ecn 122 hw 1 - 38 25 35 45 25 11 7 7 35 11 1-3 45 11 1-9...

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Page 1 of 2 ECONOMICS 122 GAME THEORY Professor Giacomo Bonanno ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ PROBLEM SET # 1 ANSWERS (1) (a) The normal form is as follows: (1) LOWEST PRICE AUCTION Value BIDS 25 35 45 Player 1 36 Player 2 32 Player 3 38 25 35 45 25 11 0 0 0 7 0 0 7 0 35 11 0 0 11 0 0 0 7 0 45 11 0 0 11 0 0 11 0 0 Player 3 bids 25 25 35 45 25 0 0 13 0 7 0 0 7 0 35 11 0 0 1 0 0 0 -3 0 45 11 0 0 1 0 0 1 0 0 Player 3 bids 35 25 35 45 25 0 0 13 0 0 13 0 7 0 35 0 0 13 0 0 3 0 -3 0 45 11 0 0 1 0 0 -9 0 0 Player 2 Player 1 Player 2 Player 1 Player 2 Player 1 (b) For Player 1 $25 is weakly dominated by $35. Player 1 does not have a dominant strategy. (c) For Player 2 $25 is weakly dominated by $35. Player 2 does not have a dominant strategy. (d) For Player 3 $25 is weakly dominated by $35 and by $45; $35 is weakly dominated by $45. Thus $45 is a weakly dominant strategy. (e) There is no dominant-strategy equilibrium, because players 1 and 2 do not have a dominant strategy.
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Page 2 of 2 (2) (a) The normal form is as follows: (2) SECOND-PRICE AUCTION Value BIDS 25 35 45 Player 1 36 Player 2 32 Player 3
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Unformatted text preview: 38 25 35 45 25 11 7 7 35 11 1-3 45 11 1-9 Player 3 bids 25 25 35 45 25 13-3-3 35 1 1-3 45 1 1-9 Player 3 bids 35 25 35 45 25 13 3-13 35 3 3-13 45-9-9-9 Player 3 bids 45 Player 2 Player 2 Player 2 Player 1 Player 1 Player 1 (b) For Player 1, $25 and $45 are weakly dominated by $35. Thus $35 is a weakly dominant strategy (c) For Player 2, $45 is weakly dominated by $35. Player 2 does not have a dominant strategy. (d) For Player 3, $25 is weakly dominated by $35 and by $45. $35 is weakly dominated by $45. Thus $45 is a weakly dominant strategy (e) There is no dominant-strategy equilibrium because player 2 does not have a dominant strategy....
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ecn 122 hw 1 - 38 25 35 45 25 11 7 7 35 11 1-3 45 11 1-9...

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