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Kuhn’s Theorem for extensive form Ellsberg games

Institution:	1. Bielefeld University, Center for Mathematical Economics, 33615 Bielefeld, Germany;2. University of Johannesburg, Faculty of Economics and Financial Sciences, South Africa;1. Walter A. Haas School of Business, University of California, Berkeley, United States;2. Krannert School of Management, Purdue University, United States;3. Department of Economics, National University of Singapore, Singapore;1. College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China;2. Department of Finance and Insurance, Lingnan University, 8 Castle Peak Road, Tuen Mun, Hong Kong;1. College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China;2. Department of Finance and Insurance, Lingnan University, Hong Kong;1. School of Business Administration, University of Miami, United States;2. Department of Economics, Faculty of Economics and Business, University of Chile, Chile

Abstract:	We propose the notions of mixed and behavioral Ellsberg strategies for extensive form games and prove that these strategies are outcome-equivalent if and only if mixed Ellsberg strategies satisfy a certain rectangularity condition. In addition, we show that not only the profile of Ellsberg strategies must be appropriately chosen but also the extensive form must satisfy further restrictions beyond those implied by perfect recall in order to ensure that each player will respect his ex ante strategy choice with the evolution of play.

Keywords:	Kuhn’s Theorem Strategic ambiguity Maxmin utility Ellsberg games
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