Projects for the exam on Game Theory
2018-2019
Groups include 3-4 people
Each project must have the following structure:
1. Lenght: ~10 pages 2. ~ 4 examples
3. ~ 4 exercises with solutions 4. At least 4 references
5. Each group will revise the work of another group.
6. The document will be written on Latex using the platform Overleaf https://www.overleaf.com/
PART I: Introduction to Game Theory
1. Games, payoff matrices and best response function
Written by Group 3 Revised by 11
2. Nash Equilibria Written by Group 12 Revised by 6
3. Evolutionary stable strategies Written by Group 10
Revised by 7
4. Games on graphs Written by Group 13 Revised by 3
PART II: Repeated and Evolutionary Games 5. Repeated and iterated games
Written by Group 5 Revised by 10
6. Evolutionary games Written by Group 8 Revised by 9
7. The replicator equation Written by Group 4
Revised by 2
8. Simulation of the replicator equation Written by Group 2
Revised by 4
9. Nash equilibria and evolutionary stable strategies
Written by Group 1 Revised by 13
PART III: Evolutionary Games on Networks 10. The replicator equation on graphs
Written by Group 7 Revised by 8
11. Mechanisms promoting cooperation in societies
Written by Group 11 Revised by 1
12. The continuous replicator equation on graphs Written by Group 6
Revised by 5
13. Games with non quadratic payoffs Written by Group 9
Revised by 12
Program and topics
Group 1
Gabriele Orsi Davide Mechini Yousef Safiran Maddalena Violetti Group 2
Andrea Cattolico Silvia Palazzi
Rachiele Maria Cassaro Group 3
Lapo Ramerini Caludia Podda Luca Cattolico
Ruggero Bianchini Group 4
Raffaele Cioccarelli Samuele Antonini Osvaldo Ranieri Filippo Cappello Group 5
Sara Cocozza
Valentina Bucaioni Elisa Baeckman
Group 6 Sreeraj
Ambra Gasperoni Federica Baccini Alberto Lolli
Group 7
Giovanni De Luca Fiorelo Odobashi Landolfi Giulia
Rossana Fulgenzi Group 8
Pietro Coniglio
Salvatore Graziano Javier Gonzalez Sergio Nevado Group 9
Riccardo Pica Ettore Cassioli Andrea Bove
Andrea Corsinovi
Group 10
Carlo Alberto Ortolani Simone Porta
Roberto Di Donato Andrea Brocchi Group 11
Gabriele Maiettini Arianna Suriano
Antonello Caporaso Group 12
Luciano Bigiotti Marta Taddei Teresa Albini
Nunzia Campino Group 13
Francesco Guerri Riccardo Nocella Kaio Borges
Nilson Gomes FIlho
Groups
1. Payoff matrices and best response function
Topics
Introduction to games
Mixed and pure strategies
Classification of two strategy games Examples of three strategy games
Group 3
Lapo Ramerini Caludia Podda Luca Cattolico
Authors
Written by group 3 Revised by group 11
Group 11
Gabriele Maiettini Arianna Suriano
Antonello Caporaso
References
M. Osborne "Introduction to Game Theory", Oxford University Press, USA, 2003, chap. 1,2,4 J. W. Weibull, Evolutionary Game Theory. Cambridge, MA, USA: MIT Press, 1995, chap. 1
2. Nash Equilibria
Topics
Calculating the Nash equilibria Nash Theorem
Classification of NE for two strategy games Examples of NE in three strategy games
Group 12
Luciano Bigiotti Marta Taddei Teresa Albini
Authors
Written by group 12 Revised by group 6
Group 6 Sreeraj
Ambra Gasperoni Federica Baccini Alberto Lolli
References
M. Osborne "Introduction to Game Theory", Oxford University Press, USA, 2003, chap. 2, 3 J. W. Weibull, Evolutionary Game Theory. Cambridge, MA, USA: MIT Press, 1995, chap. 1
3. Evolutionary stable strategies
Topics Definition Properties
Examples in 2 strategy and three strategy games
Group 10
Carlo Alberto Ortolani Simone Porta
Roberto Di Donato Andrea Brocchi
Authors
Written by group 10 Revised by group 7
Group 7
Giovanni De Luca Fiorelo Odobashi Landolfi Giulia Rossana Fulgenzi
References
J. W. Weibull, Evolutionary Game Theory. Cambridge, MA, USA: MIT Press, 1995, chap. 2
J. Hofbauer, K. Sigmund, Evolutionary Games and Population Dynamics, Cambridge Univ. Press, chap. 6
4. Games on graphs
Topics
Definition of graphs Games on graphs
Equivalence to N-players games
Group 13
Francesco Guerri Riccardo Nocella Kaio Borges
Nilson Gomes FIlho
Authors
Written by group 13 Revised by group 3
Group 3
Lapo Ramerini Caludia Podda Luca Cattolico
Ruggero Bianchini
References
Jackson, Matthew O. and Zenou, Yves, Games on Networks (January 1, 2014). Handbook of Game Theory, Vol. 4, Peyton Young and Shmuel Zamir, eds., Elsevier Science, July 2014.
