Time averages, recurrence and transience in the stochastic replicator dynamics (2009)
Hofbauer, Josef, Imhof, Lorens A.
We investigate the long-run behavior of a stochastic replicator process, which describes game dynamics for a symmetric two-player game under aggregate shocks. We establish an averaging principle that...
H. Peyton Young, Joshua Epstein, Edoardo Gallo, James Heckman, Josef Hofbauer
New ideas, products, and practices take time to diffuse, a fact that is often attributed to some form of heterogeneity among potential adopters. This paper examines three broad classes of diffusion...
Monotone methods for equilibrium selection under perfect foresight dynamics (2008)
Daisuke Oyama; Graduate School Of Economics, Hitotsubashi University, Satoru Takahashi; Department Of Economics, Princeton University, Josef Hofbauer; Department Of Mathematics, University Of Vienna
This paper studies a dynamic adjustment process in a large society of forward-looking agents where payoffs are given by a normal form supermodular game. The stationary states of the dynamics...
Monotone methods for equilibrium selection under perfect foresight dynamics (2008)
Daisuke Oyama; Graduate School Of Economics, Hitotsubashi University, Satoru Takahashi; Department Of Economics, Princeton University, Josef Hofbauer; Department Of Mathematics, University Of Vienna
[This item is a preserved copy. To view the original, visit http://econtheory.org/] This paper studies a dynamic adjustment process in a large society of forward-looking agents where payoffs are...
Time Average Replicator and Best Reply Dynamics (2008)
Hofbauer, Josef, Sorin, Sylvain, Viossat, Yannick
Using an explicit representation in terms of the logit map we show, in a unilateral framework, that the time average of the replicator dynamics is a perturbed solution of the best reply dynamics.
Time Average Replicator and Best Reply Dynamics (2008)
Hofbauer, Josef, Sorin, Sylvain, Viossat, Yannick
Using an explicit representation in terms of the logit map we show, in a unilateral framework, that the time average of the replicator dynamics is a perturbed solution of the best reply dynamics.
Stable Population Games and Integrability for Evolutionary Dynamics ∗ (2008)
We introduce a new class of population games called stable games. These games are characterized by self-defeating externalities: when agents revise their strategies, the improvements in the payoffs...
Ulf Dieckmann, Christoph Hauert, Christoph Hauert, Silvia De Monte, Silvia De Monte, Josef Hofbauer, ...
Interim Reports on work of the International Institute for Applied Systems Analysis receive only limited review. Views or opinions expressed herein do not necessarily represent those of the...
Survival of dominated strategies under evolutionary dynamics (2006)
Josef Hofbauer, William H. Sandholm
We show that any evolutionary dynamic that satisfies three mild requirements— continuity, positive correlation, and innovation—does not eliminate strictly dominated strategies in all games....
Stochastic Approximations and Differential Inclusions; Part II: Applications (2005)
Benaïm, Michel, Hofbauer, Josef, Sorin, Sylvain
Nous appliquons les résultats théoriques sur l'approximation stochastique et les inclusions differentielles développés dans Benaïm Hofbauer and Sorin (2003) à différentes procédures...
Stochastic Approximations and Differential Inclusions; Part II: Applications (2005)
Benaïm, Michel, Hofbauer, Josef, Sorin, Sylvain
Nous appliquons les résultats théoriques sur l'approximation stochastique et les inclusions differentielles développés dans Benaïm Hofbauer and Sorin (2003) à différentes procédures...
Brown-von Neumann-Nash Dynamics: The Continuous Strategy Case ∗ (2005)
Josef Hofbauer, Frank Riedel, Jörg Oechssler
In John Nash’s proofs for the existence of (Nash) equilibria based on Brouwer’s theorem, an iteration mapping is used. A continuous— time analogue of the same mapping has been studied even...
Monotone Methods for Equilibrium Selection under Perfect Foresight Dynamics (2003)
Oyama, Daisuke, Takahashi, Satoru, Hofbauer, Josef
This paper studies a dynamic adjustment process in a large society of forward-looking agents where payoffs are given by a normal form supermodular game. The stationary states of the dynamics...
Stochastic Approximations and Differential Inclusions (2003)
Benaïm, Michel, Hofbauer, Josef, Sorin, Sylvain
L'approche en termes de systèmes dynamiques de l'approximation stochastique est étendue au cas ou l'équation différentielle moyenne est remplacée par une inclusion différentielle. Le théorème...
