MB5 - Théorie des jeux / Game theory 2

Synchronization, a fundamental problem in multi-agent systems, is modeled as a large-population stochastic game on a network in this presentation. The framework of Graphon Mean Field Game yields two computationally tractable coupled equations that characterize the oscillators’ state distribution and optimal control, thereby revealing how network structure shapes synchronization.

Airline alliances shape global aviation competition, yet their effects on market efficiency remain poorly understood. This talk presents a data-driven optimization framework to redesign alliance memberships, simultaneously improving route-level competition and airlines' ability to expand into new markets. Applied to real-world flight schedule data, the approach outperforms existing alliance structures on both dimensions.

Effective pharmaceutical waste management is critical for public health and sustainability, yet reverse supply chains face trust and uncertainty challenges. This study develops a differential game model to evaluate blockchain-enabled traceability under extended producer responsibility. Results show reduced uncertainty, improved inspection accuracy, and enhanced goodwill, strengthening economic and environmental performance.

This paper addresses the decentralized coordinated charging problem for a large population of battery storage agents (e.g. residential batteries, electrical vehicles, charging station batteries) using Mean Field Game (MFG). Agents are assumed to have affine dynamics and are coupled through a price that
is continuous and monotonically increasing with respect to the difference between the average charging power and the grid’s desired average charging power. An important modeling feature of the proposed framework is the state augmentation, that is, the charging power is treated as a state variable and its rate of change (i.e. the ramp rate) as the control input. The resulting MFG equilibrium is characterized by two nonlinearly coupled forward-backward differential equations. The existence and uniqueness of the MFG equilibrium is established for any continuous and monotonically increasing nonlinear price function without additional restrictions on the time horizon. Moreover, in the special case where the price is affine in the average charging power, we further simplify the characterization
of the MFG equilibrium strategy via two separate Riccati equations, both of which admit unique positive semi-definite solutions without additional assumptions.