Jump Equilibria in Public-Good Differential Games with a Single State Variable

Johannes Schumacher, Puduru Viswanadha Reddy () and Jacob Engwerda
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Puduru Viswanadha Reddy: Indian Institute of Technology – Madras

Dynamic Games and Applications, 2022, vol. 12, issue 3, No 3, 784-812

Abstract: Abstract A simple sufficient condition is proved for symmetric Markov subgame perfect Nash equilibria in public-good differential games with a single state variable. The condition admits equilibria in feedback strategies that have discontinuous dependence on the state variable. The application of the condition is demonstrated in the Dockner–Long model for international pollution control. The existence is shown of equilibria that are arbitrarily close to Pareto dominance for all initial conditions. In the limit as the discount rate tends to 0, the equilibrium strategies differ from the optimal strategies under full coordination, but nevertheless the agents’ payoffs do converge to those obtained from the coordinated (first-best) solution. For positive values of the discount rate, the supremal value function associated with the globally Pareto dominant equilibrium is a continuously differentiable function that is not a solution of the Hamilton–Jacobi–Bellman equation.

Keywords: Public-good games; Jump equilibria; International pollution control; Discontinuous feedback (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s13235-021-00415-x

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