Network Formation with Adaptive Agents

In this paper, a reinforcement learning version of the connections game first analysed by Jackson and Wolinsky is presented and compared with benchmark results of fully informed and rational players. Using an agent-based simulation approach, the main nding is that the pattern of reinforcement learning process is similar, but does not fully converge to the benchmark results. Before these optimal results can be discovered in a learning process, agents often get locked in a state of random switching or early lock-in.agent-based computational economics; strategic network formation; network games; reinforcement learning

Distributed stochastic optimization via matrix exponential learning

In this paper, we investigate a distributed learning scheme for a broad class of stochastic optimization problems and games that arise in signal processing and wireless communications. The proposed algorithm relies on the method of matrix exponential learning (MXL) and only requires locally computable gradient observations that are possibly imperfect and/or obsolete. To analyze it, we introduce the notion of a stable Nash equilibrium and we show that the algorithm is globally convergent to such equilibria - or locally convergent when an equilibrium is only locally stable. We also derive an explicit linear bound for the algorithm's convergence speed, which remains valid under measurement errors and uncertainty of arbitrarily high variance. To validate our theoretical analysis, we test the algorithm in realistic multi-carrier/multiple-antenna wireless scenarios where several users seek to maximize their energy efficiency. Our results show that learning allows users to attain a net increase between 100% and 500% in energy efficiency, even under very high uncertainty.Comment: 31 pages, 3 figure

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 and only if the game is linearly equivalent to a zero sum game. In this case, the mixed equilibrium is also globally asymptotically stable. Global convergence to the set of perturbed equilibria is shown also for (rescaled) partnership games (also know as games of identical interest). Some applications of these result to stochastic learning models are given.Games, Learning, Best Response Dynamics, Stochastic Fictitious Play, Mixed Strategy Equilibria, Zero Sum Games