Parrondo's paradox.
Berresford, Geoffrey C., Rockett, Andrew M. (2003)
International Journal of Mathematics and Mathematical Sciences
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Berresford, Geoffrey C., Rockett, Andrew M. (2003)
International Journal of Mathematics and Mathematical Sciences
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R.S. Simon, S. Spiez, H. Torunczyk (2008)
RACSAM
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We survey results related to the problem of the existence of equilibria in some classes of infinitely repeated two-person games of incomplete information on one side, first considered by Aumann, Maschler and Stearns. We generalize this setting to a broader one of principal-agent problems. We also discuss topological results needed, presenting them dually (using cohomology in place of homology) and more systematically than in our earlier papers.
Hugo Steinhaus (1949)
Colloquium Mathematicum
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Jean-Michel Coulomb (1997)
ESAIM: Probability and Statistics
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Julio Clempner (2006)
International Journal of Applied Mathematics and Computer Science
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In this paper we introduce a new modeling paradigm for shortest path games representation with Petri nets. Whereas previous works have restricted attention to tracking the net using Bellman's equation as a utility function, this work uses a Lyapunov-like function. In this sense, we change the traditional cost function by a trajectory-tracking function which is also an optimal cost-to-target function. This makes a significant difference in the conceptualization of the problem domain,...
Tomasz Bielecki (1997)
Applicationes Mathematicae
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The purpose of this paper is to prove existence of an ε -equilib- rium point in a dynamic Nash game with Borel state space and long-run time average cost criteria for the players. The idea of the proof is first to convert the initial game with ergodic costs to an ``equivalent" game endowed with discounted costs for some appropriately chosen value of the discount factor, and then to approximate the discounted Nash game obtained in the first step with a countable state space game for which...
Krzysztof Krawiec, Wojciech Jaśkowski, Marcin Szubert (2011)
International Journal of Applied Mathematics and Computer Science
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We apply Coevolutionary Temporal Difference Learning (CTDL) to learn small-board Go strategies represented as weighted piece counters. CTDL is a randomized learning technique which interweaves two search processes that operate in the intra-game and inter-game mode. Intra-game learning is driven by gradient-descent Temporal Difference Learning (TDL), a reinforcement learning method that updates the board evaluation function according to differences observed between its values for consecutively...
John E. Walsh, Grace J. Kelleher (1970)
RAIRO - Operations Research - Recherche Opérationnelle
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Pedro Mariano, Luís Correia (2015)
International Journal of Applied Mathematics and Computer Science
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We analyse Give and Take, a multi-stage resource sharing game to be played between two players. The payoff is dependent on the possession of an indivisible and durable resource, and in each stage players may either do nothing or, depending on their roles, give the resource or take it. Despite these simple rules, we show that this game has interesting complex dynamics. Unique to Give and Take is the existence of multiple Pareto optimal profiles that can also be Nash equilibria, and a...
Sylvain Sorin, Cheng Wan (2013)
RAIRO - Operations Research - Recherche Opérationnelle
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This work studies a new strategic game called delegation game. A delegation game is associated to a basic game with a finite number of players where each player has a finite integer weight and her strategy consists in dividing it into several integer parts and assigning each part to one subset of finitely many facilities. In the associated delegation game, a player divides her weight into several integer parts, commits each part to an independent delegate and collects the sum of their...
J. M. Lasry, J. M. Morel, S. Solimini (1989)
Revista Matemática de la Universidad Complutense de Madrid
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We give a formalization of the ?knowledge games? which allows to study their decidability and convergence as a problem of mathematics. Our approach is based on a metalemma analogous to those of Von Neumann and Morgenstern at the beginning of Game Theory. We are led to definitions which characterize the knowledge games as objects is standard set theory. We then study rigorously the most classical knowledge games and, although we also prove that the ?common knowledge? in these games may...