Large-scale games in large-scale systems

Details Large-scale games in large-scale systems Large-scale games in large-scale systems

2011-11-09

arxiv.org/abs/1111.2285v3

Computer Science

Systems and Control

30 pages. Notes for the tutorial course on mean field stochastic games, March 2011

Scientific paper

Many real-world problems modeled by stochastic games have huge state and/or action spaces, leading to the well-known curse of dimensionality. The complexity of the analysis of large-scale systems is dramatically reduced by exploiting mean field limit and dynamical system viewpoints. Under regularity assumptions and specific time-scaling techniques, the evolution of the mean field limit can be expressed in terms of deterministic or stochastic equation or inclusion (difference or differential). In this paper, we overview recent advances of large-scale games in large-scale systems. We focus in particular on population games, stochastic population games and mean field stochastic games. Considering long-term payoffs, we characterize the mean field systems using Bellman and Kolmogorov forward equations.

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