Numerical Study of Game Theory
|
|
- James Terry
- 5 years ago
- Views:
Transcription
1 New Physics: Sae Mulli (The Korean Physical Society), Volume 60, Number 9, , pp DOI: /NPSM Integrated Science Laboratory, Department of Physics, Umeå University, Umeå, Sweden, ( , ).,, (sociophysics).. (Intelligent Tit-for-tat) כ.,.. :,,,,,, Numerical Study of Game Theory Seung Ki Baek Integrated Science Laboratory, Department of Physics, Umeå University, Umeå, Sweden Beom Jun Kim Department of Physics, Sungkyunkwan University, Suwon (Received 1 September, 2010 : accepted 15 September, 2010) A game-theoretic approach has been providing a powerful tool in the qualitative understanding of macroscopic social phenomena in social sciences, e.g., in economics and in political science. Recently, researchers in physics, especially in statistical physics, have also used these game-theoretic approaches, but in a more quantitative way, and have been producing a variety of interesting results in the new research area called sociophysics by studying human society as a complex system. This work introduces recent works that have tackled the combinatorial complexities arising in gametheoretic studies with the aid of simplified assumptions and numerical computations. We first show how cooperation emerges in the prisoner s dilemma game when each player s memory capacity is enhanced and suggest that the intelligent tit-for-tat strategy plays a crucial role in the history of -943-
2 -944-, Volume 60, Number 9, cooperation. Then, we numerically show that there is a certain case of simultaneous coordination among many players where the system has a high risk of failure when everyone is willing to follow the coordination, which is actually higher than when some are not concerned about it. Lastly, we discuss a mathematical treatment of an equilibrium solution for a reverse auction game, which is a variant of the minority game, and its computational approach. PACS numbers: k, Ge Keywords: Game theory, Sociophysics, Prisoners dilemma game, Tit-for-tat strategy, Pedestrian problem, Reverse auction game, Equilibrium point I. (sociophysics), [1]., [2], [3], [4], [5], [6], [7].,.,.. כ,. כ (coordination game). כ, כ (strategy)..,,.,. כ beomjun@skku.edu.., [8], [9]. [10]. II..., כ 4.,.. כ. 4. 4, כ., כ., כ כ, כ
3 -945- כ., (4 )., כ, כ כ... (, cooperation C ) (, defection D ) כ,.. (Nash equilibrium, ). כ.. (, )=(C, C), (C, D), (D, C), (D, D)., 5. C D 2 5 = b כ : b 0 b(c, C), b(c, D), b(d, C), b(d, D). b 0 (= C D) C D. C C CCCC. C CDDD (Grim Trigger, GT) C CDCD (Tit-for-tat, TFT). C CDDC (b(c, C) = C, b(d, C) = D), (b(c, D) = D, b(d, D) = C), Fig. 1. Numerical integration results of Eq. (1). (Pavlov)., 90 % C 10 % D. (C, C) 3, (C, D) 5, (D, C) 0, (D, D) 1. i p i (i = 1,, 32)., כ. כ (replicator dynamics, RD) כ. dp i dt = (U i U )p i. (1) U i i U ( j U jp j ). 32 RD (Fig. 1).., 4, GT, TFT, Pavlov C CDCC. C CDXY XY 4 (X = C, D Y = C, D).,, כ. 28 XY
4 -946-, Volume 60, Number 9, , q (q 1). (e = 0) RD כ 4 כ. כ, (1) כ. 0 < e 1, כ. C CDCC, GT, TFT Pavlov (cyclic dominance) TFT GT Pavlov TFT Pavlov GT. TFT GT Pavlov. GT כ Pavlov (D, D) C. TFT (C, D) (D, C). TFT Pavlov.,. (CC, CC) (DD, DD) = 262, כ. RD.. כ כ. Fig. 2. Characteristic results of the iterated prisoner s dilemma game on the two-dimensional square lattice with q = The error probabilities are given as (a) e = 0 and (b) e = 0.01, respectively. כ. (1),., %, כ כ. כ. 5 % Pavlov. כ. 5%. (Efficient Cooperator, EC), Pavlov. EC
5 -947- Fig. 3. Change of fractions of three representative strategies belonging to EC, ET, and I-TFT, respectively, when simulated on the square lattice. Fig. 4. Our model of a pedestrian.. GT (Efficient Trigger, ET). EC כ כ כ. Intelligent Tit-for-tat(I-TFT) כ, TFT. TFT. I-TFT כ. EC TFT כ. EC כ. I-TFT TFT,. כ. I-TFT EC Fig. 3. III. (1). (L) (R), (L,L) (R, R) 1 (R, L) (L, R) 0. p R R p L = 1 p R L (1) dp R dt = p R (1 p R )(2p R 1) (2) p R = 0, 1, 1/2. כ p R = p L = 1/2,. כ (1). כ...., q, 1 q.,,. כ כ ( )...
