Decision Making using Game Theory: An introduction for managers

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29The Lagrange method of partial derivatives(insurance, superannuation, etc.), so each time unit is valued at £60. Eachmaterials funding unit is valued at £25 and the Creative Design team is expectedto vary the balance between the two types of funding so as to maximise projectoutput while minimising expenditure for an expected 380 projects per week.Let m the number of materials funding units per week per project.Let t the number of time units per week per project.Let s the expected number of units of output 380.Let c the cost of the projects per week.Clearly,c 25m 60tand the department wishes to minimise this equation subject to theconstraint20tm 1/2 380The following three Lagrange equations must be solved:δcδm λ δsδmδcδt λδs δt20tm 1/2 380The partial derivatives are:δcδm 25δcδt 60δsδm 10tm 1/2δsδt 20m1/2
30Games of skillSS µ TTFigure 2.10Relationship between modelling output and time units in the Creative Design department.Substitution into the three Lagrange equations produces the followingset of equations:5 2λtm 1/23 λm 1/220tm 1/2 380From the second Lagrange equation,λ 3m 1/2Putting this into the Wrst equation gives:t 5m 6and substituting this for t in the third Lagrange equation gives the Wrstsolution:m 8.04Therefore, from the equation above,t 6.7
Page 2 and 3: Decision Making Using Game TheoryAn
Page 5 and 6: CAMBRIDGE UNIVERSITY PRESSCambridge
Page 7 and 8: viContents4 Sequential decision mak
Page 9 and 10: MMMM
Page 11 and 12: xPreface∑∑∑To Wnd new solutio
Page 13 and 14: 2Introductionvying for business fro
Page 16 and 17: 5TerminologyTable 1.1 The union’s
Page 18 and 19: 7Classifying gamesGAME THEORYGames
Page 20 and 21: 9A brief history of game theoryIn 1
Page 22 and 23: 11A brief history of game theoryano
Page 24 and 25: 13A brief history of game theoryIt
Page 26 and 27: 15Layoutexplained. Games involving
Page 28 and 29: 2 Games of skillIt is not from the
Page 30 and 31: 19Linear programming, optimisation
Page 38 and 39: 27The Lagrange method of partial de
Page 42 and 43: 31The Lagrange method of partial de
Page 44 and 45: 33An introduction to basic probabil
Page 46 and 47: 35An introduction to basic probabil
Page 48 and 49: 37Games of chance involving riskV(X
Page 50 and 51: 39Games of chance involving riskthe
Page 52 and 53: 41Games of chance involving riskyu(
Page 54 and 55: 43Games of chance involving riskExa
Page 56 and 57: 45Games of chance involving uncerta
Page 58 and 59: 47Games of chance involving uncerta
Page 60 and 61: 49Representing sequential decision
Page 62 and 63: 51Representing sequential decision
Page 64 and 65: 53Sequential decision making in sin
Page 78 and 79: 67Sequential decision making in two
Page 84 and 85: 73Cooperative two-person gamesapply
Page 86 and 87: 75Cooperative two-person games∑it
Page 88 and 89: 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
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141Finitely repeated gamescontinuou
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143Finitely repeated gamesBUPALarge
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145Finitely repeated gamesGHGLarge
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147Finitely repeated gamesNatureGHG
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8 Multi-person games, coalitions an
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151Mixed-motive multi-person gamesp
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153Partially cooperative multi-pers
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155Indices of power: measuring infl
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175Rationalityexperimental evidence
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177Indeterminacygot locked into a l
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179Inconsistencythe pot of £49 at
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181Conclusionpost-industrial econom
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183Appendix APlayer 1 wants to maxi
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185Appendix APlayer 1choosesrow 1Pl
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187Appendix Aon the straight line b
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189Appendix Amax p min q Σw ij p i
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191Appendix Bandp(B/A 2 )·p(A 2 )p
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193BibliographyBenoit, J.P. & Krish
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195BibliographyJenkinson, T. (Ed.)
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197BibliographyRobinson, M. (1975)
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Indexancestors and descendants 49ap
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201Indexmaximin principle, in chanc
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203Indexschool buses college cooper
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Decision Making using Game Theory: An introduction for managers

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