Atsuhiro Satoh, Yasuhito Tanaka
arXiv 17 Jun 2018 · Econometrics
arXiv:1806.07253 · PDF · DOI · OpenAlex · Extracted main text
We consider the relation between Sion's minimax theorem for a continuous function and a Nash equilibrium in an asymmetric multi-players zero-sum game in which only one player is different from other players, and the game is symmetric for the other players. Then, 1. The existence of a Nash equilibrium, which is symmetric for players other than one player, implies Sion's minimax theorem for pairs of this player and one of other players with symmetry for the other players. 2. Sion's minimax theorem for pairs of one player and one of other players with symmetry for the other players implies the existence of a Nash equilibrium which is symmetric for the other players. Thus, they are equivalent.
appendix boundary found by none_found · 100% of the source is main text. Read the extracted text to check this.
The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Kindler, J (2005) A simple proof of Sion's minimax theorem | 0.511 | 2 | 1 | 100% |
| 2 | Tanaka, Y (2013) Equivalence of Cournot and Bertrand equilibria in differentiated duopoly under relative profit maximization with linear demand self | 0.405 | 1 | 1 | 100% |
| 3 | Satoh, A. and Y. Tanaka (2014) Relative profit maximization and equivalence of Cournot and Bertrand equilibria in asymmetric duopoly self | 0.405 | 1 | 1 | 100% |
| 4 | Tanaka, Y (2013) Irrelevance of the choice of strategic variables in duopoly under relative profit maximization self | 0.405 | 1 | 1 | 100% |
| 5 | Satoh, A. and Y. Tanaka (2013) Relative profit maximization and Bertrand equilibrium with quadratic cost functions self | 0.405 | 1 | 1 | 100% |
| 6 | Komiya, H (1988) Elementary proof for Sion's minimax theorem | 0.405 | 1 | 1 | 100% |
| 7 | Matsumura, T., N. Matsushima and S. Cato (2013) Competitiveness and R&D competition revisited | 0.405 | 1 | 1 | 100% |
| 8 | Vega-Redondo, F (1997) The evolution of Walrasian behavior | 0.405 | 1 | 1 | 100% |
| 9 | Sion, M (1958) On general minimax theorems | 0.405 | 1 | 1 | 100% |
| 10 | Satoh, A. and Y. Tanaka (2014) Relative profit maximization in asymmetric oligopoly self | 0.405 | 1 | 1 | 100% |
Showing the top 10 of 10 scored citations.