Games and dynamic games:
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World Scientific Publ.
2012
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| Physical Description: | XXI, 465 S. graph. Darst. |
| ISBN: | 9789814401265 9814401269 |
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| 245 | 1 | 0 | |a Games and dynamic games |c Alain Haurie ; Jacek B. Krawczy ; Georges Zaccour |
| 264 | 1 | |a Singapore [u.a.] |b World Scientific Publ. |c 2012 | |
| 300 | |a XXI, 465 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a World Scientific - Now Publishers series in business |v 1 | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Game theory | |
| 650 | 4 | |a Cooperative games (Mathematics) | |
| 650 | 4 | |a Decision making |x Mathematical models | |
| 650 | 4 | |a Economics, Mathematical | |
| 700 | 1 | |a Krawczyk, Jacek B. |e Verfasser |4 aut | |
| 700 | 1 | |a Zaccour, Georges |d 1959- |e Verfasser |0 (DE-588)130027073 |4 aut | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-025381589 | ||
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| adam_text | Titel: Games and dynamic games
Autor: Haurie, Alain
Jahr: 2012
Contents
Preface vl1
Acknowledgments xl
1. Introduction 1
1.1 What are dynamic games?......................... 1
1.2 Objectives and contribution......................... 2
1.3 Contribution................................. 3
1.4 Origins and readership........................... 3
1.5 Organization of the book.......................... 4
1.6 About notations............................... 5
Classical Theory of Games 7
2. Description of a Game 9
2.1 Basic concepts of game theory....................... 9
2.2 Games in extensive form.......................... 10
2.2.1 Gametree............................. 10
2.2.2 Description ofmoves, Information and randomness....... 11
2.2.3 Von Neumann-Morgenstern Utility ................ 13
2.3 Additional concepts about Information................... 15
2.3.1 Complete and perfect information................. 15
2.3.2 Common knowledge........................ 16
2.3.3 Perfect recall............................ 16
2.3.4 Commitment............................ 16
2.3.5 Binding agreement......................... 16
2.4 Games in normal form........................... 16
2.4.1 Playing games through strategies................. 16
2.4.2 From extensive form to Strategie or normal form......... 17
2.4.3 Mixed and behavioral strategies.................. 20
Games and Dynamic Games
2.5 Looking for a Solution to a game in normal form .............21
2.5.1 Elimination of dominated strategies................ 21
2.5.2 Rationalizability.......................... 23
2.5.3 Toward more practical Solution concepts............. 25
2.6 What have we learned in this chapter?................... 25
2.7 Exercises .................................. 26
2.8 GE illustration: Assessmentof an international emissions agreement . . . 30
Equilibrium Solutions for Noncooperative Games 37
3.1 Introduction.................................37
3.2 Matrix games................................38
3.2.1 Definitions............................. 38
3.2.2 Security levels........................... 38
3.2.3 Saddle points ........................... 40
3.2.4 Mixed strategies.......................... 42
3.2.5 Algorithms for the computation of saddle points......... 43
3.3 Bimatrix games............................... 46
3.3.1 Best reply strategies........................ 46
3.3.2 Nash equilibria........................... 46
3.3.3 Shortcomings of the Nash equilibrium concept.......... 48
3.3.4 Algorithms for the computation of Nash equilibria in bimatrix
games ............................... 50
3.3.5 Computing all equilibria in a bimatrix game........... 54
3.3.6 Extension to m-playergames................... 54
3.3.7 Solutions obtained by iterated strict dominance or rationalizability 54
3.3.8 Rationality and importanceof Nash s concept of equilibrium . . 55
3.4 Concave m-person games.......................... 55
3.4.1 Definition ............................. 55
3.4.2 Existence of equilibria....................... 57
3.4.3 Normalized equilibria....................... 59
3.4.4 Uniqueness of equilibrium .................... 61
3.4.5 Equilibrium enforcement through taxation............ 62
3.4.6 A numerical technique....................... 63
3.4.7 A variational inequality formulation ............... 63
3.4.8 A nonlinear-complementarity formulation............ 64
3.4.9 Application to the Cournot oligopoly model........... 65
3.5 Existence of Nash equilibrium in infinite games with continuous payoffs . 69
