Decision Theory

1. Riskiness measures and gambling wealth Riskiness measures – the idea and description

• Aumann, Serrano (2008) – economic index of riskiness• Foster, Hart (2009) – operational measure of riskiness

Buying and selling price for a lottery and the connection to riskiness measures• Lewandowski (2010)

Two problems resolved by gambling wealtha) Rabin (2000) paradoxb) Buying/selling price gap (WTA/WTP disparity)

Buying and selling price correspond to WTP and WTA notions respectively – mind WTA/WTP disparity

L10 0,35 1 0,35 0 L14 0,85 1 0,85 00,65 0,25 0,163 -600 0,15 0,25 0,0375 600

0,5 0,325 600 0,5 0,075 18000,25 0,163 1800 0,25 0,0375 3000

a m b g(a) g(m) g(b)600 900 1200 -5,272 0,0095 0,037600 750 900 -5,272 -0,046 0,009750 825 900 -0,046 -0,01 0,009825 862,5 900 -0,01 0,0009 0,009825 843,8 862,5 -0,01 -0,004 9E-04843,8 853,1 862,5 -0,004 -0,002 9E-04853,1 857,8 862,5 -0,002 -3E-04 9E-04857,8 860,2 862,5 -3E-04 0,0003 9E-04857,8 859 860,1563 -3E-04 -3E-06 3E-04859 859,6 860,1563 -3E-06 0,0002 3E-04859 859,3 859,5703 -3E-06 7E-05 2E-04859 859,1 859,2773 -3E-06 4E-05 7E-05859 859,1 859,1309 -3E-06 2E-05 4E-05859 859 859,0576 -3E-06 7E-06 2E-05859 859 859,021 -3E-06 2E-06 7E-06859 859 859,0027 -3E-06 -4E-07 2E-06859 859 859,0027 -4E-07 8E-07 2E-06859 859 858,9981 -4E-07 2E-07 8E-07859 859 858,9958 -4E-07 -9E-08 2E-07859 859 858,9958 -9E-08 7E-08 2E-07859 859 858,9952 -9E-08 -1E-08 7E-08859 859 858,9952 -1E-08 3E-08 7E-08859 859 858,9951 -1E-08 8E-09 3E-08859 859 858,995 -1E-08 -1E-09 8E-09859 859 858,995 -1E-09 3E-09 8E-09859 859 858,995 -1E-09 9E-10 3E-09859 859 858,995 -1E-09 -3E-10 9E-10

1. Riskiness measures and gambling wealth Riskiness measures – the idea and description

• Aumann, Serrano (2008) – economic index of riskiness• Foster, Hart (2009) – operational measure of riskiness

Buying and selling price for a lottery and the connection to riskiness measures• Lewandowski (2010)

Two problems resolved by gambling wealtha) Rabin (2000) paradoxb) Buying/selling price gap (WTA/WTP disparity)

Two fallacies

Departing from consequentialism

Again – departing from consequentialism

Large buying/selling price spreads for small W