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S09-games-B - Game Theory and Oligopoly B ECON 201 ECON 201...

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ECON 201 1 / 34 Game Theory and Oligopoly B ECON 201
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Preliminaries Preliminaries Chaps 13 & 14 Plan Definitions Game trees, pp506-7 Subgame perfection, pp506-7 Fig 14.2 Two subgames in fig 14.2 Recipe Equilibria and strategies Example 1, p506-8 Example 2, p465 Example 3 Conclusions ECON 201 2 / 34
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Chaps 13 & 14 Preliminaries Chaps 13 & 14 Plan Definitions Game trees, pp506-7 Subgame perfection, pp506-7 Fig 14.2 Two subgames in fig 14.2 Recipe Equilibria and strategies Example 1, p506-8 Example 2, p465 Example 3 Conclusions ECON 201 3 / 34 We have covered: 1. static games and pure strategies; pp 452-463, 494-497 and still have to cover 2. sequential games; pp 464-472, 505-512
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Plan Preliminaries Chaps 13 & 14 Plan Definitions Game trees, pp506-7 Subgame perfection, pp506-7 Fig 14.2 Two subgames in fig 14.2 Recipe Equilibria and strategies Example 1, p506-8 Example 2, p465 Example 3 Conclusions ECON 201 4 / 34 Definitions Oligopoly examples: Stackelberg duopoly with discrete strategies (pp 506-8) Stackelberg duopoly with continuous strategies (pp 465-6) strategic trade with discrete strategies (Perloff does strategic trade with continuous strategies (pp 467-9), but it is a bit gnarly)
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Definitions Preliminaries Chaps 13 & 14 Plan Definitions Game trees, pp506-7 Subgame perfection, pp506-7 Fig 14.2 Two subgames in fig 14.2 Recipe Equilibria and strategies Example 1, p506-8 Example 2, p465 Example 3 Conclusions ECON 201 5 / 34 game tree (extensive form) p507 backward induction p507
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Game trees, pp506-7 Preliminaries Chaps 13 & 14 Plan Definitions Game trees, pp506-7 Subgame perfection, pp506-7 Fig 14.2 Two subgames in fig 14.2 Recipe Equilibria and strategies Example 1, p506-8 Example 2, p465 Example 3 Conclusions ECON 201 6 / 34 A game tree illustrates the extensive form of a game, showing shows (i) the order of the moves, (ii) all possible decision nodes with the relevant choices and (iii) payoffs at the terminal nodes In ECON201, we won’t draw game trees for games with simultaneous moves.
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Subgame perfection, pp506-7 Preliminaries Chaps 13 & 14 Plan Definitions Game trees, pp506-7 Subgame perfection, pp506-7 Fig 14.2 Two subgames in fig 14.2 Recipe Equilibria and strategies Example 1, p506-8 Example 2, p465 Example 3 Conclusions ECON 201 7 / 34 If players know all actions taken and events occurring before their choice, a subgame consists of all the subse- quent decision and terminal nodes A strategy profile is a subgame perfect equilibrium if it specifies a Nash equilibrium in every subgame of the orig- inal game.
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Fig 14.2, p510
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Two subgames in fig 14.2 Preliminaries Chaps 13 & 14 Plan Definitions Game trees, pp506-7 Subgame perfection, pp506-7 Fig 14.2 Two subgames in fig 14.2 Recipe Equilibria and strategies Example 1, p506-8 Example 2, p465 Example 3 Conclusions ECON 201 9 / 34 1. the game starting from the incumbent’s decision node (ie. the whole game), and 2. the game starting from the entrant’s decision node
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Recipe Preliminaries Chaps 13 & 14 Plan Definitions Game trees, pp506-7 Subgame perfection, pp506-7 Fig 14.2 Two subgames in fig 14.2 Recipe Equilibria and strategies Example 1, p506-8 Example 2, p465 Example 3 Conclusions ECON 201 10 / 34 Use backward induction to find subgame perfect equilibria
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