3.6 Stackeiberg Solution ............................ 70
3.6.1 Extensive game representation .................. 70
3.6.2 Duopoly example......................... 72
3.6.3 A geometrical illustration...................... 74
3.6.4 More to come on Stackeiberg Solution.............. 74
Contents xv
3.7 What have we learned in this chapter?................... 75
3.8 Exercises.................................. 76
3.9 GE illustration: A riverbasinpollution problem ............. 79
3.10 GE illustration: Assessment of an IEA (continued)............ 82
4. Extensions and Refinements of the Equilibrium Concepts 87
4.1 Introduction................................. 87
4.2 Correlated equilibria............................ 87
4.2.1 Relaxing the independence assumption in a Nash equilibrium . . 87
4.2.2 Example of a game with correlated equilibria........... 88
4.2.3 A general definition of correlated equilibria ........... 92
4.3 Bayesian equilibrium with incomplete Information............ 95
4.3.1 A game with an unknown player type............... 95
4.3.2 A reformulation as a game with imperfect Information...... 95
4.3.3 A general definition of Bayesian equilibria............ 98
4.4 Equilibria in behavioral strategies and subgame perfectness........ 99
4.4.1 Building up strategies at each Information set ..........99
4.4.2 Multi-agent representation of a game...............99
4.4.3 Subgame perfect equilibria....................102
4.5 Quantal-response equilibrium .......................104
4.5.1 A robust equilibrium concept...................104
4.5.2 Strategies and payoffs.......................104
4.5.3 Payoff perturbations........................105
4.5.4 Quantal-response function.....................105
4.5.5 Definition of quantal-response equilibrium............106
4.5.6 LogitQRE.............................107
4.5.7 Limit Logit Quantal Response Equilibrium (LLQRE)......107
4.6 Supermodular games............................109
4.6.1 Tarski s fixed-point theorem....................109
4.6.2 Supermodularity, increasing differences and the Topkis theorem . 114
4.6.3 Equilibrium in a supermodular game...............116
4.7 What have we learned in this chapter?...................118
4.8 Exercises..................................119
4.9 GE Illustration: A correlated equilibrium model of the Strategie alloca-
tion of ernission allowances in the EU ...................123
4.9.1 The issue of the Strategie allocation of allowances........123
4.9.2 Correlated equilibria in a two-level game.............124
4.9.3 The allocation game........................125
Deterministic Dynamic Games 131
5. Repeated Games and Memory Strategies 133
xvi Games and Dynamic Games
5.1 Introduction.................................133
5.2 Repeating a game in normal form .....................134
5.2.1 Representations of the game....................134
5.2.2 Repeated bimatrix games.....................134
5.2.3 Repeated concave games .....................135
5.2.4 Payoffs for infinite-horizon games ................136
5.2.5 Threats...............................138
5.2.6 Existence ofa trivial dynamic equilibrium............138
5.3 The folk theorem..............................138
5.3.1 Repeated games played by automata...............138
5.3.2 Minimax point and the dominating outcomes...........140
5.4 Memory-strategy equilibria in a repeated concave game..........142
5.4.1 Infinite-horizon and Nash-equilibrium threats ..........142
5.4.2 Subgame perfectness .......................144
5.4.3 Finite versus infinite-horizon games................145
5.5 What have we learned in this chapter?...................145
5.6 Exercises ..................................146
5.7 GE illustration: The European vitamin-C cartel..............149
5.7.1 Background............................150
5.7.2 The model.............................150
5.7.3 Complete Information.......................151
5.7.4 Incomplete monitoring ......................153
5.7.5 Conclusion.............................154
6. Multistage Games 157
6.1 Multistage control Systems.........................157
6.1.1 System description in a State space................ 157
6.1.2 Open-loop and closed-loop control structures........... 158
6.1.3 Linear Systems........................... 161
6.1.4 Optimal control.......................... 162
6.1.5 An optimal economic-growth model............... 164
6.2 Description of multistage games in a state-space.............. 165
6.3 Information structure............................ 169
6.4 Strategies and equilibrium solutions.................... 172
