## A Game-Theoretic Approach to the Simple Coevolutionary Algorithm (0)

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Venue: | Proceedings of the Sixth International Conference on Parallel Problem Solving from Nature (PPSN VI |

Citations: | 56 - 9 self |

### BibTeX

@INPROCEEDINGS{Ficici_agame-theoretic,

author = {Sevan G. Ficici and Jordan B. Pollack},

title = {A Game-Theoretic Approach to the Simple Coevolutionary Algorithm},

booktitle = {Proceedings of the Sixth International Conference on Parallel Problem Solving from Nature (PPSN VI},

year = {},

pages = {467--476},

publisher = {Springer}

}

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### Abstract

The fundamental distinction between ordinary evolutionary algorithms (EA) and co-evolutionary algorithms lies in the interaction between coevolving entities. We believe that this property is essentially game-theoretic in nature. Using game theory, we describe extensions that allow familiar mixing-matrix and Markov-chain models of EAs to address coevolutionary algorithm dynamics. We then employ concepts from evolutionary game theory to examine design aspects of conventional coevolutionary algorithms that are poorly understood.

### Citations

1461 |
An Introduction to Genetic Algorithms
- Mitchell
- 1999
(Show Context)
Citation Context ...se premature convergence. These problems have lead to the development of many alternative selection methods for evolutionary algorithms, such as truncation selection, (; )-ES selection, and ranking [1=-=7-=-]. We have used EGT to test these selection methods and have shown that none of them are able to attain polymorphic attractors, even if the population is innite [6]. Instead, these selection methods e... |

640 | Evolutionary Game Theory
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(Show Context)
Citation Context ...pulation. This is not necessarily true for weak dominance [12]. That replicator dynamics removes strategies that are strictly dominated (by pure strategies, in the case of non-overlapping generations =-=[25]-=-) suggests that it is performing an operation akin to multi-objective optimization, where every strategy represents an objective of the coevolutionary problem. That is, in comparing two strategies, s ... |

440 |
Co-evolving Parasites Improve Simulated Evolution as an Optimization Procedure
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- 1992
(Show Context)
Citation Context ...y algorithm dynamics remain to be explicated, for the gap between the hypothesized potential of coevolutionary algorithms and realized practice is substantial|the many successes of coevolution (e.g., =-=[11, 22, 13]-=-) are balanced by many irksome modes of failure that commonly recur (e.g., as discussed in [7, 18]). Investigation into these modes of failure has proven to be a challenge. We believe that an understa... |

414 |
Nonlinear Dynamics and Chaos
- Strogatz
- 1994
(Show Context)
Citation Context ...xed point. Further, if a point attractor ^ p exists and the game is not constant-sum, then ^ p may easily be composed of a phenotype other than the mostst phenotype in p 0 . Linear stability analysis =-=[23]-=- tells us that the strategies in support of a coevolutionary point attractor|that is, all strategies i where ^ p i > 0|must be the highest scoring strategies in all population states within some epsil... |

401 |
Evolution Games and Population Dynamics
- Sigmund, K
- 1998
(Show Context)
Citation Context ...volving entities. We believe that this property of coevolution is fundamentally game-theoretic in nature. Thus, we incorporate notions from evolutionary game theory (EGT) [15] and replicator dynamics =-=[12]-=- into the familiar mixing-matrix [26] and Markov-chain [24] models of (noncoevolutionary) EAs to arrive at a preliminary, yet principled framework for coevolutionary algorithm analysis. While we are u... |

334 | Evolving 3D morphology and behavior by competition
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(Show Context)
Citation Context ...y algorithm dynamics remain to be explicated, for the gap between the hypothesized potential of coevolutionary algorithms and realized practice is substantial|the many successes of coevolution (e.g., =-=[11, 22, 13]-=-) are balanced by many irksome modes of failure that commonly recur (e.g., as discussed in [7, 18]). Investigation into these modes of failure has proven to be a challenge. We believe that an understa... |

181 |
Fun and Games; A Text on Game Theory
- Binmore
- 1992
(Show Context)
Citation Context ...ing coevolutionary algorithms for optimization, and understand the coevolutionary domain to be representable by a payo matrix, then the appropriate optimality concept is that of the Nash equilibrium [=-=2-=-]. This is a strategy that, when used by one player, oers no better alternative to the second player than to use the same strategy. If there exists another alternative that does no worse than the Nash... |

