Department of Mathematics and Modelling, Institute of Mathematics and Basic Science, Hungarian University of Agriculture and Life Sciences, Godollo, Hungary.
Department of Ecological and Biological Sciences, Tuscia University, Viterbo, Italy.
Environ Geochem Health. 2022 Jul;44(7):2021-2035. doi: 10.1007/s10653-021-00871-9. Epub 2021 Apr 12.
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rate and daily time durations of pumping, and the player's utility or payoff is proportional to the total quantity of withdrawn thermal water in a given time period.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.
伊斯基亚岛是意大利的活火山之一，是著名的温泉疗养胜地。温泉是从具有广泛化学成分、盐度和温度的地下水中抽取的。在自然条件下，水文地质系统由降雨和深部流体补给；排泄则是朝向大海和泉水。在旅游旺季高峰时，大约有 240 口井同时运行，含水层会有大量额外的海水和深部流体上涌补给。尽管这不会影响地下水的供应，但抽水往往会导致地下水中的成分和温度随时间发生变化。相反，保持温泉水的稳定质量是在温泉中治疗用途的要求之一。本研究旨在通过竞争用户（温泉）在同一含水层流管内建立博弈论模型，以确定该岛地下水资源的最佳可持续开采方案。在博弈中，温泉是参与者，参与者的策略包括固定的抽水率和每日抽水时间，参与者的效用或收益与给定时间段内抽取的总热水量成正比。得到了一种特殊的约束帕累托最优策略选择，被视为博弈的合作解决方案。帕累托最优意味着没有其他策略选择可以使一个参与者受益而不使其他参与者受损。
