On the Evolution of Continuous Types Under Replicator and Gradient Dynamics: Two Examples

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• 作者：Jean Paul Rabanal
• 关键词：Population games ; Evolutionary dynamics ; Corporate social responsibility ; Mixed oligopoly ; Public goods
• 刊名：Dynamic Games and Applications
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：7
• 期：1
• 页码：76-92
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Game Theory, Economics, Social and Behav. Sciences; Economic Theory/Quantitative Economics/Mathematical Methods; Operations Research, Management Science; Economics, general; Communications Engineering
• 出版者：Springer US
• ISSN：2153-0793
• 卷排序：7

文摘

This paper illustrates techniques for assessing the dynamic stability of games where a continuum of types might be present by re-analyzing two models under incomplete information, the Lohman et al. (Unpublished manuscript, 2001) public goods game and the Kopel et al. (J Econ Dyn Control 48:394–409, 2014) Cournot duopoly game. The evolution of continuous types follows either replicator dynamics Oechssler and Riedel (Econ Theory 17:141–162, 2001; J Econ Theory 107:223–252 2002) or gradient dynamics Friedman and Ostrov (J Math Econ 46:691–707, 2010; J Econ Theory 148:743–777, 2013). The techniques rely on a system of partial differential equations. Numerical solutions obtained through replicator and gradient dynamics highlight the differences and the similarities that arise under both approaches. In the public goods game, the dynamic system affects the stationary distribution of types while in the Cournot duopoly model, the types evolve to a single mass point regardless of the dynamics used. Lastly, these techniques allow us to endogenize the distribution of player types.