6 -948-, Volume 60, Number 9, Fig. 5. Occurrence of jamming observed in the pedestrian model... (q = 1)., כ. כ. (dead-lock)... t 1. (free flow) כ, (jamming) כ. כ (steady state). ρ φ,. Fig. 6 ρ φ 1 0, τ. φ 1 0 כ.. ρp q=1 ρ(1 p) q=1/2 כ. (ρ, p) φ, Fig. 7. Fig. 6. Results from the numerical simulations where the size of the road is set to be X Y = Fig. 7. Average flow as a function of the pedestrian density and the fraction of rule followers. The road sizes are (a) and (b) , respectively. כ, כ (p = 1). p = 1 (Fig. 8)... כ כ.., RD כ,
7 -949- Fig. 8. Typical configuration at t = 1000 when started with ρ = 0.2 and p = 1 on a road of כ (transient phenomenon) כ. RD כ,. כ כ. IV.. (anti-coordination). כ כ כ. כ. כ. n 1 n. כ n, i p i כ. p i = 1.? (evolutionarily stable strategy), כ כ. (neutrally stable strategy),,. n = 3. {p i }? 9 {π i }. (, )=(1,1), p , π 2 + π כ π i p i כ. כ n 3. כ. n = 3 Z 0 = (p 1 + p 2 + p 3 ) ? 9 p 1 1 כ כ.. Z 0 p 1 p 1 0 כ., 1. Z 1 = Z 0 p 1 [dz 0 /dp 1 ](p 1 = 0) (3), 2 Z 1. Z 2 = Z 1 p 2 [dz 1 /dp 2 ](p 2 = 0) (4), i 1 i Z i 1 p i = 0. c i = [Z i 1 ](p i = 0) (5). W = c i π i (6) π i = 1 c i i {π i } W. c i כ n 1
8 -950-, Volume 60, Number 9, Fig. 10. Numerical results when players imitate successful strategies. The black dotted lines show the analytically obtained equilibrium solutions. Fig. 9. Equilibrium solutions of the reverse auction game. Both panels (a) and (b) depict the same data but panel (b) scales both axes in terms of n to compare the outcomes with the uniform solution. n 1 {p i }. Fig 9., (p i = π i ), p i = 1/n. n כ., כ. כ n. כ n = n כ. כ. π i p i כ. p i n 1 כ.,. V.,,., -,,,,.,, כ. [1] C. Castellano, S. Fortunato and V. Loreto, Rev. Mod. Phys. 81, 591 (2009). [2] D. Helbing, I. Farkas and T. Vicsek, Nature 407, 487 (2000). [3] F. Vazquez and V. M. Eguiluz, New J. Phys. 10, (2008). [4] V.M. Eguiluz and M. G Zimmermann, Phys. Rev. Lett. 85, 5659 (2000). [5] D. Helbing, Rev. Mod. Phys. 73, 1067 (2001).
9 -951- [6] A.-L. Barabasi, Nature 435, 207 (2005); C. Song, Z. Qu, N. Blumm and A.-L. Barabasi, Science 327, 1018 (2009). [7] G. Szabo and G. Fath, Phys. Rep. 446, 97 (2007). [8] S.K. Baek and B.J. Kim, Phys. Rev. E 78, (2008). [9] S.K. Baek, P. Minnhagen, S. Bernhardsson, K. Choi and B. J. Kim, Phys. Rev. E 80, (2009). [10] S.K. Baek and S. Bernhardsson, Fluctuation Noise Lett. 9, 61 (2010).
