Game-theoretic learning and allocations in robust dynamic coalitional games

M. Smyrnakis, D. Bauso, H. Tembine

Research output: Contribution to journalArticlepeer-review

Abstract

The problem of allocation in coalitional games with noisy observations and dynamic environments is considered. The evolution of the excess is modeled by a stochastic differential inclusion involving both deterministic and stochastic uncertainties. The main contribution is a set of linear matrix inequality conditions which guarantee that the distance of any solution of the stochastic differential inclusions from a predefined target set is second-moment bounded. As a direct consequence of the above result we derive stronger conditions still in the form of linear matrix inequalities to hold in the entire state space, which guarantee second-moment boundedness. Another consequence of the main result is conditions for convergence almost surely to the target set, when the Brownian motion vanishes in proximity of the set. As a further result we prove convergence conditions to the target set of any solution to the stochastic differential equation if the stochastic disturbance has bounded support. We illustrate the results on a simulated intelligent mobility scenario involving a transport network.

Original languageEnglish (US)
Pages (from-to)2902-2923
Number of pages22
JournalSIAM Journal on Control and Optimization
Volume57
Issue number4
DOIs
StatePublished - 2019

Keywords

  • Differential inclusions
  • Intelligent mobility network
  • Robust dynamic coalitional games
  • Second-moment stability
  • Stable core

ASJC Scopus subject areas

  • Control and Optimization
  • Applied Mathematics

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