Game Theory_lecture3_08_handouts

Game Theory_lecture3_08_handouts - EF4484_Game...

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EF4484_Game Theory_Lecture 3 1 Static (or Simultaneous- Move) Games of Complete Information Cournot models of duopoly and oligopoly Concave Function and Maximization Bertrand model Public Goods EF4484-Game Theory 2 Outline of Static Games of Complete Information Introduction to games Normal-form (or strategic-form) representation Iterated elimination of strictly dominated strategies Nash equilibrium Review of concave functions, optimization Applications of Nash equilibrium Mixed strategy equilibrium 9/17/08 EF4484-Game Theory 3 Agenda Review of previous classes Cournot models of duopoly and oligopoly Solving maximization problem Concave functions Bertrand Public Goods 9/17/08 EF4484-Game Theory 4 Definition: Nash Equilibrium (Review) Given others’ choices, player i cannot be better- off if she deviates from s i * Prisoner 2 Mum Confess Prisoner 1 Mum -1 , -1 -9 , 0 Confess 0 , -9 -6 , -6 9/17/08
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EF4484_Game Theory_Lecture 3 2 EF4484-Game Theory 5 Nash equilibrium survive iterated elimination of strictly dominated strategies (Review) 1 , 0 1 , 2 0 , 1 0 , 3 0 , 1 2 , 0 Player 1 Player 2 Middle Up Down Left Right 9/17/08 EF4484-Game Theory 6 Comparing solutions via iterated elimination of strictly dominated strategies to Nash equilibrium strategies (Review) Player 2 L’ C’ R’ Player 1 T’ 0 , 4 4 , 0 3 , 3 M’ 4 , 0 0 , 4 3 , 3 B’ 3 , 3 3 , 3 3.5 , 3.6 9/17/08 EF4484-Game Theory 7 IEDS vs. Nash Summary (Review) In an n -player normal-form game, if iterated elimination of strictly dominated strategies eliminates all but the strategies ( s 1 * , s 2 * , . .., s n * ), then ( s 1 * , s 2 * , . .., s n * ) is the unique Nash equilibrium. In an n -player normal-form game, if the strategies ( s 1 * , s 2 * , . .., s n * ) is a Nash equilibrium then they survive iterated elimination of strictly dominated strategies. But the strategies that survive iterated elimination of weakly dominated strategies do not necessarily find all the Nash equilibrium strategies. With iterated elimination of weakly dominated strategies, order of elimination may matter. 9/17/08 Cournot Model Augustin Cournot introduced first formal model of oligopoly in 1838 oligopoly firms choose how much to produce at same time as in prisoners' dilemma game, firms are playing noncooperative game of imperfect information each firm chooses its output level before knowing what other firm will choose firms may choose any output level they want 9/17/08 8 EF4484-Game Theory
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EF4484_Game Theory_Lecture 3 3 EF4484-Game Theory 9 Basic model of Cournot duopoly A product is produced by only two firms: firm 1 and firm 2. The quantities are denoted by
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Game Theory_lecture3_08_handouts - EF4484_Game...

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