175 |
Evolutionary phenomena in simple dynamics
- Lindgren
- 1992
(Show Context)
Citation Context ...n general [24, 26, 21], co-evolutionary algorithms, in particular, still have few formal tools for their analysis|investigations of coevolutionary algorithm dynamics are typically empirical in nature =-=[7, 3, 1, 14, 16-=-]. The reason for this divide stems from the need to formally account for the dening characteristic of coevolutionary algorithms: the interaction of coevolving entities. We believe that this property ... |

168 | Competitive environments evolve better solutions for complex tasks
- Angeline, Pollack
- 1993
(Show Context)
Citation Context ...n general [24, 26, 21], co-evolutionary algorithms, in particular, still have few formal tools for their analysis|investigations of coevolutionary algorithm dynamics are typically empirical in nature =-=[7, 3, 1, 14, 16-=-]. The reason for this divide stems from the need to formally account for the dening characteristic of coevolutionary algorithms: the interaction of coevolving entities. We believe that this property ... |

162 |
The Simple Genetic Algorithm
- Vose
- 1999
(Show Context)
Citation Context ...me theory to examine design aspects of conventional coevolutionary algorithms that are poorly understood. 1 Introduction While formal models of evolutionary algorithm (EA) dynamics burgeon in general =-=[24, 26, 21]-=-, co-evolutionary algorithms, in particular, still have few formal tools for their analysis|investigations of coevolutionary algorithm dynamics are typically empirical in nature [7, 3, 1, 14, 16]. The... |

145 | Tracking the Red Queen: Measurements of adaptive progress in co-evolutionary simulations
- Cliff, Miller
- 1995
(Show Context)
Citation Context ...n general [24, 26, 21], co-evolutionary algorithms, in particular, still have few formal tools for their analysis|investigations of coevolutionary algorithm dynamics are typically empirical in nature =-=[7, 3, 1, 14, 16-=-]. The reason for this divide stems from the need to formally account for the dening characteristic of coevolutionary algorithms: the interaction of coevolving entities. We believe that this property ... |

137 |
Evolution and the Theory of Games
- Maynard-Smith
- 1982
(Show Context)
Citation Context ...ithms: the interaction of coevolving entities. We believe that this property of coevolution is fundamentally game-theoretic in nature. Thus, we incorporate notions from evolutionary game theory (EGT) =-=[15]-=- and replicator dynamics [12] into the familiar mixing-matrix [26] and Markov-chain [24] models of (noncoevolutionary) EAs to arrive at a preliminary, yet principled framework for coevolutionary algor... |

107 | Co-evolution in the successful learning of backgammon strategy
- Pollack, Blair
- 1998
(Show Context)
Citation Context ...tionary algorithms and realized practice is substantial|the many successes of coevolution (e.g., [11, 22, 13]) are balanced by many irksome modes of failure that commonly recur (e.g., as discussed in =-=[7, 18]-=-). Investigation into these modes of failure has proven to be a challenge. We believe that an understanding of evolutionary game theory and replicator dynamics will help to meet this challenge. Our fu... |

90 | The dynamical theory of coevolution: a derivation from stochastic ecological processes
- Dieckmann, Law
- 1996
(Show Context)
Citation Context ...layer games implied by the pair-wise contests frequently used by the EC community. Coevolutionary dynamics have also been studied from the perspective of mathematical biology, for example in [10] and =-=[5]. The-=- \street-car" theory of the former study is concerned with reconciling the peculiar constraints of Mendelian genetics with game-theoretic notions of phenotypic stability. In contrast, the latter ... |

75 | Challenges in coevolutionary learning: Arms-race dynamics, open-endedness, and mediocre stable states
- Ficici, Pollack
- 1998
(Show Context)
Citation Context |

74 | Coevolutionary search among adversaries
- Rosin
- 1997
(Show Context)
Citation Context ...erent approach, computational learning theory (COLT) has been used to analyze machine learning of competitive (zero-sum) two-player games and construct a specialized form of coevolutionary algorithm [=-=20]-=-. Thus, we see that many sources exist for insight into coevolutionary dynamics. Nevertheless, neither theselds of economics nor biology ultimately concern themselves with modeling coevolutionary algo... |

