Game Theory and Control

Plants made of interacting parts with conflicting interests require game-theoretic modeling tools.

Players - independent decision makers

Actions - available decisions

Payoff - resulting outcome for each player, dependent on other players as well!

The outcome for both cars depends on both cars' simultaneous decisions.

What's their "best" decision?

Nash Equilibrium

No player can unilaterally improve their outcome

Things become more complicated when decisions are taken sequentially.

Stackelberg Equilibrium

Leader: chooses first - Follower: responds

From performance...

(H2 norm, settling time, bandwidth, MPC,...)

... to equilibrium, efficiency, and fairness

Traffic congestion

Traffic would be optimized if we allow urgent users to use a fast lane.

How to choose them?

(you can't let them decide...)

Tolls?

Karma!

You can try it at https://www.elokda.info/karma

Energy Market

Various issues give raise to all type of games

Stackelberg games

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Source: MAESTRO

Games (even Stackelberg) should be fun!

Taking a role of the Leader you

have to learn your Followers' needs and how to guide them

Check the projects on SIROP!

Games (even Stackelberg) should be fun!

Or you could do the opposite,

and try to become as ungovernable as possible!

Check the projects on SIROP and send email to ishilov@ethz.ch if you're interested!

Receding Horizon Games

Model Predictive Control + Game Theory

Playing a game coupled in cost, dynamics and constraints in receding horizon.

Lots of interesting applications:

(i) Energy, (ii) Autonomous driving,

(iii) Drone coordination, (iv) Network routing ....

Many open theoretical questions:

(i) Stability using terminal ingredients,

(iii) Recursive feasibility,

(iv) Transient performance bounds and more...

Send an email to shall@ethz.ch if you are interested in working on any of these questions!

Receding Horizon Games

For fair and sustainable ground water management

Who gets how much water?

When, why and at what price?

Manage water distribution automatically using game-theoretic MPC.

Ensure the controller works with the physical system dynamics & constraints while respecting the self-interested nature of agents.

We have detailed models, data, a well developed code base and lots of interesting theoretical & fairness questions!

Check the project on Sirop.