Game Theory

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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 . . . . . . . . . . . . . . . . . . . 2.2.5 Amendments . . . . . . . . . . . . . . . . . . . . . 2.2.6 Borda Count . . . . . . . . . . . . . . . . . . . . . 2.2.7 Complementary scores . . . . . . . . . . . . . . . . 2.2.8 Divide the cake . . . . . . . . . . . . . . . . . . . . 2.2.9 Outvoting thresholds . . . . . . . . . . . . . . . . . 2.2.10 The power of the agenda-setter . . . . . . . . . . . . 2.2.11 4 proposals in a 3-person committee . . . . . . . . . 2.2.12 Agenda setting in two-dimensional space . . . . . . 2.2.13 Four voters in R2 space . . . . . . . . . . . . . . . . 2.2.14 Strategic voting . . . . . . . . . . . . . . . . . . . . 2.2.15 Strategic voting: The general result . . . . . . . . . 2.3 Electoral competition . . . . . . . . . . . . . . . . . . . . . 2.3.1 Inferring voting behavior from empirical frequencies 2.3.2 Two-party electoral competition . . . . . . . . . . . 3

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4 2.3.3 Dominant point that is a bliss point: additional properties . . . . . . . 2.3.4 Three opportunistic parties . . . . . . . . . . . . . . . . . . . . . . . 2.3.5 Making a rational voter under multi-party competition a sincere voter 2.3.6 Probabilistic voting . . . . . . . . . . . ....
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