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Pricing in Non-cooperative Dynamic Games

Explore incentive theory and mechanism design to coordinate competitive agents in a dynamic environment by shaping utilities through pricing. This study focuses on inducing cooperation in LQ games, quadratic pricing mechanisms, and convex feasibility problems to find revenue-neutral cost modifications for applications such as network security and energy management. Discover the inefficiencies of Nash equilibrium and the benefits of cost redistribution with varying agent preferences. Future work includes applying mechanism design theory to real-world scenarios and relaxing assumptions to enhance problem formulations.

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Pricing in Non-cooperative Dynamic Games

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  1. Pricing in Non-cooperative Dynamic Games Lillian Ratliff, Sam Coogan, Daniel Calderone 20 August 2012

  2. Competitive Collaboration • Incentive theory is used to study problems with socio-economic considerations where agents have private information. • In general, resources are scarce causing competition amongst self interested agents. • Mechanism design is the tool used to coordinate competitive agents. • In a dynamic environment, we aim to design prices to shape utilities of competitive agents for the purpose of coordination in engineering problems.

  3. Competitive Collaboration • Network Security • Efficient Energy Management in Buildings • Controlled Diffusion in Multi-Agent Networks

  4. Outline • Problem Formulation • Convex Program • Applications • Future Work

  5. Inducing Cooperation in LQ Games Selfish Agents Social Planner

  6. Inducing Cooperation in LQ Games Quadratic Pricing Mechanism Problem Statement:

  7. Convex Feasibility Problem to Find Prices

  8. Revenue Neutral Cost Modifications

  9. Applications - Energy Management

  10. Varying Thermal Conductivity Between Zones Less insulation between zones results in higher savings. : player i’s cost with pricing : player i’s portion of the social cost : player i’s cost at Nash Equilibrium given their nominal utility. Inefficiency of Nash Comparing Nash to Pricing Cost Redistribution of Social Cost

  11. Varying Agent Preferences 1 2 3 • Vary Q:R ratios – the team and Nash costs vary depending on the ratio of the comfort cost matrices and the nominal energy cost matrices of the agents. 4 5 6 7 8 9

  12. Future Work • Applying mechanism design theory to real world scenarios such asSutardja Dai Hall. In this formulation, we consider a VAV type HVAC system and a switched linear model of the thermodynamics (in collaboration with Anil Aswani). • Relaxing assumptions of the problem such as: perfect state knowledge (both social planner and selfish agents, i.e. allow for observations of the form ), perfect knowledge of player utilities as well as the linear quadratic assumptions.

  13. References

  14. Minimizing Impact of Non-Local Controls

  15. Constrained Inverse LQR

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