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KAKEN_17K03629seika.pdf
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Title |
Title |
ゲーム理論における双対・反双対性の基礎研究と応用
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ゲーム リロン ニ オケル ソウツイ・ハンソウツイセイ ノ キソ ケンキュウ ト オウヨウ
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Gēmu riron ni okeru sōtsui hansōtsuisei no kiso kenkyū to ōyō
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Duality and anti-duality in game theory : theory and applications
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穂刈, 享
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ホカリ, トオル
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Hokari, Tōru
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慶應義塾大学・経済学部 (三田) ・教授
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Research team head
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科研費研究者番号 : 20344856
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大石, 尊之
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オオイシ, タカユキ
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Ōishi, Takayuki
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明星大学・経済学部・准教授
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Research team member
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科研費研究者番号 : 50439220
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2020
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科学研究費補助金研究成果報告書
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2019
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Abstract |
Oishi et al. (2016, J Math Econ) の双対性・反双対性アプローチでは、従来からある「双対ゲーム」の概念を用いて、協力ゲームの分野における諸結果を関連付け、いくつかの新たな結果を見つけ出したのだが、本研究では、代替的な双対ゲームの概念で、従来のものと同様の効果をもち、新たな結果を生み出し得るものについて検討し、3人ゲームについてはそのような代替的な双対ゲームのクラスを全て求めることができ、一般的なn人ゲームについては1つの例を示すことができた。
また、それと並行して、協力ゲームの公理的分析の分野におけるいくつかの未解決問題を解決した。
In the duality/anti-duality approach of Oishi et al. (2016, J Math Econ), by using the standard notion of "dual games", some hidden relations among allocation rules, axioms, and axiomatization results are discovered. We were interested in finding other alternative notions of dual games, that might have a similar impact on the field of axiomatic analysis of cooperative games as the standard one. We were able to characterize all such alternative notions of dual game in the three-person case, and provide an example in the general n person case.
We have also solved some open problems in this field.
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研究種目 : 基盤研究 (C) (一般)
研究期間 : 2017~2019
課題番号 : 17K03629
研究分野 : ゲーム理論 (協力ゲーム)
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