33 | A statistical mechanical formulation of the dynamics of genetic algorithms
- Shapiro, Prügel-Bennett, et al.
- 1994
(Show Context)
Citation Context ...me theory to examine design aspects of conventional coevolutionary algorithms that are poorly understood. 1 Introduction While formal models of evolutionary algorithm (EA) dynamics burgeon in general =-=[24, 26, 21]-=-, co-evolutionary algorithms, in particular, still have few formal tools for their analysis|investigations of coevolutionary algorithm dynamics are typically empirical in nature [7, 3, 1, 14, 16]. The... |

29 |
1998]. “On the instability of evolutionary stable strategies in small populations,” Ecological Modeling 109
- Andrews, Fogel
(Show Context)
Citation Context ...aving only the problem of selection), and therefore dubious in a real-world algorithm. Indeed, we have shown [8] that the use of truncation selection is one reason why the simulations by Fogel, et al =-=[9]-=- lead them to claim that EGT loses predictive power insnite populations. 3.4 Population Structures Coevolutionary algorithms that use two genetically isolated populations typically involve asymmetric ... |

27 |
Darwinian adaptation, population genetics and the streetcar theory of evolution
- Hammerstein
- 1996
(Show Context)
Citation Context ...the two-player games implied by the pair-wise contests frequently used by the EC community. Coevolutionary dynamics have also been studied from the perspective of mathematical biology, for example in =-=[10] and -=-[5]. The \street-car" theory of the former study is concerned with reconciling the peculiar constraints of Mendelian genetics with game-theoretic notions of phenotypic stability. In contrast, the... |

25 | A game-theoretic investigation of selection methods used in evolutionary algorithms
- Ficici, Melnik, et al.
- 2000
(Show Context)
Citation Context ..., where R computes the rank of each agent based onstness, r i = n : : : 1 (higherstness results in higher rank values). Implementations of other selection methods for innite populations are found in [=-=6-=-]. We discuss the eects of alternative selection methods below. G = MsSsF (7) 3 Evolutionary Game Theory If we are using coevolutionary algorithms for optimization, and understand the coevolutionary d... |

18 | Learning and Behavioral Stability: An economic interpretation of genetic algorithms
- Riechmann
- 1999
(Show Context)
Citation Context ...unity, we have discovered at least two precedents that originate, perhaps not surprisingly, from the economics community, which has come increasingly to study agent-based models of economic evolution =-=[4, 19]-=-. Both discuss Markov-chain models of genetic algorithms (GA) (i.e., bit-string encodings) where agentstness is dependent upon population state. While the game structure assumed in the former study is... |

8 |
A markov chain analysis of genetic algorithms with a state dependent tness function
- Dawid
- 1994
(Show Context)
Citation Context ...unity, we have discovered at least two precedents that originate, perhaps not surprisingly, from the economics community, which has come increasingly to study agent-based models of economic evolution =-=[4, 19]-=-. Both discuss Markov-chain models of genetic algorithms (GA) (i.e., bit-string encodings) where agentstness is dependent upon population state. While the game structure assumed in the former study is... |

6 | The artificial evolution of cooperation - Meuleau, Lattaud - 1995 |

3 | A Review of Models for Simple Genetic Algorithms and Cellular Genetic Algorithms
- Whitley
- 1995
(Show Context)
Citation Context ...me theory to examine design aspects of conventional coevolutionary algorithms that are poorly understood. 1 Introduction While formal models of evolutionary algorithm (EA) dynamics burgeon in general =-=[24, 26, 21]-=-, co-evolutionary algorithms, in particular, still have few formal tools for their analysis|investigations of coevolutionary algorithm dynamics are typically empirical in nature [7, 3, 1, 14, 16]. The... |

2 |
Coevolving the \ideal" trainer: Application to the discovery of cellular automata rules
- Juille, Pollack
- 1998
(Show Context)
Citation Context ...y algorithm dynamics remain to be explicated, for the gap between the hypothesized potential of coevolutionary algorithms and realized practice is substantial|the many successes of coevolution (e.g., =-=[11, 22, 13]-=-) are balanced by many irksome modes of failure that commonly recur (e.g., as discussed in [7, 18]). Investigation into these modes of failure has proven to be a challenge. We believe that an understa... |

1 |
Eects of populations on evolutionary stable strategies
- Ficici, Pollack
- 2000
(Show Context)
Citation Context ...lue that each agent (and genotype) playing strategy i receives after complete mixing, i.e., pair-wise encounters with every agent in the population (including itself, in the case of asnite population =-=[8-=-]). As shown in Equation 3, wesrst calculate for each strategysi a weighted sum of the payos in row i of G, the weights being determined by the phenotypic composition of the population, p; this operat... |