Game-theoretical model for the sustainable use of thermal water resources: the case of Ischia volcanic Island (Italy)

The Island of Ischia, one of the Italian active volcanoes, is a famous tourist resort for spa treatments. Spas are supplied by withdrawals from groundwaters which are characterized by a wide range of chemical compositions, salinity and temperature. In natural conditions, the hydrogeological system is recharged by rainfall and by deep fluids; the discharge is towards the sea and the springs. During the peak of the tourist season, when approximately 240 wells are operating simultaneously, a significant additional recharge of the aquifers derives from seawater and from upwelling increase in deep fluids. Although this does not compromise the availability of groundwater, the pumping often determines variation in composition and temperature of groundwater over time. Conversely, the maintenance of a stable quality of thermal waters represents one of the requirements for their therapeutic use in the spas. The study aims to establish game-theoretical modeling of the optimal sustainable exploitation of the groundwater resources of the island by competing users (spas) falling in the same flow tube of the aquifer. In the game the spas are the players, the strategy of a player consists of a fixed pumping rate and daily time durations of pumping, and the player’s utility or payoff is proportional to the total quantity of withdrawn thermal water in a given time period. A special constrained Pareto optimal strategy choice is obtained, considered as a cooperative solution of the game. Pareto optimality means that there is no other strategy choice that makes one player better off without making some other player worse off.