012 Coordination Problems and Other...

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