5. Repeated and iterated games
Topics
Strategies: TIT for TAT Other strategies
Finite populations
Group 5
Sara Cocozza
Valentina Bucaioni Elisa Baeckman
Authors
Written by group 5 Revised by group 10
Group 10
Carlo Alberto Ortolani Simone Porta
Roberto Di Donato
References
Martin Nowak, "Evolutionary Dynamics", Belknap Press of Harvard University Press, 2006, chap. 5, 6 J. Hofbauer, K. Sigmund, Evolutionary Games and Population Dynamics, Cambridge Univ. Press, chap. 9
6. Evolutionary games
Topics
Populations, payoffs and fitness Replication, selection, mutation Population dynamics with density dependent fitness
Group 8
Pietro Coniglio
Salvatore Graziano Javier Gonzalez Sergio Nevado
Topics
Written by group 8 Revised by group 9
Group 9
Riccardo Pica Ettore Cassioli Andrea Bove
Andrea Corsinovi
References
Martin Nowak, "Evolutionary Dynamics", Belknap Press of Harvard University Press, 2006, chap. 2, 4
7. The replicator equation
Topics
Properties of the replicator equation NE of the equation
Group 4
Raffaele Cioccarelli Samuele Antonini Osvaldo Ranieri Filippo Cappello
Authors
Written by group 4 Revised by group 2
Group 2
Andrea Cattolico Silvia Palazzi
Rachiele Maria Cassaro
References
J. W. Weibull, Evolutionary Game Theory. Cambridge, MA, USA: MIT Press, 1995, chap. 3
Martin Nowak, "Evolutionary Dynamics", Belknap Press of Harvard University Press, 2006, chap. 4
8. Simulation of the replicator equation
Authors
Written by group 2 Revised by group 4
Group 2
Andrea Cattolico Silvia Palazzi
Rachiele Maria Cassaro Topics
Simulation of ODEs
Simulation of the symplex
Dynamics of the replicator dynamics
Group 4
Raffaele Cioccarelli Samuele Antonini Osvaldo Ranieri Filippo Cappello
References
MATLAB simulation of ODEs (see the notes of the course on Complex Dynamic Systems
9. Nash equilibria and
evolutionary stable strategies
Topics
Comparative analisys and examples Stability and evolutionary stability
Group 1
Gabriele Orsi Davide Mechini Yousef Safiran
Auhtors
Written by group 1 Revised by group 13
Group 13
Francesco Guerri Riccardo Nocella Kaio Borges
Nilson Gomes FIlho
References
J. W. Weibull, Evolutionary Game Theory. Cambridge, MA, USA: MIT Press, 1995, chap. 3 par. 3.3, 3.5, 3.6
10. The replicator equation on graphs
Topics Graphs
Birth-death mechanisms
Group 7
Giovanni De Luca Fiorelo Odobashi Landolfi Giulia Rossana Fulgenzi
Authors
Written by group 7 Revised by group 8
Group 8
Pietro Coniglio
Salvatore Graziano Javier Gonzalez Sergio Nevado
References
Ohtsuki, H. & Nowak, M. A. The replicator equation on graphs. J. theoretical biology 243, 86–97 (2006).
11. Mechanisms promoting cooperation in societies
Topics
Direct recipropcity Indirect reciprocity Punishment
Reputation Group 11
Gabriele Maiettini Arianna Suriano
Antonello Caporaso Riccardo Gimignani
Authors
Written by group 11 Revised by group 1
Group 1
Gabriele Orsi Davide Mechini Yousef Safiran
References
Nowak, M. A. Five rules for the evolution of cooperation. Science 314, 1560–1563 (2006).
Helbing, D. & Johansson, A. Cooperation, norms, and revolutions: a unified game-theoretical approach. PloS one 5, e12530 (2010).
12. The continuous replicator equation on graphs
Topics
Equivalent player
The self regulation mechanism
Group 6 Sreeraj
Ambra Gasperoni Federica Baccini Alberto Lolli
Authors
Written by group 6 Revised by group 5
Group 5
Sara Cocozza
Valentina Bucaioni Elisa Baeckman
References
Madeo, D. & Mocenni, C. Game interactions and dynamics on networked populations. IEEE Trans.
on Autom. Control. 60, 1801–1810 (2015).
D. Madeo and C. Mocenni, “Self-regulation promotes cooperation in social networks”, arXiv preprint arXiv:1807.07848, 2018.
13. Games with non quadratic payoffs
Topics
Nonlinear payoff functions Point of view of games
Point of view of replicator equation Group 9
Riccardo Pica Ettore Cassioli Andrea Bove
Andrea Corsinovi
Authors
Written by group 9 Revised by group 12
Group 12
Luciano Bigiotti Marta Taddei Teresa Albini
References To be done
