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Differential games of common resources that are governed by linear accumulation constraints have several applications. Examples include political rent-seeking groups expropriating public infrastructure, oligopolies expropriating common resources, industries using specific common infrastructure or equipment, capital-flight problems, pollution, etc. Most of the theoretical literature employs specific parametric examples of utility functions. For symmetric differential games with linear constraints and a general time-separable utility function depending only on the player’s control variable, we provide an exact formula for interior symmetric Markovian-strategies. This exact solution, (a) serves as a guide for obtaining some new closed-form solutions and for characterizing multiple equilibria, and (b) implies that, if the utility function is an analytic function, then the Markovian strategies are analytic functions, too. This analyticity property facilitates the numerical computation of interior solutions of such games using polynomial projection methods and gives potential to computing modified game versions with corner solutions by employing a homotopy approach.
We develop a dynamic recursive model where political and economic decisions interact, to study how excessive debt-GDP ratios affect political sustainability of prudent fiscal policies. Rent seeking groups make political decisions – to cooperate (or not) – on the allocation of fiscal budgets (including rents) and issuance of sovereign debt. A classic commons problem triggers collective fiscal impatience and excessive debt issuing, leading to a vicious circle of high borrowing costs and sovereign default. We analytically characterize debt-GDP thresholds that foster cooperation among rent seeking groups and avoid default. Our analysis and application helps in understanding the politico-economic sustainability of sovereign rescues, emphasizing the need for fiscal targets and possible debt haircuts. We provide a calibrated example that quantifies the threshold debt-GDP ratio at 137%, remarkably close to the target set for private sector involvement in the case of Greece.