### January 27, 2020

**Pierre Ohlmann**(IRIF)

Bertrand et al. (2017) introduced a model of parameterised

systems, where each agent is represented by a finite state system, and

studied the following control problem: for any number of agents, does

there exist a controller able to bring all agents to a target state? They

showed that the problem is decidable and EXPTIME-complete in the

adversarial setting, and posed as an open problem the stochastic setting,

where the agent is represented by a Markov decision process. In this

paper, we show that the stochastic control problem is decidable. Our

solution makes significant uses of well quasi orders, of the max-flow min-

cut theorem, and of the theory of regular cost functions.