Decision Making using Game Theory: An introduction for managers

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191Appendix Bandp(B/A 2 )·p(A 2 )p(A 2 /B) p(B/A 1 )·p(A 1 ) p(B/A 2 )·p(A 2 )where p(A 2 ) 1 p(A 1 ) of course.ProofBy deWnition,p(A i and B) p(B/A i )·p(A i )andp(A i and B) p(A i /B) · p(B)Equating these two gives:p(A i /B) p(B/A i)·p(A i )p(B)orp(B) · p(A i /B) p(B/A i )·p(A i )Summing both sides over i gives:p(B) Σ i p(A i /B) Σ i p(B/A i )·p(A i )But we know thatΣ i p(A i /B) 1so(1)p(B) Σ i p(B/A i )·p(A i ) (2)Substituting (1) into (2) gives the result:p(A i /B) p(B/A i)·p(A i )Σ i p(B/A i )·p(A i )
BibliographyAbreu, D. (1986) Extremal equilibria of oligopolistic supergames, Journal of EconomicTheory, Vol.39, No.1, pp.191–225.Aliprantis, C. & Chakrabarti, S. (2000) Games and Decision Making (New York, OxfordUniversity Press).Aumann, R.J. (1975) Values of markets with a continuum of traders, Econometrica, Vol.43,No.4, pp.611–46.Aumann, R.J. (1987) Correlated equilibrium as an expression of Bayesian ignorance,Econometrica, Vol.55, No.1, pp.1–18.Aumann, R.J. (1988) Preliminary Notes on Integrating Irrationality into Game Theory,Mimeo, International Conference on Economic Theories of Politics, Haifa. [Quoted inMcKelvey & Palfrey (1992)].Aumann, R.J. (1989) Game theory, in: J. Eatwell, M. Milgate & P. Newman (Eds) The NewPalgrave: Game Theory (London, Macmillan). [First published in 1987 as The NewPalgrave: A Dictionary of Economics.]Aumann, R.J. & Peleg, B. (1960) Von Neumann–Morgenstern solutions to cooperativegames without side payments, Bulletin of the American Mathematical Society, Vol.66,pp.173–9.Axelrod, R. (1981) The emergence of cooperation among egoists, American Political ScienceReview, Vol.75, No.2, pp.306–18.Axelrod, R. (1984) The Evolution of Cooperation (New York, Basic Books). [1990 edition,London, Penguin Books.]Bacon, N.T. (1897) Researches into the Mathematical Principles of the Theory of Wealth byAugustin Cournot, 1838 (New York, Macmillan).Banzhaf, J. (1965) Weighted voting doesn’t work: a mathematical analysis, Rutgers LawReview, Vol.19, pp.317–43.Beck, L.W. (1960) A Commentary on Kant’s Critique of Practical Reason (Chicago, IL,University of Chicago Press).Beck, L.W. (Ed) (1969) Kant Studies Today (La Salle, IL, Open Court).Beck, L.W. (1988) Kant Selections (New York, Macmillan).Benoit, J.P. & Krishna, V. (1985) Finitely repeated games, Econometrica, Vol.53, No.4,pp.905–22.192
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Decision Making Using Game TheoryAn
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CAMBRIDGE UNIVERSITY PRESSCambridge
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viContents4 Sequential decision mak
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MMMM
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xPreface∑∑∑To Wnd new solutio
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2Introductionvying for business fro
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5TerminologyTable 1.1 The union’s
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7Classifying gamesGAME THEORYGames
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9A brief history of game theoryIn 1
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11A brief history of game theoryano
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13A brief history of game theoryIt
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15Layoutexplained. Games involving
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2 Games of skillIt is not from the
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19Linear programming, optimisation
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27The Lagrange method of partial de
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33An introduction to basic probabil
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35An introduction to basic probabil
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37Games of chance involving riskV(X
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39Games of chance involving riskthe
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41Games of chance involving riskyu(
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43Games of chance involving riskExa
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45Games of chance involving uncerta
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47Games of chance involving uncerta
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49Representing sequential decision
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51Representing sequential decision
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53Sequential decision making in sin
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67Sequential decision making in two
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73Cooperative two-person gamesapply
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75Cooperative two-person games∑it
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5 Two-person zero-sum games ofstrat
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79Representing zero-sum gamesPlayer
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81Games with saddle pointsFigure 5.
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83Games with saddle pointsSurgeonSt
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85Games with saddle pointsPlayer 1a
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87Games with no saddle pointsPlayer
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89Games with no saddle pointsStrate
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91Large matrices generallybigger th
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93Interval and ordinal scales for p
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99Representing mixed-motive games a
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101Representing mixed-motive games
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103Mixed-motive games without singl
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113Summary of features of mixed-mot
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115The Cournot, von Stackelberg and
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129Solving games without Nash equil
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7 Repeated gamesLife is an offensiv
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137Infinitely repeated gamesincenti
Page 152 and 153: 141Finitely repeated gamescontinuou
Page 154 and 155: 143Finitely repeated gamesBUPALarge
Page 156 and 157: 145Finitely repeated gamesGHGLarge
Page 158 and 159: 147Finitely repeated gamesNatureGHG
Page 160 and 161: 8 Multi-person games, coalitions an
Page 162 and 163: 151Mixed-motive multi-person gamesp
Page 164 and 165: 153Partially cooperative multi-pers
Page 166 and 167: 155Indices of power: measuring infl
Page 186 and 187: 175Rationalityexperimental evidence
Page 188 and 189: 177Indeterminacygot locked into a l
Page 190 and 191: 179Inconsistencythe pot of £49 at
Page 192 and 193: 181Conclusionpost-industrial econom
Page 194 and 195: 183Appendix APlayer 1 wants to maxi
Page 196 and 197: 185Appendix APlayer 1choosesrow 1Pl
Page 198 and 199: 187Appendix Aon the straight line b
Page 200 and 201: 189Appendix Amax p min q Σw ij p i
Page 204 and 205: 193BibliographyBenoit, J.P. & Krish
Page 206 and 207: 195BibliographyJenkinson, T. (Ed.)
Page 208 and 209: 197BibliographyRobinson, M. (1975)
Page 210 and 211: Indexancestors and descendants 49ap
Page 212 and 213: 201Indexmaximin principle, in chanc
Page 214 and 215: 203Indexschool buses college cooper
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