Coalgebraic Analysis of Subgame-perfect Equilibria in Infinite Games without Discounting


Abramsky, Samson ; Winschel, Viktor


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URL: https://ub-madoc.bib.uni-mannheim.de/32525
URN: urn:nbn:de:bsz:180-madoc-325256
Document Type: Working paper
Year of publication: 2012
The title of a journal, publication series: Working Paper Series
Volume: 12-17
Place of publication: Mannheim
Publication language: English
Institution: School of Law and Economics > VWL, Internat. Wirtschaftsbeziehungen (Adam)
MADOC publication series: Department of Economics > Working Paper Series
Subject: 330 Economics
Abstract: We present a novel coalgebraic formulation of infinite extensive games. We define both the game trees and the strategy profiles by possibly infinite systems of corecursive equations. Certain strategy profiles are proved to be subgame perfect equilibria using a novel proof principle of predicate coinduction which is shown to be sound by reducing it to Kozen’s metric coinduction. We characterize all subgame perfect equilibria for the dollar auction game. The economically interesting feature is that in order to prove these results we do not need to rely on continuity assumptions on the payoffs which amount to discounting the future. In particular, we prove a form of one-deviation principle without any such assumptions. This suggests that coalgebra supports a more adequate treatment of infinite-horizon models in game theory and economics.

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Abramsky, Samson ; Winschel, Viktor (2012) Coalgebraic Analysis of Subgame-perfect Equilibria in Infinite Games without Discounting. Open Access Working Paper Series Mannheim 12-17 [Working paper]
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