Game Theory, Population Dynamics, Social Aggregation. Daniele Vilone (CSDC - Firenze) Namur
Game Theory, Population Dynamics, Social Aggregation Daniele Vilone (CSDC - Firenze) Namur - 18.12.2008 Summary Introduction ( GT ) General concepts of Game Theory Game Theory and Social Dynamics Application:
More informationarxiv: v1 [physics.soc-ph] 27 May 2016
The Role of Noise in the Spatial Public Goods Game Marco Alberto Javarone 1, and Federico Battiston 2 1 Department of Mathematics and Computer Science, arxiv:1605.08690v1 [physics.soc-ph] 27 May 2016 University
More informationPhase transitions in social networks
Phase transitions in social networks Jahan Claes Abstract In both evolution and economics, populations sometimes cooperate in ways that do not benefit the individual, and sometimes fail to cooperate in
More informationUnderstanding and Solving Societal Problems with Modeling and Simulation
Understanding and Solving Societal Problems with Modeling and Simulation Lecture 8: The Breakdown of Cooperation ETH Zurich April 15, 2013 Dr. Thomas Chadefaux Why Cooperation is Hard The Tragedy of the
More informationEvolutionary Game Theory
Evolutionary Game Theory ISI 330 Lecture 18 1 ISI 330 Lecture 18 Outline A bit about historical origins of Evolutionary Game Theory Main (competing) theories about how cooperation evolves P and other social
More informationarxiv: v2 [q-bio.pe] 18 Dec 2007
The Effect of a Random Drift on Mixed and Pure Strategies in the Snowdrift Game arxiv:0711.3249v2 [q-bio.pe] 18 Dec 2007 André C. R. Martins and Renato Vicente GRIFE, Escola de Artes, Ciências e Humanidades,
More informationBelief-based Learning
Belief-based Learning Algorithmic Game Theory Marcello Restelli Lecture Outline Introdutcion to multi-agent learning Belief-based learning Cournot adjustment Fictitious play Bayesian learning Equilibrium
More informationProblems on Evolutionary dynamics
Problems on Evolutionary dynamics Doctoral Programme in Physics José A. Cuesta Lausanne, June 10 13, 2014 Replication 1. Consider the Galton-Watson process defined by the offspring distribution p 0 =
More informationEvolutionary prisoner s dilemma game on hierarchical lattices
PHYSICAL REVIEW E 71, 036133 2005 Evolutionary prisoner s dilemma game on hierarchical lattices Jeromos Vukov Department of Biological Physics, Eötvös University, H-1117 Budapest, Pázmány Péter sétány
More informationGame Theory. Professor Peter Cramton Economics 300
Game Theory Professor Peter Cramton Economics 300 Definition Game theory is the study of mathematical models of conflict and cooperation between intelligent and rational decision makers. Rational: each
More informationSpatial three-player prisoners dilemma
Spatial three-player prisoners dilemma Rui Jiang, 1 Hui Deng, 1 Mao-Bin Hu, 1,2 Yong-Hong Wu, 2 and Qing-Song Wu 1 1 School of Engineering Science, University of Science and Technology of China, Hefei
More informationCollective Evolution of Turn-taking Norm in Dispersion Games
ollective Evolution of Turn-taking Norm in ispersion Games Akira NAMATAME ept. of omputer Science National efense Academy Yokosuka,239-8686,Japan E-mail: nama@nda.ac.jp http//www.nda.ac.jp/~nama/ Outline
More informationBounded Rationality, Strategy Simplification, and Equilibrium
Bounded Rationality, Strategy Simplification, and Equilibrium UPV/EHU & Ikerbasque Donostia, Spain BCAM Workshop on Interactions, September 2014 Bounded Rationality Frequently raised criticism of game
More informationPhase Transition of Finance Chia Cheng Chang
Phase Transition of Finance Chia Cheng Chang Introduction to Two-phase Phenomena Observed in Finance Phase transition in nature is understood to be an emergent phenomena due to the collective behavior
More informationResearch Article Snowdrift Game on Topologically Alterable Complex Networks
Mathematical Problems in Engineering Volume 25, Article ID 3627, 5 pages http://dx.doi.org/.55/25/3627 Research Article Snowdrift Game on Topologically Alterable Complex Networks Zhe Wang, Hong Yao, 2
More informationarxiv: v3 [cs.gt] 25 Feb 2012
Equilibrium strategy and population-size effects in lowest unique bid auctions Simone Pigolotti,, Sebastian Bernhardsson,, Jeppe Juul, Gorm Galster, and Pierpaolo Vivo Niels Bohr Institute, Blegdamsvej
More informationDamon Centola.
http://www.imedea.uib.es/physdept Konstantin Klemm Victor M. Eguíluz Raúl Toral Maxi San Miguel Damon Centola Nonequilibrium transitions in complex networks: a model of social interaction, Phys. Rev. E
More informationScale-invariant behavior in a spatial game of prisoners dilemma
PHYSICAL REVIEW E, VOLUME 65, 026134 Scale-invariant behavior in a spatial game of prisoners dilemma Y. F. Lim and Kan Chen Department of Computational Science, National University of Singapore, Singapore
More informationEvolution & Learning in Games
1 / 27 Evolution & Learning in Games Econ 243B Jean-Paul Carvalho Lecture 2. Foundations of Evolution & Learning in Games II 2 / 27 Outline In this lecture, we shall: Take a first look at local stability.
