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Logit Dynamics [Blume, Games and Economic Behavior, 1993] are randomized best response dynamics for strategic games: at every time step a player is selected uniformly at random and she chooses a new strategy according to a probability…
We present the first general bounds on the mixing time of the Markov chain associated to the logit dynamics for wide classes of strategic games. The logit dynamics with inverse noise beta describes the behavior of a complex system whose…
Logit choice dynamics are a family of randomized best response dynamics based on the logit choice function [McFadden, 1974], used for modeling players with limited rationality and knowledge. In this paper we study the all-logit dynamics,…
We present a new family of logit-Q dynamics for efficient learning in stochastic games by combining the log-linear learning (also known as logit dynamics) for the repeated play of normal-form games with Q-learning for unknown Markov…
One of the main criticisms to game theory concerns the assumption of full rationality. Logit dynamics is a decentralized algorithm in which a level of irrationality (a.k.a. "noise") is introduced in players' behavior. In this context, the…
Logit dynamics is a form of randomized game dynamics where players have a bias towards strategic deviations that give a higher improvement in cost. It is used extensively in practice. In congestion (or potential) games, the dynamics…
Animal behavior and evolution can often be described by game-theoretic models. Although in many situations, the number of players is very large, their strategic interactions are usually decomposed into a sum of two-player games. Only…
Logit dynamics are dynamical systems describing transitions and equilibria of actions of interacting players under uncertainty. An uncertainty is embodied in logit dynamic as a softmax type function often called a logit function originating…
The paper presents a model of two-speed evolution in which the payoffs in the population game (or, alternatively, the individual preferences) slowly adjust to changes in the aggregate behavior of the population. The model investigates how,…
We present new learning dynamics combining (independent) log-linear learning and value iteration for stochastic games within the auxiliary stage game framework. The dynamics presented provably attain the efficient equilibrium (also known as…
We present new learning dynamics combining (independent) log-linear learning and value iteration for stochastic games within the auxiliary stage game framework. The dynamics presented provably attain the efficient equilibrium (also known as…
A common assumption employed in most previous works on evolutionary game dynamics is that every individual player has full knowledge about and full access to the complete set of available strategies. In realistic social, economical, and…
One of the proposed solutions to the equilibrium selection problem for agents learning in repeated games is obtained via the notion of stochastic stability. Learning algorithms are perturbed so that the Markov chain underlying the learning…
Individual cooperative strategy influences the surrounding dynamic population, which in turn affects cooperative strategy. To better model this phenomenon, we develop a Markov decision chain based game transitions model and examine the…
Game-theoretic solution concepts, such as the Nash equilibrium, have been key to finding stable joint actions in multi-player games. However, it has been shown that the dynamics of agents' interactions, even in simple two-player games with…
Understanding the strategic behavior of miners in a blockchain is of great importance for its proper operation. A common model for mining games considers an infinite time horizon, with players optimizing asymptotic average objectives.…
Mean field games formalize dynamic games with a continuum of players and explicit interaction where the players can have heterogeneous states. As they additionally yield approximate equilibria of corresponding $N$-player games, they are of…
Without mutation and migration, evolutionary dynamics ultimately leads to the extinction of all but one species. Such fixation processes are well understood and can be characterized analytically with methods from statistical physics.…
Various social contexts ranging from public goods provision to information collection can be depicted as games of strategic interactions, where a player's well-being depends on her own action as well as on the actions taken by her…
We study linear quadratic dynamic games where players are uncertain about each other's control policies or goals and consequently seek to be strategically robust. Building on recent work on strategically robust and risk-averse game theory,…