Game-theoretic learning and allocations in robust dynamic coalitional games

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.