More informationOptimal Decision Rules in Repeated Games Where Players Infer an Opponent s Mind via Simplified Belief Calculation
games Article Optimal Decision Rules in Repeated Games Where Players Infer an Opponent s Mind via Simplified Belief Calculation Mitsuhiro Nakamura * and Hisashi Ohtsuki Department of Evolutionary Studies
More informationGame Theory and Algorithms Lecture 2: Nash Equilibria and Examples
Game Theory and Algorithms Lecture 2: Nash Equilibria and Examples February 24, 2011 Summary: We introduce the Nash Equilibrium: an outcome (action profile) which is stable in the sense that no player
More informationEvolution of Cooperation in Continuous Prisoner s Dilemma Games on Barabasi Albert Networks with Degree-Dependent Guilt Mechanism
Commun. Theor. Phys. 57 (2012) 897 903 Vol. 57, No. 5, May 15, 2012 Evolution of Cooperation in Continuous Prisoner s Dilemma Games on Barabasi Albert Networks with Degree-Dependent Guilt Mechanism WANG
More informationThe Stability for Tit-for-Tat
e-issn:31-6190 p-issn:347-94 The Stability for Tit-for-Tat Shun Kurokawa 1,* 1 Kyoto University, Oiwake-cho, Kitashirakawa, Sakyo-ku, Kyoto, Japan Key Lab of Animal Ecology and Conservation Biology, Institute
More informationUmeå University. Access to the published version may require subscription.
Umeå University This is an accepted version of a paper published in Physical Review E. Statistical, Nonlinear, and Soft Matter Physics. This paper has been peer-reviewed but does not include the final
More informationOutline. 3. Implementation. 1. Introduction. 2. Algorithm
Outline 1. Introduction 2. Algorithm 3. Implementation What s Dynamic Traffic Assignment? Dynamic traffic assignment is aimed at allocating traffic flow to every path and making their travel time minimized
More informationReciprocity in evolving social networks
J Evol Econ (2009) 19:379 396 DOI 10.1007/s00191-008-0117-5 REGULAR ARTICLE Reciprocity in evolving social networks Tackseung Jun Rajiv Sethi Published online: 30 August 2008 Springer-Verlag 2008 Abstract
More informationVII. Cooperation & Competition
VII. Cooperation & Competition A. The Iterated Prisoner s Dilemma Read Flake, ch. 17 4/23/18 1 The Prisoners Dilemma Devised by Melvin Dresher & Merrill Flood in 1950 at RAND Corporation Further developed
More informationDiversity-optimized cooperation on complex networks
Diversity-optimized cooperation on complex networks Han-Xin Yang, 1 Wen-Xu Wang, 2 Zhi-Xi Wu, 3 Ying-Cheng Lai, 2,4 and Bing-Hong Wang 1,5 1 Department of Modern Physics, University of Science and Technology
More informationGraph topology and the evolution of cooperation
Provided by the author(s) and NUI Galway in accordance with publisher policies. Please cite the published version when available. Title Graph topology and the evolution of cooperation Author(s) Li, Menglin
More informationarxiv: v1 [quant-ph] 30 Dec 2012
Strategies in a Symmetric Quantum Kolkata Restaurant Problem Puya Sharif and Hoshang Heydari arxiv:1212.6727v1 [quant-ph] 0 Dec 2012 Physics Department, Stockholm University 10691 Stockholm, Sweden E-mail:ps@puyasharif.net
More informationPrisoner s Dilemma. Veronica Ciocanel. February 25, 2013
n-person February 25, 2013 n-person Table of contents 1 Equations 5.4, 5.6 2 3 Types of dilemmas 4 n-person n-person GRIM, GRIM, ALLD Useful to think of equations 5.4 and 5.6 in terms of cooperation and
More informationEVOLUTIONARY STABILITY FOR TWO-STAGE HAWK-DOVE GAMES
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS olume 25, Number 1, Winter 1995 EOLUTIONARY STABILITY FOR TWO-STAGE HAWK-DOE GAMES R. CRESSMAN ABSTRACT. Although two individuals in a biological species often interact
More informationEvolution of public cooperation on interdependent networks: The impact of biased utility functions
February 2012 EPL, 97 (2012) 48001 doi: 10.1209/0295-5075/97/48001 www.epljournal.org Evolution of public cooperation on interdependent networks: The impact of biased utility functions Zhen Wang 1,2, Attila
More informationEvolutionary dynamics of cooperation in neutral populations
PAPER OPEN ACCESS Evolutionary dynamics of cooperation in neutral populations To cite this article: Attila Szolnoki and Matjaž Perc 2018 New J. Phys. 20 013031 View the article online for updates and enhancements.
More informationEvolutionary games on complex network
Evolutionary games on complex network Wen-Xu Wang 1,2 and Bing-Hong Wang 1,3 1 Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China 2 Department of Electronic
More informationBehavior of Collective Cooperation Yielded by Two Update Rules in Social Dilemmas: Combining Fermi and Moran Rules
Commun. Theor. Phys. 58 (2012) 343 348 Vol. 58, No. 3, September 15, 2012 Behavior of Collective Cooperation Yielded by Two Update Rules in Social Dilemmas: Combining Fermi and Moran Rules XIA Cheng-Yi
More informationUnderstanding Emergence of Cooperation using tools from Thermodynamics
Understanding Emergence of Cooperation using tools from Thermodynamics Pranjal Ralegankar May 13, 2018 Abstract Understanding how cooperation emerged in evolutionary biological systems is a long studied
More informationMeaning, Evolution and the Structure of Society
Meaning, Evolution and the Structure of Society Roland Mühlenbernd November 7, 2014 OVERVIEW Game Theory and Linguistics Pragm. Reasoning Language Evolution GT in Lang. Use Signaling Games Replicator Dyn.
