Invited Session Mon.2.MA 043

Monday, 13:15 - 14:45 h, Room: MA 043

Cluster 8: Game theory [...]

Large games and networks: Control and approachability


Chair: Dario Bauso



Monday, 13:15 - 13:40 h, Room: MA 043, Talk 1

Giacomo Como
Stability analysis of transportation networks with multiscale driver decisions

Coauthors: Daron Acemoglu, Munther A. Dahleh, Emilio Frazzoli, Ketan Savla


Stability of Wardrop equilibria is analyzed for dynamical transportation networks in which the drivers' route choices are influenced by information at multiple temporal and spatial scales. The considered model involves a continuum of drivers commuting between a common origin/destination pair in an acyclic transportation network. The drivers' route choices are affected by their, relatively infrequent, perturbed best responses to global information about the current network congestion levels, as well as their instantaneous local observation of the immediate surroundings as they transit through the network. A novel model is proposed for the drivers' route choice behavior, exhibiting local consistency with their preference toward globally less congested paths as well as myopic decisions in favor of locally less congested paths. The main result shows that, if the frequency of updates of path preferences is sufficiently small as compared to the frequency of the traffic flow dynamics, then the state of the transportation network ultimately approaches a neighborhood of the Wardrop equilibrium. The presented results may be read as a further evidence in support of Wardrop's postulate of equilibrium.



Monday, 13:45 - 14:10 h, Room: MA 043, Talk 2

Dario Bauso
Time-averaged consensus and distributed approachability in large multi-agent networks

Coauthors: Giuseppe Notarstefano, Raffaele Pesenti


We consider a doubly (over time and space) distributed averaging algorithm in a large multi-agent network. At every iteration, each single agent first computes a weighted average of its own time-averaged estimate and those of his neighbors and then generates a new estimate in order to drive the time-averaged estimate towards a pre-assigned set. The main contribution of the paper is to prove that under certain assumptions, i) all agents reach consensus on time-averaged estimates, and ii) the estimates approach the pre-assigned set. Conditions for this to happen are related to the connectivity over time of the communication topology and to the approachability principle. Motivations arise in the context of repeated coalitional games with transferable utilities (TU). Here, the algorithm represents a distributed allocation process converging to the core of the game in the limit.



Monday, 14:15 - 14:40 h, Room: MA 043, Talk 3

Roland Malhame
Nash equilibria in radial communication networks via mean field game theory

Coauthors: Peter Caine, Zhongjing Malhame


Mean Field Game theory is developed and applied in
this paper to call admission control in a point process model of
communication networks. In general the MFG methodology establishes the
of approximate Nash equilibria for large populations of agents which
employ only local feedback and precomputed
solutions to the Mean Field equations. In this paper dynamic
communication network are modelled by highly symmetric radial loss
networks driven by Poisson call request point processes subject to
decentralized admission control. A key concept introduced in the analysis
in this paper is that of the so-called network decentralized state (NDS)
which is a state induced asymptotically (in population size) in a given
network under any (randomized) local admission control law when it is
common to all agents. Under appropriate assumptions, an analysis of
networks in an NDS establishes the existence of Nash equilibria which
are achieved for all sufficiently large populations. Computational
illustrations of the methodology are included.


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