Coevolutionary Intransitivity in Games: A Landscape Analysis

Intransitivity is supposed to be a main reason for deficits in coevolutionary progress and inheritable superiority. Besides, coevolutionary dynamics is characterized by interactions yielding subjective fitness, but aiming at solutions that are superior with respect to an objective measurement. Such an approximation of objective fitness may be, for instance, generalization performance. In the paper a link between rating– and ranking–based measures of intransitivity and fitness landscapes that can address the dichotomy between subjective and objective fitness is explored. The approach is illustrated by numerical experiments involving a simple random game with continuously tunable degree of randomness.

[1]  Peter Tiño,et al.  Measuring Generalization Performance in Coevolutionary Learning , 2008, IEEE Transactions on Evolutionary Computation.

[2]  Edwin D. de Jong Objective fitness correlation , 2007, GECCO '07.

[3]  R. A. Bradley,et al.  RANK ANALYSIS OF INCOMPLETE BLOCK DESIGNS THE METHOD OF PAIRED COMPARISONS , 1952 .

[4]  H. Ohtsuki,et al.  Evolution of cooperation by phenotypic similarity , 2009, Proceedings of the National Academy of Sciences.

[5]  Edwin D. de Jong,et al.  Coevolutionary Principles , 2012, Handbook of Natural Computing.

[6]  Simon M. Lucas,et al.  Coevolving Game-Playing Agents: Measuring Performance and Intransitivities , 2013, IEEE Transactions on Evolutionary Computation.

[7]  Rients P. T. van Wijngaarden,et al.  Evaluation and Diversity in Co-evolution , 2008, PPSN.

[8]  M. Nowak,et al.  Evolutionary dynamics in structured populations , 2010, Philosophical Transactions of the Royal Society B: Biological Sciences.

[9]  A. Elo The rating of chessplayers, past and present , 1978 .

[10]  R. A. Bradley,et al.  RANK ANALYSIS OF INCOMPLETE BLOCK DESIGNS , 1952 .

[11]  Hendrik Richter,et al.  Fitness Landscapes That Depend on Time , 2014 .

[12]  Hendrik Richter Codynamic fitness landscapes of coevolutionary minimal substrates , 2014, 2014 IEEE Congress on Evolutionary Computation (CEC).

[13]  F. Harary,et al.  Cluster Inference by using Transitivity Indices in Empirical Graphs , 1982 .

[14]  Pablo Funes,et al.  Intransitivity revisited coevolutionary dynamics of numbers games , 2005, GECCO '05.

[15]  J. Pollack,et al.  Coevolutionary dynamics in a minimal substrate , 2001 .

[16]  L. Kallel,et al.  Theoretical Aspects of Evolutionary Computing , 2001, Natural Computing Series.

[17]  C. Reeves,et al.  Properties of fitness functions and search landscapes , 2001 .

[18]  Martin A. Nowak,et al.  Evolution of cooperation by phenotypic similarity , 2008, Proceedings of the National Academy of Sciences.

[19]  R. A. Bradley,et al.  Rank Analysis of Incomplete Block Designs: I. The Method of Paired Comparisons , 1952 .

[20]  Andries P. Engelbrecht,et al.  Recent Advances in the Theory and Application of Fitness Landscapes , 2013 .

[21]  Siang Yew Chong,et al.  Improving Generalization Performance in Co-Evolutionary Learning , 2012, IEEE Transactions on Evolutionary Computation.

[22]  R. Duncan Luce,et al.  Individual Choice Behavior , 1959 .

[23]  Thomas Miconi,et al.  Why Coevolution Doesn't "Work": Superiority and Progress in Coevolution , 2009, EuroGP.

[24]  Edwin D. de Jong,et al.  Intransitivity in Coevolution , 2004, PPSN.

[25]  David J. Hand,et al.  Who's #1? The science of rating and ranking , 2012 .