On the robustness of learning in games with stochastically perturbed payoff observations

Motivated by the scarcity of accurate payoff feedback in practical applications of game theory, we examine a class of learning dynamics where players adjust their choices based on past payoff observations that are subject to noise and random disturbances. First, in the single-player case (corresponding to an agent trying to adapt to an arbitrarily changing environment), we show that the stochastic dynamics under study lead to no regret almost surely, irrespective of the noise level in the player's observations. In the multi-player case, we find that dominated strategies become extinct and we show that strict Nash equilibria are stochastically stable and attracting; conversely, if a state is stable or attracting with positive probability, then it is a Nash equilibrium. Finally, we provide an averaging principle for 2-player games, and we show that in zero-sum games with an interior equilibrium, time averages converge to Nash equilibrium for any noise level.Comment: 36 pages, 4 figure

Economic Games as Estimators

Discrete event games are discrete time dynamical systems whose state transitions are discrete events caused by actions taken by agents within the game. The agents’ objectives and associated decision rules need not be known to the game designer in order to impose struc- ture on a game’s reachable states. Mechanism design for discrete event games is accomplished by declaring desirable invariant properties and restricting the state transition functions to conserve these properties at every point in time for all admissible actions and for all agents, using techniques familiar from state-feedback control theory. Building upon these connections to control theory, a framework is developed to equip these games with estimation properties of signals which are private to the agents playing the game. Token bonding curves are presented as discrete event games and numerical experiments are used to investigate their signal processing properties with a focus on input-output response dynamics.Series: Working Paper Series / Institute for Cryptoeconomics / Interdisciplinary Researc

Evolutionary dynamics in heterogeneous populations: a general framework for an arbitrary type distribution

A general framework of evolutionary dynamics under heterogeneous populations is presented. The framework allows continuously many types of heterogeneous agents, heterogeneity both in payoff functions and in revision protocols and the entire joint distribution of strategies and types to influence the payoffs of agents. We clarify regularity conditions for the unique existence of a solution trajectory and for the existence of equilibrium. We confirm that equilibrium stationarity in general and equilibrium stability in potential games are extended from the homogeneous setting to the heterogeneous setting. In particular, a wide class of admissible dynamics share the same set of locally stable equilibria in a potential game through local maximization of the potential

Mean-Field-Type Games in Engineering

A mean-field-type game is a game in which the instantaneous payoffs and/or the state dynamics functions involve not only the state and the action profile but also the joint distributions of state-action pairs. This article presents some engineering applications of mean-field-type games including road traffic networks, multi-level building evacuation, millimeter wave wireless communications, distributed power networks, virus spread over networks, virtual machine resource management in cloud networks, synchronization of oscillators, energy-efficient buildings, online meeting and mobile crowdsensing.Comment: 84 pages, 24 figures, 183 references. to appear in AIMS 201