Dynamic games and competition for water resources

Individuals, cities, and nations compete for limited resources in many areas of the world. The social costs generated by competition include the over-exploitation of renewable resources and the depletion of non-renewable resources. This dissertation examines the problem of competition for limited resources in a game-theoretic framework. The goal is to gain insight regarding how economic agents choose strategies and programs regarding resources, so that we may design public policies that will motivate individuals, firms, and nations to generate greater values with limited resources. This dissertation demonstrates how to estimate those gains using game theory models involving Nash bargaining solutions and Markov perfect equilibria. Empirical versions of the models are solved using dynamic programming and numerical methods. In Manuscript One, a Nash bargaining model is applied to the problem of competition for limited water resources along the Rio Grande in southwestern Texas. Two cities, El Paso, Texas and Ciudad Juarez in Chihuahua, Mexico, withdraw water for municipal and industrial uses from the Hueco Bolson aquifer that lies beneath the international border. This empirical application of a bargaining model provides insight regarding the potential gains from cooperation regarding water resource management in the region. Finding solutions to dynamic, economic problems can require sophisticated mathematical tools, particularly when working with stochastic systems and when seeking solutions with desirable properties, such as subgame perfection. Two methods that can be used to solve non-cooperative dynamic game theory models are described in Manuscript Two: Ricatti equation methods and collocation. Either approach can be used to obtain Markov perfect equilibrium solutions to dynamic problems. Each has advantages and disadvantages. In Manuscript Three, numerical methods are used to solve non-cooperative dynamic game theory models involving the depletion of a non-renewable resource and the optimal rate of investment in a backstop technology. Desalination is chosen as the example of a backstop technology, given its importance in arid regions where water resources are not sufficient to support increasing populations, such as the Middle East, northern Africa, and portions of the American southwest. Optimal investment policies and the impact of subsidies that encourage faster investment are examined