More informationHerd Behavior and Phase Transition in Financial Market
Herd Behavior and Phase Transition in Financial Market Minghao Guo December 13, 2009 Abstract In this paper, I brief reviewed the herd behavior in financial market. Benerjee model and EZ model are introduced.
More informationCS 798: Multiagent Systems
CS 798: Multiagent Systems and Utility Kate Larson Cheriton School of Computer Science University of Waterloo January 6, 2010 Outline 1 Self-Interested Agents 2 3 4 5 Self-Interested Agents We are interested
More informationGroup Formation: Fragmentation Transitions in Network Coevolution Dynamics
- Mallorca - Spain Workshop on Challenges and Visions in the Social Sciences, ETH August 08 Group Formation: Fragmentation Transitions in Network Coevolution Dynamics MAXI SAN MIGUEL CO-EVOLUTION Dynamics
More informationA Dynamic Level-k Model in Games
Dynamic Level-k Model in Games Teck Ho and Xuanming Su UC erkeley March, 2010 Teck Hua Ho 1 4-stage Centipede Game 4 2 16 8 1 8 4 32 1 2 3 4 64 16 5 Outcome Round 1 2 3 4 5 1 5 6.2% 30.3% 35.9% 20.0% 7.6%
More informationEvolution of a social network: The role of cultural diversity
PHYSICAL REVIEW E 73, 016135 2006 Evolution of a social network: The role of cultural diversity A. Grabowski 1, * and R. A. Kosiński 1,2, 1 Central Institute for Labour Protection National Research Institute,
More informationMinimal-Agent Control of Evolutionary Games on Tree Networks
21st International Symposium on Mathematical Theory of Networks and Systems July 7-11, 2014. Minimal-Agent Control of Evolutionary Games on Tree Networks James R. Riehl and Ming Cao Abstract We investigate
More informationCommunities and Populations
ommunities and Populations Two models of population change The logistic map The Lotke-Volterra equations for oscillations in populations Prisoner s dilemma Single play Iterated play ommunity-wide play
More information6 The Principle of Optimality
6 The Principle of Optimality De nition A T shot deviation from a strategy s i is a strategy bs i such that there exists T such that bs i (h t ) = s i (h t ) for all h t 2 H with t T De nition 2 A one-shot
More informationUC Berkeley Haas School of Business Game Theory (EMBA 296 & EWMBA 211) Summer 2016
UC Berkeley Haas School of Business Game Theory (EMBA 296 & EWMBA 211) Summer 2016 More on strategic games and extensive games with perfect information Block 2 Jun 12, 2016 Food for thought LUPI Many players
More informationQuantum Games. Quantum Strategies in Classical Games. Presented by Yaniv Carmeli
Quantum Games Quantum Strategies in Classical Games Presented by Yaniv Carmeli 1 Talk Outline Introduction Game Theory Why quantum games? PQ Games PQ penny flip 2x2 Games Quantum strategies 2 Game Theory
More informationarxiv: v2 [physics.soc-ph] 29 Aug 2017
Conformity-Driven Agents Support Ordered Phases in the Spatial Public Goods Game Marco Alberto Javarone, 1, Alberto Antonioni, 2, 3, 4 and Francesco Caravelli 5, 6 1 Department of Mathematics and Computer
More informationGame Theory -- Lecture 4. Patrick Loiseau EURECOM Fall 2016
Game Theory -- Lecture 4 Patrick Loiseau EURECOM Fall 2016 1 Lecture 2-3 recap Proved existence of pure strategy Nash equilibrium in games with compact convex action sets and continuous concave utilities
More informationGame Theory for Linguists
Fritz Hamm, Roland Mühlenbernd 4. Mai 2016 Overview Overview 1. Exercises 2. Contribution to a Public Good 3. Dominated Actions Exercises Exercise I Exercise Find the player s best response functions in
More informationInterdependent network reciprocity in evolutionary games
1 / 12 2013.03.31. 13:34 nature.com Sitemap Cart Login Register Search 2013 January Article SCIENTIFIC REPORTS ARTICLE OPEN Interdependent network reciprocity in evolutionary games Zhen Wang, Attila Szolnoki
More informationThe Evolution of Cooperation in Self-Interested Agent Societies: A Critical Study
The Evolution of Cooperation in Self-Interested Agent Societies: A Critical Study Lisa-Maria Hofmann Karlsruhe Institute of Technology Karlsruhe, Germany lisamariahofmann@gmail.com Nilanjan Chakraborty
More informationEvolution of Cooperation in Evolutionary Games for Heterogeneous Interactions
Commun. Theor. Phys. 57 (2012) 547 552 Vol. 57, No. 4, April 15, 2012 Evolution of Cooperation in Evolutionary Games for Heterogeneous Interactions QIAN Xiao-Lan ( ) 1, and YANG Jun-Zhong ( ) 2 1 School
More informationPareto-Improving Congestion Pricing on General Transportation Networks
Transportation Seminar at University of South Florida, 02/06/2009 Pareto-Improving Congestion Pricing on General Transportation Netorks Yafeng Yin Transportation Research Center Department of Civil and
More informationEvolutionary prisoner s dilemma games coevolving on adaptive networks
Journal of Complex Networks (27), 23 doi:.93/comnet/cnx8 Evolutionary prisoner s dilemma games coevolving on adaptive networks Hsuan-Wei Lee Department of Sociology, University of Nebraska Lincoln, 4 R
More informationEmotional Agents at the Square Lattice
Vol. 117 (2010) ACTA PHYSICA POLONICA A No. 4 Proceedings of the 4th Polish Symposium on Econo- and Sociophysics, Rzeszów, Poland, May 7 9, 2009 Emotional Agents at the Square Lattice A. Czaplicka, A.
