What is it about?

We consider games for networked systems, where the players act through boundary control action at the boundary nodes of the network graph. We show that for a star-shaped graph a unique Nash equilibrium exists for quadratic objective functions.

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Why is it important?

In gas pipeline network, the players act as customers or gas suppliers through the boundary of the network where they act on the states at the input nodes and the output nodes. The TSO has the task to assign feasible set (booking capacities) to the players in such a way that the operation of the system remains stable. Models from game theory help to understand the situation.

Perspectives

In mean field games, distributed pde-dynamics are involved. Here we consider networked systems where pdes govern the dynamics on a given graph. The players influence the system state through the boundary nodes of the graph. This type of system is motivated by the application to gas pipeline networks, but can also be applied to other situations where the system state is defined on a graph.

Martin Gugat
Friedrich-Alexander-Universitat Erlangen-Nurnberg

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This page is a summary of: Dynamic boundary control games with networks of strings, ESAIM Control Optimisation and Calculus of Variations, October 2018, EDP Sciences, DOI: 10.1051/cocv/2017082.
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