Stationary Cost Nodes in Infinite Horizon LQG-GMFGs
Rinel Foguen Tchuendom, Shuang Gao, and Peter E. Caines
TL;DR
This paper analyzes infinite horizon LQG mean field games on dense infinite graphs, deriving explicit Nash values and revealing that nodes with maximal network degree tend to have minimal costs at equilibrium.
Contribution
It provides analytical expressions for Nash values in infinite horizon LQG-GMFGs and links network degree to cost minimization at equilibrium.
Findings
Explicit formulas for Nash values at nodes.
Nodes with highest degree have lowest costs.
Results apply to dense infinite graphs.
Abstract
An analysis of infinite horizon linear quadratic Gaussian (LQG) Mean Field Games is given within the general framework of Graphon Mean Field Games (GMFG) on dense infinite graphs (or networks) introduced in Caines and Huang (2018). For a class of LQG-GMFGs, analytical expressions are derived for the infinite horizon Nash values at the nodes of the infinite graph. Furthermore, under specific conditions on the network and the initial population means, it is shown that the nodes with strict local maximal infinite network degree are also nodes with strict local minimal cost at equilibrium.
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Taxonomy
TopicsGame Theory and Applications · Economic theories and models · Stochastic processes and financial applications