More informationA (Brief) Introduction to Game Theory
A (Brief) Introduction to Game Theory Johanne Cohen PRiSM/CNRS, Versailles, France. Goal Goal is a Nash equilibrium. Today The game of Chicken Definitions Nash Equilibrium Rock-paper-scissors Game Mixed
More informationQuantum Bertrand duopoly of incomplete information
INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS A: MATHEMATICAL AND GENERAL J. Phys. A: Math. Gen. 38 (2005) 4247 4253 doi:10.1088/0305-4470/38/19/013 Quantum Bertrand duopoly of incomplete information
More informationarxiv:math/ v1 [math.oc] 29 Jun 2004
Putting the Prisoner s Dilemma in Context L. A. Khodarinova and J. N. Webb Magnetic Resonance Centre, School of Physics and Astronomy, University of Nottingham, Nottingham, England NG7 RD, e-mail: LarisaKhodarinova@hotmail.com
More informationEvolution of Cooperation in the Snowdrift Game with Incomplete Information and Heterogeneous Population
DEPARTMENT OF ECONOMICS Evolution of Cooperation in the Snowdrift Game with Incomplete Information and Heterogeneous Population André Barreira da Silva Rocha, University of Leicester, UK Annick Laruelle,
More informationAsymmetric cost in snowdrift game on scale-free networks
September 29 EPL, 87 (29) 64 doi:.29/295-575/87/64 www.epljournal.org Asymmetric cost in snowdrift game on scale-free networks W.-B. u,x.-b.ao,2,m.-b.hu 3 and W.-X. Wang 4 epartment of omputer Science
More informationSONDERFORSCHUNGSBEREICH 504
SONDERFORSCHUNGSBEREICH 504 Rationalitätskonzepte, Entscheidungsverhalten und ökonomische Modellierung No. 02-03 Two-Speed Evolution of Strategies and Preferences in Symmetric Games Possajennikov, Alex
More informationCooperation Stimulation in Cooperative Communications: An Indirect Reciprocity Game
IEEE ICC 202 - Wireless Networks Symposium Cooperation Stimulation in Cooperative Communications: An Indirect Reciprocity Game Yang Gao, Yan Chen and K. J. Ray Liu Department of Electrical and Computer
More informationIterated Strict Dominance in Pure Strategies
Iterated Strict Dominance in Pure Strategies We know that no rational player ever plays strictly dominated strategies. As each player knows that each player is rational, each player knows that his opponents
More informationRepeated Games and Direct Reciprocity Under Active Linking
Repeated Games and Direct Reciprocity Under Active Linking The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation Pacheco,
More informationarxiv:physics/ v1 [physics.soc-ph] 9 Jun 2006
EPJ manuscript No. (will be inserted by the editor) arxiv:physics/6685v1 [physics.soc-ph] 9 Jun 26 A Unified Framework for the Pareto Law and Matthew Effect using Scale-Free Networks Mao-Bin Hu 1, a, Wen-Xu
More informationAnalytical investigation on the minimum traffic delay at a two-phase. intersection considering the dynamical evolution process of queues
Analytical investigation on the minimum traffic delay at a two-phase intersection considering the dynamical evolution process of queues Hong-Ze Zhang 1, Rui Jiang 1,2, Mao-Bin Hu 1, Bin Jia 2 1 School
More informationIntroduction to Game Theory. Outline. Topics. Recall how we model rationality. Notes. Notes. Notes. Notes. Tyler Moore.
