A Nash Equilibrium for Differential Games with Moving-Horizon Strategies

Greenhouse gases mitigation: global externalities and short-termism

“…12 Formal definitions of the N-player equilibrium consistent with model predictive control are provided by Van den Broek (2002) and Saltari et al (2021). The former focuses on the LQ case, the latter generalizes the concept to non-linear model predictive control.…”

“…13 In each of instant of time the solution of (3) involve the search of a fixed point, where optimal strategies are mutually consistent. For a formal description, see Van den Broek (2002) or Saltari et al (2021).…”

“…As expected, the non-cooperative equilibrium (Scenario 1) leads to a higher level of CO2 concentration compared with the cooperative policy (Scenario 2). In the beginning, there is not a great 19 Specifically, to solve the game we used the algorithm described in Saltari et al (2021) based on the codes developed by Grüne and Pannek (2017) and illustrated in Grüne et al (2015). difference in CO2 concentration for two policies, but after 2039 we can observe a notable increase in its level under non-cooperative scenario, which eventually will reach 1456 ppm (5.2 as a normalized form) in 2100.…”

“…Instead, we directly formalized the policy horizon by introducing model predictive control techniques. We are thus indebted to some studies that adapt model predictive control methodology to strategic interactions, focusing on public debt dynamics ( Van den Broek, 2002;Saltari et al, 2021). We borrow the concept of policy equilibrium from the latter 9 and interpret it along the lines of Di Bartolomeo et al (2018) by using a traditional public choice view.…”

“…For an example of a compact integrated assessment model that integrates the global economy and the climate in a unified framework, seeHassler et al (2016).8 The relevance of considering strategic interactions in analyzing climate issues has a long tradition. See, among others,Barrett (2003),Kemfert et al (2004),Finus (2008),Nkuiya (2015), orAcocella and Di Bartolomeo (2019).9Van den Broek (2002) focuses on the linear-quadratic case (providing a detailed analysis of the approach properties, e.g., uniqueness and convergence), whileSaltari et al (2021) generalize the approach to further non-linear cases and provide a solution algorithm.…”