Emergence of Long Run Behaviours in a Game Theoretic Setting with Host and Guest Populations : Residents and Tourists

In this paper we model tourism in the framework of multi-population dynamics and analyze the time pattern of its development through the evolving interaction between two populations feeding on a common space-resource. Each population might be structured in two (or more) "clubs" of members sharing social and economic interests as to the management of the relevant resource. Such situation will be modeled by a version of the well known replicator dynamics. The strategies are characterized as environmentalist and not environmentalist behaviors of residents and tourist. We show that the properties of an environmentalist behavior as stable strategy, Nash equilibrium and dynamic replicator solution