6.4.1 Open-loop Nash equilibria in multistage games .........172
6.4.2 FNE in multistage games.....................176
6.4.3 Dynamic programming for multistage games...........178
6.4.4 Open-loop versus feedback in deterministic games........182
6.5 A feedback-Nash equilibrium Solution to a fishery-management model . . 183
6.5.1 Intuition..............................183
6.5.2 Identifying a Solution to the dynamic-programming equations . . 183
6.5.3 Economic Interpretation......................187
Contents xvii
6.6 FNE in infinite-horizon discounted games.................189
6.6.1 Verification theorem........................ 189
6.6.2 An application: An infinite-horizon feedback-Nash equilibrium
Solution to the fishery s problem ................. 192
6.7 Linear-quadratic games........................... 197
6.7.1 General presentation........................197
6.7.2 Infinite-horizon LQ game.....................201
6.7.3 An example of a linear-quadratic game..............202
6.8 Two-person zero-sum linear-quadratic game and robust Controller design . 207
6.8.1 Problem formulation........................207
6.8.2 Open-loop saddle-point Solution .................208
6.8.3 Feedback saddle-point Solution..................210
6.9 Equilibria in aclassofmemory strategies for infinite-horizon games . . .212
6.9.1 Other equilibria..........................212
6.9.2 Example: Self-enforcing climate treaties.............213
6.9.3 Memory-strategy equilibria in a non-discounted infinite-horizon
multistage game..........................220
6.10 What have we learned in this chapter?...................225
6.11 Exercises..................................226
6.12 GE illustration: Growth-rate divergence between countries with the same
fundamentals................................231
6.12.1 A macroeconomic problem....................231
6.12.2 An endogenous growth model...................233
6.12.3 Game Solutions ..........................234
7. Differential Games 243
7.1 Introduction.................................243
7.2 Elements of a differential game.......................244
7.3 Nash equilibrium..............................246
7.3.1 Thedefinition...........................246
7.3.2 Identifying an MNE using a sufficientmaximumprinciple . . . .248
7.3.3 Identifying an OLNE using the maximum principle.......251
7.3.4 Identifying an MNE using Hamilton-Jacobi-Bellman equations . 251
7.4 The infinite-horizon case..........................254
7.4.1 Several Performance criteria....................254
7.4.2 Sufficient infinite-horizon transversality conditions for the
maximum principle........................257
7.4.3 Sufficient infinite-horizon boundary conditions for the HJB
equations..............................258
7.5 Time consistency and subgame perfectness ................260
7.6 Differential games with special structures.................261
7.7 Examples of the Identification of Nash equilibria.............264
xviii Games and Dynamic Games
7.7.1 An infinite-horizon example....................265
7.7.2 A finite-horizon example .....................268
7.8 On the non-uniqueness of feedback equilibria...............270
7.8.1 A linear-quadratic infinite-horizon differential game in R . . . .270
7.8.2 Linear feedback-equilibrium strategies..............271
7.8.3 Nonlinear feedback-equilibrium strategies............271
7.9 Stackeiberg equilibria............................275
7.9.1 Open-loop Stackeiberg equilibria.................275
7.9.2 Markovian Stackeiberg Equilibria.................277
7.10 An example of the identification of Stackeiberg equilibria ........278
7.11 Time consistency of Stackeiberg equilibria.................281
7.12 Memory strategies and collusive equilibria.................282
7.12.1 Engineering a subgame-perfect equilibrium ...........282
7.12.2 An example............................285
7.13 Remarks on zero-sum and pursuit-evasion games.............287
7.14 What have we learned in this chapter?...................289
7.15 Exercises..................................290
7.16 GE illustration: Subsidies and guaranteed buys of anew technology . . .296
7.16.1 The model.............................298
7.16.2 An open-loop Stackeiberg equilibrium..............300
Stochastic Games 303
8. Equilibria in Games Played over Event Trees 305
8.1 Introduction.................................305
8.2 S-adapted strategies and classical game theory...............306
8.2.1 A two-player game in extensive form...............306
8.2.2 Normal-form representation....................307
8.3 S-adapted strategies in dynamic games...................308
