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Coalgebraic analysis of subgame-perfect equilibria in infinite games without discounting

Published online by Cambridge University Press:  23 July 2015

Department of Computer Science, University of Oxford, Oxford, Oxfordshire, U.K. Email:
Department of Management, Technology, and Economics, ETH Zurich, Zurich, Switzerland Email:


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. 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 pay-offs 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.

Copyright © Cambridge University Press 2015 

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Fudenberg, D. and Levine, D. (1983). Subgame-perfect equilibria of finite- and infinite-horizon games. Journal of Economic Theory 31 (2) 251268.CrossRefGoogle Scholar
Fudenberg, D. and Tirole, J. (1991). Game Theory, MIT Press.Google Scholar
Harsanyi, J. C. (1967). Games with incomplete information played by ‘Bayesian’ players, I-III. Part I. The basic model. Management Science 14 (3) 159182.CrossRefGoogle Scholar
Honsell, F. and Lenisa, M. (2011). Conway games, algebraically and coalgebraically. preprint arXiv:1107.1351.Google Scholar
Honsell, F., Lenisa, M. and Redamalla, R. (2012). Categories of coalgebraic games. In: Proceedings of the 37th International Symposium, Mathematical Foundations of Computer Science, Springer 503–515.Google Scholar
Jacobs, B. (2005). Introduction to coalgebra. Towards Mathematics of States and Observations. Available at, 22.Google Scholar
Jacobs, B. and Rutten, J. (1997). A tutorial on (co) algebras and (co) induction. Bulletin-European Association for Theoterical Computer Science 62 222259.Google Scholar
Knaster, B. (1928). Un théoreme sur les fonctions d'ensembles. Annales de la Société Polonaise de Mathématique 6 (133) 2013134.Google Scholar
Kozen, D. and Ruozzi, N. (2007). Applications of metric coinduction. In: Proceedings of the 2nd International Conference on Algebra and Coalgebra in Computer Science, Springer-Verlag 327–341.Google Scholar
Lambek, J. (1968). A fixpoint theorem for complete categories. Mathematische Zeitschrift 103 (2) 151161.CrossRefGoogle Scholar
Lescanne, P. (2011). Rationality and escalation in infinite extensive games. preprint arXiv:1112.1185.Google Scholar
Lescanne, P. and Perrinel, M. (2012). “Backward'' coinduction, Nash equilibrium and the rationality of escalation. Acta Informatica 49 (3) 117137.CrossRefGoogle Scholar
Ljungqvist, L. and Sargent, T. J. (2004). Recursive Macroeconomic Theory, 2nd edition, MIT Press.Google Scholar
Moss, L. (1999). Coalgebraic logic. Annals of Pure and Applied Logic 96 (1) 277317.CrossRefGoogle Scholar
Moss, L. S. and Viglizzo, I. D. (2004). Harsanyi type spaces and final coalgebras constructed from satisfied theories. Electronic Notes in Theoretical Computer Science 106 279295.CrossRefGoogle Scholar
Rößiger, M. (2000). Coalgebras and modal logic. Electronic Notes in Theoretical Computer Science 33 294315.CrossRefGoogle Scholar
Rutten, J. (2000). Universal coalgebra: A theory of systems. Theoretical Computer Science 249 (1) 380.CrossRefGoogle Scholar
Shubik, M. (1971). The dollar auction game: A paradox in noncooperative behavior and escalation. Journal of Conflict Resolution 109–111.CrossRefGoogle Scholar
Tarski, A. (1955). A lattice-theoretical fixpoint theorem and its applications. Pacific Journal of Mathematics 5 (2) 285309.CrossRefGoogle Scholar