Upper Expected Meeting Times for Interdependent Stochastic Agents

Thomas Krak, Marco Sangalli, Erik Quaeghebeur

Abstract:

We analyse the problem of meeting times for interdependent
stochastic agents: random walkers whose behaviour is stochastic
but controlled by their selections from some set of allowed actions, and
the inference problem of when these agents are all in the same state for
the first time. We consider the case where we are epistemically uncertain
about the selected actions of these agents, and show how their behaviour
can be modelled using imprecise Markov chains. This allows us to use
results and algorithms from the literature, to exactly compute bounds
on their meeting time, which are tight with respect to our epistemic uncertainty
models. After focussing on the two-agent case, we analyse and
discuss how it can be extended to an arbitrary number of agents, and
how the corresponding combinatorial explosion can be partly mitigated
by exploiting symmetries inherent in the problem.