Game-theoretic learning and allocations in robust dynamic coalitional games

The problem of allocation in coalitional games with noisy observations and dynamic4 environments is considered. The evolution of the excess is modelled by a stochastic differential5 inclusion involving both deterministic and stochastic uncertainties. The main contribution is a6 set of linear matrix inequality conditions which guarantee that the distance of any solution of the7 stochastic differential inclusions from a predefined target set is second-moment bounded. As a direct8 consequence of the above result we derive stronger conditions still in the form of linear matrix9 inequalities to hold in the entire state space, which guarantee second-moment boundedness. Another10 consequence of the main result are conditions for convergence almost surely to the target set, when the11 Brownian motion vanishes in proximity of the set. As further result we prove convergence conditions12 to the target set of any solution to the stochastic differential equation if the stochastic disturbance13 has bounded support. We illustrate the results on a simulated intelligent mobility scenario involving14 a transport network.