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Global games are a class of incomplete information games where the payoffsexhibit strategic complementarity leading to an incentive for the agents tocoordinate their actions. Such games have been used to model scenarios in manysocioeconomic phenomena, where the private signals available to the agents aretypically assumed to be Gaussian. We study an instance of a global game wherethe agents observe Poisson random variables, which are inspired by applicationsin microbiology where information signals are disseminated via discretemolecular signals rather than continuous. Although this observation modelviolates the essential technical assumptions present in the Gaussian case, wepresent preliminary results on the existence of Bayesian Nash equilibria inpure threshold policies in two variants of the underlying randomstate-of-the-world: an arbitrarily distributed discrete binary state and acontinuous state with uniform distribution.

Global games with Poisson observations: Bio-inspired distributed coordination of multi-agent systems