8.3.1 Strategies as variables indexed on an event tree..........308
8.3.2 Rewards and constraints......................309
8.3.3 Normal form game and 5-adapted equilibrium..........310
8.3.4 Concave-game properties and variational-inequality
reformulation ...........................310
8.4 A stochastic-control formulation......................311
8.4.1 A multistage-game formulation..................311
8.4.2 Lagrange multipliers and the maximum principle.........313
8.5 Properties of 5-adaptedequilibria .....................315
8.5.1 General properties.........................315
8.5.2 Subgame perfectness .......................315
8.5.3 Time consistency .........................315
Contents xix
8.6 What have we learned in this chapter?...................316
8.7 Exercises..................................316
8.8 GE illustration: The European gas market.................319
8.8.1 The structure of the European gas market.............319
8.8.2 Modeling the gas contracts....................320
8.8.3 A model of competition under uncertainty............321
8.8.4 The equilibrium strategies.....................323
8.8.5 Twenty years later.........................324
8.8.6 In summary ............................327
9. Markov Games 329
9.1 Overview..................................329
9.2 Shapley s Markov games..........................330
9.2.1 Controlled transition probabilities................330
9.2.2 Numerical example........................330
9.3 Information structure and strategies ....................331
9.3.1 The extensive form of the game at a given State s.........331
9.3.2 Strategies, normal form and saddle-point Solution........332
9.4 Shapley-Denardo s Operator formalism...................335
9.4.1 Dynamic-programming Operators.................335
9.4.2 Existence of sequential saddle points...............336
9.4.3 Numerical illustration.......................338
9.5 How to compute a Solution to a Markov game...............340
9.5.1 Shapley value iteration algorithm.................340
9.5.2 Hoffman and Karp algorithm...................340
9.5.3 Pollatschek and Avi-Itzhak policy iteration algorithm......341
9.5.4 Newton-type methods for Markov games.............342
9.5.5 Multiagent reinforcement learning for Markov games......343
9.6 Nonzero-sum stochastic games with finite State and action sets......344
9.6.1 Stochastic game data .......................344
9.6.2 Stationary-Markov strategies and feedback-Nash equilibria . . .345
9.6.3 Denardo-Whitt Operator formalism................346
9.6.4 Existence of a feedback-Nash equilibrium............347
9.7 Stochastic games with continuous State variables .............348
9.7.1 Description of the game......................348
9.7.2 Dynamic-programming formalism................349
9.7.3 The case of supermodular stochatic games............353
9.7.4 Links with the existence ofcorrelated equilibria.........360
9.7.5 Another existence theorem for supermodular Markov games. . .362
9.8 Memory, trigger and communication strategies ..............365
9.8.1 A stochastic repeated duopoly...................366
9.8.2 A class of trigger strategies based on a monitoring device . . . .367
xx Games and Dynamic Games
9.8.3 Interpretation as a communication device.............369
9.9 What have we learned in this chapter?...................369
9.10 Exercises ..................................370
9.11 GE illustration: A fishery-management game...............371
9.11.1 A cumulative State variable....................371
9.11.2 Stochastic sequential-game formulation..............373
9.11.3 Collusive equilibrium.......................380
10. Piecewise Deterministic Differential Games 383
10.1 Introduction and definitions.........................383
10.2 A stochastic duopoly model ........................385
10.2.1 System s dynamics and payoffs..................385
10.2.2 Markov-game representation...................386
10.2.3 The associated infinite-horizon open-loop differential games . .387
10.2.4 Numerical illustration.......................389
10.3 What have we learned in this chapter?...................393
10.4 Exercises..................................393
10.5 GE illustration: Competitive timing ofclimate policies..........395
10.5.1 Introduction............................395
10.5.2 Characterization of Nash-equilibrium Solutions..........400
10.5.3 Solving the deterministic equivalent dynamic games.......404
11. Stochastic-Diffusion Games 407
11.1 Introduction.................................407
11.2 Stochastic diffusions and stochastic calculus................407
