On Social Learning and Robust Evolutionary Algorithm Design in the Cournot Oligopoly Game

Alkemade, Floortje; Poutré, JA Han La; Amman, Hans M.

doi:10.1111/j.1467-8640.2007.00300.x

Cited by 11 publications

(29 citation statements)

References 41 publications

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“…Our research is inspired by results reported by Alkemade et al (2006Alkemade et al ( , 2007Alkemade et al ( , 2009; see also Waltman and Van Eck 2009b). Alkemade et al show that under certain conditions an EA that is employed for modeling purposes may exhibit premature convergence.…”

Section: Introductionmentioning

confidence: 97%

“…To facilitate comparison, we consider exactly the same Cournot market as Alkemade et al (2006Alkemade et al ( , 2007Alkemade et al ( , 2009). For other studies in which quantity competition among firms is modeled using EAs, we refer to Arifovic (1994), Price (1997), Dawid and Kopel (1998), Franke (1998), Vriend (2000, Arifovic and Maschek (2006), Wheeler et al (2006), Casari (2008), and Maschek (2010.…”

Section: Cournot Oligopoly Marketmentioning

confidence: 99%

“…For early research in which genetic algorithms are employed, we refer to Miller (1986Miller ( , 1996, Axelrod (1987), Marks (1992), Arifovic (1994Arifovic ( , 1996, Andreoni and Miller (1995), and Dawid (1996). Examples of more recent research can be found in the work of, among others, Lux and Schornstein (2005), Alkemade et al (2006Alkemade et al ( , 2007Alkemade et al ( , 2009), Arifovic and Maschek (2006), Wheeler et al (2006), Xu (2006), Casari (2008), and Maschek (2010).…”

Section: Introductionmentioning

confidence: 99%

“…If the agents whose behavior is being modeled have to make decisions that are intrinsically binary, such as decisions between cooperation and defection in a prisoner's dilemma (e.g., Axelrod 1987), the use of a binary encoding of strategies is a very natural choice. However, in the case of nonbinary decisions, such as decisions by firms on their production level (e.g., Arifovic 1994;Price 1997;Dawid and Kopel 1998;Franke 1998;Vriend 2000;Alkemade et al 2006Alkemade et al , 2007Alkemade et al , 2009; Arifovic and Maschek 2006;Wheeler et al 2006;Casari 2008;Maschek 2010), there is no clear reason for the use of a binary encoding of strategies.…”

Section: Introductionmentioning

confidence: 99%

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Economic modeling using evolutionary algorithms: the effect of a binary encoding of strategies

2010

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We are concerned with evolutionary algorithms that are employed for economic modeling purposes. We focus in particular on evolutionary algorithms that use a binary encoding of strategies. These algorithms, commonly referred to as genetic algorithms, are popular in agent-based computational economics research. In many studies, however, there is no clear reason for the use of a binary encoding of strategies. We therefore examine to what extent the use of such an encoding may influence the results produced by an evolutionary algorithm. It turns out that the use of a binary encoding can have quite significant effects. Since these effects do not have a meaningful economic interpretation, they should be regarded as artifacts. Our findings indicate that in general the use of a binary encoding is undesirable. They also highlight the importance of employing evolutionary algorithms with a sensible economic interpretation.

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Section: Introductionmentioning

confidence: 97%

Section: Cournot Oligopoly Marketmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Economic modeling using evolutionary algorithms: the effect of a binary encoding of strategies

2010

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“…

In the original papers by Alkemade et al (2006Alkemade et al ( , 2007, their evolutionary algorithms (EAs) exhibited an extreme degree of premature convergence when they were run according to approach I. This seemed a quite curious result.

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confidence: 99%

Robust Evolutionary Algorithm Design for Socio-Economic Simulation: Some Comments

Waltman

2008

Comput Econ

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In the original papers by Alkemade et al. (2006Alkemade et al. ( , 2007, their evolutionary algorithms (EAs) exhibited an extreme degree of premature convergence when they were run according to approach I. This seemed a quite curious result. We are happy that the correction (Alkemade et al. 2008) makes clear that the degree of premature convergence is much lower than originally reported. There are three further comments that we would like to make on the work of Alkemade et al.First, Alkemade et al. state that "convergence behavior differs for different values of the EA parameters such as initial density and chromosome length". We would like to emphasize that the behavior of an EA depends on the initial density parameter only in the short run. In the long run, the initial density parameter has no effect on the behavior of an EA. This is because from a mathematical point of view an EA (or, more precisely, a genetic algorithm) is an ergodic Markov chain (e.g., Nix and Vose 1992; Dawid 1996). In the long run, the state of such a Markov chain no longer depends on the initial state. We agree with Alkemade et al. that the behavior of an EA depends on the chromosome length. This is the case not only in the short run but also in the long run. Since the chromosome length is a technical parameter that usually does not have a clear economic interpretation, we regard the dependence of EA behavior on the chromosome length as a disadvantage of the use of EAs for economic modeling.Second, Alkemade et al. point out that two popular approaches to the use of EAs for economic modeling can yield quite different results. This is a very interesting observation, especially since earlier studies usually simply took one of the two approaches

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Particle Swarm Optimization in Agent‐Based Economic Simulations of the Cournot Market Model

Maschek

2015

Intell. Sys. Acc. Fin. Mgmt.

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Summary The numerous variations of the particle swarm optimization (PSO) algorithm originally proposed by Kennedy and Eberhart (. Particle swarm optimization. In Proceedings of the IEEE International Conference on Neural Networks IV. IEEE: Piscataway, NJ; 1942–1948) have proven to be powerful optimization methods that rely on exploiting simple analogues of social interaction. In this study, PSO is adopted in lieu of the social or individual evolutionary learning algorithms as a model of individual adaptation in an agent‐based computational model. In this examination of the simple Cournot market framework, each agent's individual strategy evolves according to the PSO algorithm. The model is one in which agents’ strategies must adapt interdependently. That is, a change in one particle may not only affect its performance but also other particles within the same swarm simultaneously. The dynamics and convergence properties associated with this model are compared with those where evolutionary learning algorithms are employed. Similar to evolutionary learning, convergence to equilibrium is dependent on the scope of learning, social or individual. While convergence is dependent on some of the algorithm parameters, prices resulting from the individual PSO are nearest the Cournot equilibrium and those from social PSO are nearest the Walrasian equilibrium in all cases. For particular parameterizations, certain advantages over evolutionary algorithms exist: in the main, decreasing volatility in market prices does not require an election operator or the addition of free parameters through two‐level learning. Copyright © 2015 John Wiley & Sons, Ltd.

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On Social Learning and Robust Evolutionary Algorithm Design in the Cournot Oligopoly Game

Cited by 11 publications

References 41 publications

Economic modeling using evolutionary algorithms: the effect of a binary encoding of strategies

Economic modeling using evolutionary algorithms: the effect of a binary encoding of strategies

Robust Evolutionary Algorithm Design for Socio-Economic Simulation: Some Comments

Particle Swarm Optimization in Agent‐Based Economic Simulations of the Cournot Market Model

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