Stochastic Approximations and Differential Inclusions (2003)
Benaïm, Michel, Hofbauer, Josef, Sorin, Sylvain
L'approche en termes de systèmes dynamiques de l'approximation stochastique est étendue au cas ou l'équation différentielle moyenne est remplacée par une inclusion différentielle. Le théorème...
Evolutionary game dynamics (2003)
Josef Hofbauer, Karl Sigmund, William D. Hamilton, John Maynard, Smith The
Abstract. Evolutionary game dynamics is the application of population dynamical methods to game theory. It has been introduced by evolutionary biologists, anticipated in part by classical game...
Sophisticated Imitation in Cyclic Games (2000)
SCHLAG, Karl H., HOFBAUER, Josef
Individuals belonging to two large populations are repeatedly randomly matched to play a cyclic $2\times 2$ game such as Matching Pennies. Between matching rounds, individuals sometimes change their...
Sophisticated Imitation in Cyclic Games (2000)
SCHLAG, Karl H., HOFBAUER, Josef
Individuals belonging to two large populations are repeatedly randomly matched to play a cyclic $2\times 2$ game such as Matching Pennies. Between matching rounds, individuals sometimes change their...
Diagonal Dominance and Harmless Off-Diagonal Delays (2000)
. Systems of linear differential equations with constant coefficients, as well as Lotka--Volterra equations, with delays in the off--diagonal terms are considered. Such systems are shown to be...
Dass. Ausz. 6 S. 8
Brown-von Neumann-Nash Dynamics: The Continuous Strategy Case
Hofbauer, Josef, Oechssler, Jörg, Riedel, Frank
In John Nash’s proofs for the existence of (Nash) equilibria based on Brouwer’s theorem, an iteration mapping is used. A continuous— time analogue of the same mapping has been studied even...
Ross Cressman, Josef Hofbauer, Frank Riedel
The replicator equation model for the evolution of individual behaviors in a single-species with a multi-dimensional continuous trait space is developed as a dynamics on the set of probability...
Evolution and Learning in Games with Randomly Disturbed Payoffs
Josef Hofbauer, William H. Sandholm
We consider four models of evolution and learning in games which rely on perturbations of payoffs, including stochastic fictitious play. In all cases, we establish global stability results for...
Monotone Methods for Equilibrium Selection under Perfect Foresight Dynamics
Deisuke Oyama, Satoru Takahashi, Josef Hofbauer
This paper studies equilibrium selection in supermodular games based on perfect foresight dynamics. A normal form game is played repeatedly in a large society of rational agents. There are frictions:...
Brown-von Neumann-Nash Dynamics: The Continuous Strategy Case
Josef Hofbauer, Jörg Oechssler, Frank Riedel
In John Nash’s proofs for the existence of (Nash) equilibria based on Brouwer’s theorem, an iteration mapping is used. A continuous—time analogue of the same mapping has been studied even...
Monotone Methods for Equilibrium Selection under Perfect Foresight Dynamics
Oyama, Daisuke, Takahashi, Satoru, Hofbauer, Josef
This paper studies a dynamic adjustment process in a large society of forward-looking agents where payoffs are given by a normal form supermodular game. The stationary states of the dynamics...
Brown-von Neumann-Nash Dynamics: The Continuous Strategy Case
Josef Hofbauer, Jörg Oechssler
In John Nash’s proofs for the existence of (Nash) equilibria based on Brouwer’s theorem, an iteration mapping is used. A continuous- time analogue of the same mapping has been studied even...
Sophisticated Imitation in Cyclic Games
Hofbauer, Josef, Karl H. Schlag
Consider a large population of individuals that are repeatedly randomly matched to play a cyclic 2x2 game such as Matching Pennies with fixed roles assigned in the game. Some learn by sampling...
Monotone methods for equilibrium selection under perfect foresight dynamics
Oyama, Daisuke, Takahashi, Satoru, Hofbauer, Josef
This paper studies a dynamic adjustment process in a large society of forward-looking agents where payoffs are given by a normal form supermodular game. The stationary states of the dynamics...
