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

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  • Abramsky, Samson
  • Winschel, Viktor
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    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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    File URL: https://ub-madoc.bib.uni-mannheim.de/32525/1/Abramsky_%26_Winschel_12%2D17.pdf
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    Bibliographic Info

    Paper provided by University of Mannheim, Department of Economics in its series Working Papers with number 12-17.

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    Date of creation: 2012
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    Handle: RePEc:mnh:wpaper:32525

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    1. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, December.
    2. Lars Ljungqvist & Thomas J. Sargent, 2004. "Recursive Macroeconomic Theory, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 026212274x, December.
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