Introduction to Game Theory Tyler Moore Tandy School of Computer Science, University of Tulsa Slides are modified from version written by Benjamin Johnson, UC Berkeley Lecture 15 16 Outline 1 Preferences
More informationarxiv:cond-mat/ v1 [cond-mat.other] 4 Aug 2004
Conservation laws for the voter model in complex networks arxiv:cond-mat/0408101v1 [cond-mat.other] 4 Aug 2004 Krzysztof Suchecki, 1,2 Víctor M. Eguíluz, 1 and Maxi San Miguel 1 1 Instituto Mediterráneo
More informationTime-Series Based Prediction of Dynamical Systems and Complex. Networks
Time-Series Based Prediction of Dynamical Systems and Complex Collaborators Networks Ying-Cheng Lai ECEE Arizona State University Dr. Wenxu Wang, ECEE, ASU Mr. Ryan Yang, ECEE, ASU Mr. Riqi Su, ECEE, ASU
More informationThe Cross Entropy Method for the N-Persons Iterated Prisoner s Dilemma
The Cross Entropy Method for the N-Persons Iterated Prisoner s Dilemma Tzai-Der Wang Artificial Intelligence Economic Research Centre, National Chengchi University, Taipei, Taiwan. email: dougwang@nccu.edu.tw
More informationWriting Game Theory in L A TEX
Writing Game Theory in L A TEX Thiago Silva First Version: November 22, 2015 This Version: November 13, 2017 List of Figures and Tables 1 2x2 Matrix: Prisoner s ilemma Normal-Form Game............. 3 2
More informationBasic Game Theory. Kate Larson. January 7, University of Waterloo. Kate Larson. What is Game Theory? Normal Form Games. Computing Equilibria
Basic Game Theory University of Waterloo January 7, 2013 Outline 1 2 3 What is game theory? The study of games! Bluffing in poker What move to make in chess How to play Rock-Scissors-Paper Also study of
More informationEvolutionary Games on Networks. Wen-Xu Wang and G Ron Chen Center for Chaos and Complex Networks
Evolutionary Games on Networks Wen-Xu Wang and G Ron Chen Center for Chaos and Complex Networks Email: wenxuw@gmail.com; wxwang@cityu.edu.hk Cooperative behavior among selfish individuals Evolutionary
More informationObservations on Cooperation
Introduction Observations on Cooperation Yuval Heller (Bar Ilan) and Erik Mohlin (Lund) PhD Workshop, BIU, January, 2018 Heller & Mohlin Observations on Cooperation 1 / 20 Introduction Motivating Example
More informationEmergence of Cooperation and Evolutionary Stability in Finite Populations
Emergence of Cooperation and Evolutionary Stability in Finite Populations The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters. Citation
More informationSome Thought-ettes on Artificial Agent Modeling and Its Uses
Some Thought-ettes on Artificial Agent Modeling and Its Uses Steven O. Kimbrough University of Pennsylvania http://opim-sun.wharton.upenn.edu/ sok/ kimbrough@wharton.upenn.edu ECEG, Washington, D.C., 1/26/04
More informationIntroduction to Game Theory
COMP323 Introduction to Computational Game Theory Introduction to Game Theory Paul G. Spirakis Department of Computer Science University of Liverpool Paul G. Spirakis (U. Liverpool) Introduction to Game
More informationA lattice traffic model with consideration of preceding mixture traffic information
Chin. Phys. B Vol. 0, No. 8 011) 088901 A lattice traffic model with consideration of preceding mixture traffic information Li Zhi-Peng ) a), Liu Fu-Qiang ) a), Sun Jian ) b) a) School of Electronics and
More informationGame Theory, Evolutionary Dynamics, and Multi-Agent Learning. Prof. Nicola Gatti
Game Theory, Evolutionary Dynamics, and Multi-Agent Learning Prof. Nicola Gatti (nicola.gatti@polimi.it) Game theory Game theory: basics Normal form Players Actions Outcomes Utilities Strategies Solutions
More informationComputational Problems Related to Graph Structures in Evolution
BACHELOR THESIS Štěpán Šimsa Computational Problems Related to Graph Structures in Evolution Department of Applied Mathematics Supervisor of the bachelor thesis: Study programme: Study branch: Prof. Krishnendu
More informationOpinion Formation and Social Systems
Opinion Formation and Social Systems p. 1/51 Opinion Formation and Social Systems Marcello Delitala marcello.delitala@polito.it Department of Mathematics Politecnico di Torino Opinion Formation and Social
More informationModeling Dynamic Evolution of Online Friendship Network
Commun. Theor. Phys. 58 (2012) 599 603 Vol. 58, No. 4, October 15, 2012 Modeling Dynamic Evolution of Online Friendship Network WU Lian-Ren ( ) 1,2, and YAN Qiang ( Ö) 1 1 School of Economics and Management,
More informationTopology-independent impact of noise on cooperation in spatial public goods games
