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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 build a search-and-matching algorithm of network dynamics with decision-making under incomplete information, seeking to understand the determinants of the observed gradual downgrading of expert opinion on complicated issues and the decreasing trust in science. Even without fake news, combining the internet’s ease of forming networks with (a) individual biases, such as confirmation bias or assimilation bias, and (b) people’s tendency to align their actions with those of peers, produces populist and polarization network dynamics. Homophily leads to actions with more weight on biases and less weight on expert opinion, and such actions lead to more homophily.