The Search for Nash Equilibrium Solutions with Replicator Equations Derived from Gradient Dynamics on a Simplex

• OKAMOTO Takashi

  Graduate School of Science and Technology, Keio University/JSPS Research Fellow (DC2)

• AIYOSHI Eitaro

  Faculty of Science and Technology, Keio University

抄録

In this paper, we discuss continuous game problems for which a normalization constraint (unit simplex constraint) constrains each player's decision-making. These problems can be classified into two types by their constraints. For one type, the simplex constraint applies to the variables for each player independently, such as occurs in a product ability assignment problem. For the other type, the simplex constraint applies to interferences among all the players, such as in a market share competition problem. We assume that the problems have Nash equilibrium solutions, and then we derive gradient system dynamics, which converge to the Nash solutions without violations of the simplex constraints. We discuss the equivalence of the derived dynamics and the replicator dynamics. Lastly, the effectiveness of the derived dynamics is shown by its application to simple example problems.

収録刊行物

• 計測自動制御学会論文集

  計測自動制御学会論文集 43 (2), 118-127, 2007

  公益社団法人 計測自動制御学会

キーワード

• game problem
• Nash equilibrium solution
• simplex constraint
• replicator dynamics

詳細情報

• CRID: 1390282679479791360
• NII論文ID: 130003792078
• NII論文ID: 10018544375
• NII書誌ID: AN00072392
• DOI: 10.9746/ve.sicetr1965.43.118
• ISSN: 18838189
• ISSN: 04534654
• NDL書誌ID: 8724121
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I8724121
• Web Site: https://www.jstage.jst.go.jp/article/sicetr1965/43/2/43_118/_pdf
• 本文言語コード: en
• データソース種別:
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  • NDL
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