Game Theory
Workbook for Game Theory and Political Economy1
Martin Gregor IES, Charles University in Prague January 23, 2012
set of sample exercises has been created for the undergraduate course JEB064 Game Theory and Political Economy given by Martin Gregor at IES, Charles University, Prague. Each exercise includes a full solution. The workbook is a work in permanent construction. Any comment is more than welcome.
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Contents
1 Essentials in game theory 1.1 Centipede game (Rasmusen 2007) . . . . . . . . . . 1.2 Dirty campaign (lecture notes by Boehmke) . . . . . 1.3 George W. Bush in 2004 (lecture notes by Boehmke) 1.4 The Monty Hall problem (Rasmusen 2007) . . . . . 1.5 Elmer’s apple pie (Rasmusen 2007) . . . . . . . . . 1.6 Cancer tests (McMillan 1992) . . . . . . . . . . . . 1.7 The Battleship Problem (Nalebuff 1988) . . . . . . . 1.8 Joint ventures (Rasmusen 2007) . . . . . . . . . . . 7 7 8 9 10 11 12 13 13 17 17 17 18 19 19 20 20 21 22 22 22 23 25 26 26 27 28 30 31 32 32 33 33 34
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2 Voting 2.1 Preferences . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Asymmetric utilities . . . . . . . . . . . . . . . . . 2.1.2 Condorcet winner . . . . . . . . . . . . . . . . . . . 2.1.3 Euclidean preferences . . . . . . . . . . . . . . . . 2.1.4 Dominant point . . . . . . . . . . . . . . . . . . . . 2.2 Majority voting . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 3-person committee . . . . . . . . . . . . . . . . . . 2.2.2 Ancient letter . . . . . . . . . . . . . . . . . . . . . 2.2.3 Median voter . . . . . . . . . . . . . . . . . . . . . 2.2.4 Referendum test . . . . .
Martin Gregor IES, Charles University in Prague January 23, 2012
set of sample exercises has been created for the undergraduate course JEB064 Game Theory and Political Economy given by Martin Gregor at IES, Charles University, Prague. Each exercise includes a full solution. The workbook is a work in permanent construction. Any comment is more than welcome.
1 This
2
Contents
1 Essentials in game theory 1.1 Centipede game (Rasmusen 2007) . . . . . . . . . . 1.2 Dirty campaign (lecture notes by Boehmke) . . . . . 1.3 George W. Bush in 2004 (lecture notes by Boehmke) 1.4 The Monty Hall problem (Rasmusen 2007) . . . . . 1.5 Elmer’s apple pie (Rasmusen 2007) . . . . . . . . . 1.6 Cancer tests (McMillan 1992) . . . . . . . . . . . . 1.7 The Battleship Problem (Nalebuff 1988) . . . . . . . 1.8 Joint ventures (Rasmusen 2007) . . . . . . . . . . . 7 7 8 9 10 11 12 13 13 17 17 17 18 19 19 20 20 21 22 22 22 23 25 26 26 27 28 30 31 32 32 33 33 34
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2 Voting 2.1 Preferences . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1.1 Asymmetric utilities . . . . . . . . . . . . . . . . . 2.1.2 Condorcet winner . . . . . . . . . . . . . . . . . . . 2.1.3 Euclidean preferences . . . . . . . . . . . . . . . . 2.1.4 Dominant point . . . . . . . . . . . . . . . . . . . . 2.2 Majority voting . . . . . . . . . . . . . . . . . . . . . . . . 2.2.1 3-person committee . . . . . . . . . . . . . . . . . . 2.2.2 Ancient letter . . . . . . . . . . . . . . . . . . . . . 2.2.3 Median voter . . . . . . . . . . . . . . . . . . . . . 2.2.4 Referendum test . . . . .