Monotone Methods for Equilibrium Selection under Perfect Foresight Dynamics
Josef Hofbauer, Daisuke Oyama, Satoru Takahashi
The paper studies equilibrium selection in supermodular games based on a class of perfect foresight dynamics, introduced by Matsui and Matsuyama (JET 1995) and further developed by Hofbauer and...
On the Global Convergence of Stochastic Fictitious Play
Josef Hofbauer, William H. Sandholm
We establish global convergence results for stochastic fictitious play for four classes of games: games with an interior ESS, zero sum games, potential games, and supermodular games. We do so by...
Irrational behavior in the Brown-von Neumann-Nash dynamics
We present a class of games with a pure strategy being strictly dominated by another pure strategy such that the former survives along most solutions of the Brown-von Neumann-Nash dynamics.
Brown-von Neumann-Nash Dynamics: The Continuous Strategy Case
Josef Hofbauer, Joerg Oechssler, Frank Riedel
In John Nash’s proofs for the existence of (Nash) equilibria based on Brouwer’s theorem, an iteration mapping is used. A continuous— time analogue of the same mapping has been studied even...
Learning in Games with Unstable Equilibria
Ed Hopkins, Josef Hofbauer, Michel Benaim
We investigate games whose Nash equilibria are mixed and are unstable under fictitious play-like learning processes. We show that when players learn using weighted stochastic fictitious play and so...
Learning in Perturbed Asymmetric Games
We investigate the stability of mixed strategy equilibria in 2 person (bimatrix) games under perturbed best response dynamics. A mixed equilibrium is asymptotically stable under all such dynamics if...
Stochastic Approximations and Differential Inclusions; Part II: Applications
Michel Benaïm, Josef Hofbauer, Sylvain Sorin
Nous appliquons les résultats théoriques sur l'approximation stochastique et les inclusions differentielles développés dans Benaïm Hofbauer and Sorin (2003) à différentes procédures...
Stochastic Approximations and Differential Inclusions
Michel Benaïm, Josef Hofbauer, Sylvain Sorin
L'approche en termes de systèmes dynamiques de l'approximation stochastique est étendue au cas ou l'équation différentielle moyenne est remplacée par une inclusion différentielle. Le théorème...
Stochastic Approximations and Differential Inclusions; Part II: Applications
Michel Benaïm, Josef Hofbauer, Sylvain Sorin
Nous appliquons les résultats théoriques sur l'approximation stochastique et les inclusions differentielles développés dans Benaïm Hofbauer and Sorin (2003) à différentes procédures...
Stochastic Approximations and Differential Inclusions
Michel Benaïm, Josef Hofbauer, Sylvain Sorin
L'approche en termes de systèmes dynamiques de l'approximation stochastique est étendue au cas ou l'équation différentielle moyenne est remplacée par une inclusion différentielle. Le théorème...
Sophisticated imitation in cyclic games
Josef Hofbauer, Karl H. Schlag
Individuals belonging to two large populations are repeatedly randomly matched to play a cyclic $2\times 2$ game such as Matching Pennies. Between matching rounds, individuals sometimes change their...
Stochastic Approximations and Differential Inclusions; Part II: Applications
Michel Benaïm, Josef Hofbauer, Sylvain Sorin
Nous appliquons les résultats théoriques sur l'approximation stochastique et les inclusions differentielles développés dans Benaïm Hofbauer and Sorin (2003) à différentes procédures...
Stochastic Approximations and Differential Inclusions
Michel Benaïm, Josef Hofbauer, Sylvain Sorin
L'approche en termes de systèmes dynamiques de l'approximation stochastique est étendue au cas ou l'équation différentielle moyenne est remplacée par une inclusion différentielle. Le théorème...
Time Average Replicator and Best Reply Dynamics
Josef Hofbauer, Sylvain Sorin, Yannick Viossat
Using an explicit representation in terms of the logit map we show, in a unilateral framework, that the time average of the replicator dynamics is a perturbed solution of the best reply dynamics.
Learning in games with unstable equilibria
Benaïm, Michel, Hofbauer, Josef, Hopkins, Ed
We propose a new concept for the analysis of games, the TASP, which gives a precise prediction about non-equilibrium play in games whose Nash equilibria are mixed and are unstable under fictitious...
Stable games and their dynamics
Hofbauer, Josef, Sandholm, William H.
We study a class of population games called stable games. These games are characterized by self-defeating externalities: when agents revise their strategies, the improvements in the payoffs of...