04.SimultaneousMove2

04.SimultaneousMove2 - SIMULTANEOUS-MOVE GAMES - EXAMPLES...

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SIMULTANEOUS-MOVE GAMES --- EXAMPLES I. STRUCTURE OF THE PRISONER’S DILEMMA PL .2 PL. 1 COOP DEFECT COOP CC1 , CC2 CD1 , CD2 DEFECT DC1 , DC2 DD1 , DD2 1. {COOP , COOP} IS MUTUALLY PREFERRED TO {DEFECT , DEFECT}……. CC1 > DD1 AND C C2 > DD2 . 2. BUT {COOP , COOP} IS NOT A NASH EQUILIBRIUM: EACH PLAYER WOULD DEVIATE TO “DEFECT” IF THE OTHER IS CHOOSING “COOP”…. DC1 > CC1 AND CD2 > CC2 . 3. {DEFECT , DEFECT} IS A NASH EQUILIBRIUM: DD1 > CD1 AND DD2 > DC2 . PL .2 PL. 1 COOP DEFECT COOP 5 , 3 1 , 6 DEFECT 8 , 0 2 , 1 1
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REAL-LIFE EXAMPLES THAT (POTENTIALLY) HAVE THE STRUCTURE OF A PRISONER’S DILEMMA : CONTRIBUTIONS TO A PUBLIC GOOD. Strategic thinking runs as follows: “I cannot bear the entire cost of this public good alone… So if others don’t contribute, I will not contribute either. .” Example : (Ballroom Dancing) N couples are present in a ballroom. Slow music begins and couples want to dance, but no couple wants to be the first to dance. “Being first to dance” is “to offer a public good” (it benefits everyone). CONFLICTS IN WHICH COOPERATION IS NOT SUSTAINABLE WITHOUT ENFORCEMENT. Example : Israeli-Palestinian conflict. Each side can benefit from cooperation as long as the other side genuinely cooperates and does not try to get a unilateral advantage. Example : States against ethnic groups with potential use of terrorist groups. State can “cooperate” to introduce reforms, and the ethnic group can “cooperate” to commit itself to democratic participation. But the state can also adopt a hard stance and defect, while the ethnic group can also deviate and use terrorism. STATE ETHNIC GR. REFORM TOUGH COOP X , 3 1 , 2 TERRORISM 3 , 0 2 , 1 If X < 3 , the Ethnic group has a dominant strategy to keep making additional demands and use terrorism to force more concessions from the state. Example: Two firms sharing a market can best “cooperate” and maintain their high prices, but each has an incentive to deviate and undercut its rival’s price to capture the entire market… 2
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Example: Firms often devote too much resource on advertisement because their rivals do. They would altogether be better off if they jointly reduce advertising. However each firm would take advantage from unilaterally increasing its advertisement when its rival’s is low. II. STRUCTURE OF THE COORDINATION GAME PL. 2 PL. 1 X Y X X1 , X2 A XY , B XY Y A YX , B YX Y1 , Y2 1. {X,X} AND {Y,Y} ARE NASH EQUILIBRIA:…. X1 > A YX AND X2 > B XY Y1 > A XY AND Y2 > B YX 2. EACH PLAYER PREFERS {X,X} AND {Y,Y} OUTCOMES TO THE OTHER TWO OUTCOMES IN ADDITION TO THE TWO CONDITIONS ABOVE, X1 > A XY AND X2 > B YX Y1 > A YX AND Y2 > B XY PL. 2 PL. 1 X Y X 4 , 3 1 , 2 Y 0 , 0 6 , 6 EXAMPLES: 3
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● Meeting a friend in one of the two possible locations, X or Y. ● Coordination of Central Bank’s (Monetary) policies with the Treasury’s
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04.SimultaneousMove2 - SIMULTANEOUS-MOVE GAMES - EXAMPLES...

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