PHYSIAL REVIEW E 80, 056109 2009 Topology-independent impact of noise on cooperation in spatial public goods games Attila Szolnoki, 1 Matjaž Perc, 2 and György Szabó 1 1 Research Institute for Technical
More informationInternalization. a Game-Theoretic Approach. Rolf Ziegler Institute of Sociology University of Munich
Sanctioning Strategies and Internalization a Game-Theoretic Approach Rolf Ziegler Institute of Sociology University of Munich Rational Choice Sociology: Theory and Empirical Applications Venice International
More informationADAPTIVE GROWING NETWORKS COEVOLVING WITH THE SPREAD OF DISEASES
International Journal of Bifurcation and Chaos, Vol. 22, No. 7 (2012) 1250168 (8 pages) c World Scientific Publishing Company DOI: 10.1142/S0218127412501684 ADAPTIVE GROWING NETWORKS COEVOLVING WITH THE
More informationVector fields and phase flows in the plane. Geometric and algebraic properties of linear systems. Existence, uniqueness, and continuity
Math Courses Approved for MSME (2015/16) Mth 511 - Introduction to Real Analysis I (3) elements of functional analysis. This is the first course in a sequence of three: Mth 511, Mth 512 and Mth 513 which
More informationEvolutionary Bargaining Strategies
Evolutionary Bargaining Strategies Nanlin Jin http://cswww.essex.ac.uk/csp/bargain Evolutionary Bargaining Two players alternative offering game x A =?? Player A Rubinstein 1982, 1985: Subgame perfect
More informationLectures Road Map
Lectures 0 - Repeated Games 4. Game Theory Muhamet Yildiz Road Map. Forward Induction Examples. Finitely Repeated Games with observable actions. Entry-Deterrence/Chain-store paradox. Repeated Prisoners
More informationStatic (or Simultaneous- Move) Games of Complete Information
Static (or Simultaneous- Move) Games of Complete Information Introduction to Games Normal (or Strategic) Form Representation Teoria dos Jogos - Filomena Garcia 1 Outline of Static Games of Complete Information
More informationComputing Minmax; Dominance
Computing Minmax; Dominance CPSC 532A Lecture 5 Computing Minmax; Dominance CPSC 532A Lecture 5, Slide 1 Lecture Overview 1 Recap 2 Linear Programming 3 Computational Problems Involving Maxmin 4 Domination
More informationarxiv: v1 [physics.soc-ph] 9 Jan 2010
arxiv:1001.1441v1 [physics.soc-ph] 9 Jan 2010 Spontaneous reorientations in a model of opinion dynamics with anticonformists Grzegorz Kondrat and Katarzyna Sznajd-Weron Institute of Theoretical Physics,
More informationEvolutionary Game Theory and Frequency Dependent Selection
Evolutionary Game Theory and Frequency Dependent Selection 1 Game Theory A major component of economics Given a set of rules, predict how would rational beings behave in an interaction Who is in the game?
More informationGlobalization-polarization transition, cultural drift, co-evolution and group formation
- Mallorca - Spain CABDyN, Reference Saïdof Business research School, project Oxford, &/or name November of conference 7 Globalization-polarization transition, cultural drift, co-evolution and group formation
More informationarxiv: v1 [cs.gt] 18 Dec 2017
Invincible Strategies of Iterated Prisoner s Dilemma Shiheng Wang and Fangzhen Lin Department of Computer Science The Hong Kong University of Science and Technology Clear Water Bay,Kowloon,Hong Kong arxiv:1712.06488v1
More informationAn Interruption in the Highway: New Approach to Modeling the Car-Traffic
EJTP 7, No. 23 (21) 123 136 Electronic Journal of Theoretical Physics An Interruption in the Highway: New Approach to Modeling the Car-Traffic Amin Rezaeezadeh Electrical Engineering Department, Sharif
More informationEvolutionary Games and Computer Simulations
Evolutionary Games and Computer Simulations Bernardo A. Huberman and Natalie S. Glance Dynamics of Computation Group Xerox Palo Alto Research Center Palo Alto, CA 94304 Abstract The prisoner s dilemma
More informationApproximate Nash Equilibria with Near Optimal Social Welfare
Proceedings of the Twenty-Fourth International Joint Conference on Artificial Intelligence (IJCAI 015) Approximate Nash Equilibria with Near Optimal Social Welfare Artur Czumaj, Michail Fasoulakis, Marcin
More informationA Folk Theorem For Stochastic Games With Finite Horizon
A Folk Theorem For Stochastic Games With Finite Horizon Chantal Marlats January 2010 Chantal Marlats () A Folk Theorem For Stochastic Games With Finite Horizon January 2010 1 / 14 Introduction: A story
More information