Education Material on Evolutionary Game Theory & Experimental Economics


Recently Developing (2014)

XYZW (2011-02)

CFH  (2012-07,WP) Cycles and Instability in a Rock-Paper-Scissors Population Game: a Continuous Time Experiment (also) by Timothy N. Cason, Daniel Friedman, Ed Hopkins (Histroy, Program for the 2012 International ESA Conference, New York, Download June-26th-2012 version (also) Published version, 2013-07-15, Reviews of Economics Studies, Comment CFH 2014 by Zhijian Wang, Siqian Zhu, BinXu @harvard.edu papers for students to presen (also)

HSNG (2012-02,WP) An experimental test of Nash equilibrium versus evolutionary stability (also) by Moshe Hoffman, Sigrid Suetens, Martin A. Nowak, Uri Gneezy

XW  (2010-12, WP) Dynamical Pattern in a 2 x 2 Game with Human Subjects (Chinese) (also)

XW   (2011-04, Pubilished in Book Page 1313-1326) Evolutionary Dynamical Pattern of 'Coyness and Philandering': Evidence from Experimental Economics 

XYZW (2011-02, WP) Laboratory RPS Game Experimental Evaluations of the Evolutionary Dynamics Theories

XW   (2012-08, WP)  Cycles in RPS games 

XWW  (2012-08, WP) Periodic frequencies of the cycles in 2 × 2 games   presentation in ITP 2012-12-13 

XW   (2012-09, Published in Results in Physics) Test MaxEnt in social strategy transitions with experimental two-person constant sum 2 × 2 games 

BJLLP (2014-05, How Facebook Can Deepen our Understanding of Behavior in Strategic Settings: Evidence from a Million Rock-Paper-Scissors Games ) 

WXZ (2014-04, Social cycling and conditional responses in the Rock-Paper-Scissors game 20140421, arxiv:1404.5199 ) 
Citation Citation Fr Citation Phi 1404.5199v1 in News   paper in Scientific Reports DOI: 10.1038/srep05830  @Cornell.edu Game Theory and Rock Paper Scissors and Nash equilibrium

HSGN (2015-03) An experimental investigation of evolutionary dynamics in the Rock-Paper-Scissors game  doi:10.1038/srep08817

 
Syllabus 
Sandholm (2013 Spring) Department of Mathematics, École Polytechnique 
Syllabus: Population Games and Deterministic Evolutionary Dynamics  Planning of Course
Martin Nowak (Spring 2013)  Harvard Math 243 Syllabus 2013  EVOLUTIONARY DYNAMICS
Christoph Hauert (2012 Spring) MATH 564: Evolutionary Dynamics 
Sandhlom Introduction   Brief introduction(2007)

UCSC Econ 204B (2013 Spring)  // Prof. Dan Friedman

Advanced Microeconomic Theory II The second quarter of the Ph.D. microeconomics sequence
On evolutionary game theory, look in the S&E library for books by William Sandholm (2010) and Joergen Weibull (1997). Draft chapters from Dan's book with Barry Sinervo (due in 2014) can be downloaded  2  the magic word isGameTheoryRPS. 
A submitted paper is also attached below, reporting an experiment with rock-paper-scissors. Also, and older paper with KC Fung applying EvGames to an IO/Trade issue.

博弈论 耶鲁大学公开课 
第11集 进化稳定-合作,突变,与平衡 or  game1  game2 
Evolutionary game theory: molecules as players

Mixed strategy Nash equilibrium as a non-equilibrium steady state - Zhijian Wang 20140729 

Chaos in Rock-Paper-Scissors by Sandholm 
Follwoing Sato, Akiyama, and Farmer (2002), we consider the evolution of the population's behavior under the replicator dynamic. This dynamic is defined by the property that the percentage growth rate in the use of each strategy is given by the strategy's excess payoff - that is, by the difference between its payoff and the average payoff obtained in the relevant population. ... Evidently, the evolution of behavior is chaotic: rather than converging to an equilibrium or approaching a periodic orbit, the trajectory traverses the state space in an irregular and unpredictable manner. 

 

       
       


Population Games and Evolutionary Dynamics by William H. Sandholm. MIT Press, December 2010
Exploration dynamics in evolutionary games PNAS 2009


Eric Smith, Santafe.edu: Statistical and institutional foundations of economics
Daniel Dennett: How Life is Like a Game of Rock-Paper-Scissors

Von Huyck  Figure 1a graphs the vector field under the continuous time limit of the two population logit response dynamic with the noise parameter, , set equal to 1. The axes measure the frequency of action 1 in the first and second population respectively. The points (1,0) and (0,1) represent pure strategy equilibria in which everyone in one population takes the action opposite to the action taken by everyone in the second population. The mixed equilibrium in the center of the space is unstable, but vectors forcing the populations away from the center are small. (As the vector’s color goes from black to red it represents smaller values. The tail of the vector is also proportional to size, but the head is not.) Note also that the logit equilibria with equal 1, denoted by red dots, are shifted slightly towards the center of the space. The shift will be more dramatic in the bargaining game reviewed next. The grey shading represents states in which all players have a pecuniary incentive to conform to the emerging convention.

   

1

2

3

1

3,3

3,0

6,4

2

0,3

5,5

0,0

3

4,6

0,0

0,0

Figure 2a graphs the logistic response vector field for the game that results when action 2 becomes extinct in game DS, which will be denoted BOS. The black dots denote Nash equilibria and the red dots denote logistic equilibria (again with equal 1). The grey shaded regions indicate states in which everyone has a pecuniary incentive to conform to the emerging convention. Figure 2b graphs the results for five sessions run by hand and figure 2c graphs the results for three sessions run by computer. Again the points denote five period sums of action 1 for the row and column population. The sums can range from 0 to 35 (seven subjects choosing action 1 for five periods). Dots denote states in which the equal division action is extinct and circles denote states in which it is not. Numbers sequence the states by the time order they were observed.

 

Friendman 2009  Figure 4 shows an apparent pattern to the resolutions. It plots the Hawk fraction only in the last 20 second time interval of each period. Except in Session 3, we see that the separation trend builds over time, and that we approach an asymmetric Nash equilibrium. The same data are replotted
in Figure 5, using the conventions of Figure 1 and a trianglar smoother to help detect trends. In sessions 2 and 4 we observe near convergence to a corner pure NE, while in session 1 we observe decisive movement only after period 16.

Optimization incentives and coordination failure in laboratory stag hunt games
Battalio, L Samuelson Huyck - Econometrica, 2001


Human strategy updating in evolutionary games (pdf, PNAS 2010) Evolutionary game dynamics describe not only frequency-dependent genetic evolution, but also cultural evolution in humans. In this context, successful strategies spread by imitation. It has been shown that the details of strategy update rules can have a crucial impact on evolutionary dynamics in theoretical models and, for example, can significantly alter the level of cooperation in social dilemmas. What kind of strategy update rules can describe imitation dynamics in humans? Here, we present a way to measure such strategy update rules in a behavioral experiment.

 Experimental Economics

      Handbook(2008) C. Plott, V. Smith
      Huyck2001  Data Replication Result

Mixed Strategy Nash Equilibrium