11.2.1 Stochastic-differential equation and stochastic integral......407
11.2.2 Ito sformula............................409
11.2.3 Application oflto s formulato option valuation.........410
11.2.4 Ito s formula and calculation of a value function as the expected
discounted sum of rewards ....................412
11.3 Dynamic-programming equations for feedback-Nash equilibrium.....414
11.4 The Grenadier model for the equilibrium investment strategies of firms . .416
11.5 Subgame perfect collusive equilibria in infinite-horizon stochastic games .419
11.5.1 A stochastic game of a fishery exploited by two companies . . .420
11.5.2 Feedback versus memory strategies................422
11.6 HJB equations for equilibrium policies...................427
11.6.1 HJB equations for the original diffusion game..........427
11.6.2 HJB equations for the associated switching-diffusion game . . .427
11.7 Numerical approximations to equilibria in stochastic-differential games . 428
11.7.1 Ageneral formulation of HJB equations.............428
11.7.2 Discretization scheme.......................428
11.7.3 Policy-improvement algorithm..................430
Contents xxi
11.7.4 Grid selection techniques.....................430
11.8 Calibration of the game...........................431
11.8.1 Parameter specification......................431
11.8.2 Boundary conditions and grid management............431
11.9 Numerical results..............................432
11.10 What have we learned in this chapter?...................435
11.11 Exercises..................................436
11.12 GE Illustration: A differential game of debt-contract valuation......436
i 1.12.1 Introduction............................436
1.12.2 The firm and the debt contract...................437
11.12.3 Stochastic-game formulation...................439
1.12.4 Equivalent risk-neutral valuation.................441
1.12.5 Debt and equity valuations for Nash-equilibrium strategies . . .445
11.12.6 Conclusion.............................447
Bibliography 449
Index 461
|
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| id | DE-604.BV040535585 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:25:59Z |
| institution | BVB |
| isbn | 9789814401265 9814401269 |
| language | English |
| lccn | 2012405953 |
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| physical | XXI, 465 S. graph. Darst. |
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| series | World Scientific - Now Publishers series in business |
| series2 | World Scientific - Now Publishers series in business |
| spelling | Haurie, Alain 1940- Verfasser (DE-588)123581176 aut Games and dynamic games Alain Haurie ; Jacek B. Krawczy ; Georges Zaccour Singapore [u.a.] World Scientific Publ. 2012 XXI, 465 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier World Scientific - Now Publishers series in business 1 Mathematisches Modell Game theory Cooperative games (Mathematics) Decision making Mathematical models Economics, Mathematical Krawczyk, Jacek B. Verfasser aut Zaccour, Georges 1959- Verfasser (DE-588)130027073 aut World Scientific - Now Publishers series in business 1 (DE-604)BV040608183 1 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025381589&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Haurie, Alain 1940- Krawczyk, Jacek B. Zaccour, Georges 1959- Games and dynamic games World Scientific - Now Publishers series in business Mathematisches Modell Game theory Cooperative games (Mathematics) Decision making Mathematical models Economics, Mathematical |
| title | Games and dynamic games |
| title_auth | Games and dynamic games |
| title_exact_search | Games and dynamic games |
| title_full | Games and dynamic games Alain Haurie ; Jacek B. Krawczy ; Georges Zaccour |
| title_fullStr | Games and dynamic games Alain Haurie ; Jacek B. Krawczy ; Georges Zaccour |
| title_full_unstemmed | Games and dynamic games Alain Haurie ; Jacek B. Krawczy ; Georges Zaccour |
| title_short | Games and dynamic games |
| title_sort | games and dynamic games |
| topic | Mathematisches Modell Game theory Cooperative games (Mathematics) Decision making Mathematical models Economics, Mathematical |
| topic_facet | Mathematisches Modell Game theory Cooperative games (Mathematics) Decision making Mathematical models Economics, Mathematical |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025381589&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV040608183 |
| work_keys_str_mv | AT hauriealain gamesanddynamicgames AT krawczykjacekb gamesanddynamicgames AT zaccourgeorges gamesanddynamicgames |