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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rate and daily time durations of pumping, and the player's utility or payoff is proportional to the total quantity of withdrawn thermal water in a given time period.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.While much of the scholarly wor
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