Dynamic Voluntary Provision of Public Goods: A Generalization

Abstract

In this note we examine if the proposition offered by Fershtman and Nitzan (1991) and Wirl (1996) in the context of a dynamic voluntary provision model with a linear production function can be generalized to a more general CES formulation. By comparing the steady-state stocks of a public good in open-loop and feedback Nash equilibria with that under the cooperative solution, we demonstrate that their ranking among the steady-state stocks is indeed preserved under the CES framework. Copyright � 2009 Wiley Periodicals, Inc..

Mixed Market Structure and R&D: A Differential Game Approach

“…where c(k i ) is the cost of R&D investment k i . Firm i chooses x i to maximize (10). The first-order condition for profit maximization is…”

“…The model that we use in this paper is a variant of the dynamic game of voluntary provision of public goods analyzed by Fershtman and Nitzan (1991), Wirl (1996), Itaya and Shimomura (2001), Yanase (2006), Benchekroun and Long (2008), Fujiwara and Matsueda (2009), and Battaglini et al (2014), in which private agents voluntarily contribute to a public good, the stock of which accumulates over time and affects the agents' utility. 3 In contrast to these studies, in which the private agents' objective function is exogenously determined and no market competition is considered, we focus on the interaction between market competition and dynamic game outcomes.…”

Selection of a Markov Perfect Nash Equilibrium in a Class of Differential Games

“…All these papers have considered pre-play negotiations between the players, implicitly or explicitly, with the aim of reaching an agreement on the selection of the pair of strategies. The following is a non-exhaustive list of works which can be classified in the first stream of the literature: Dockner and Long (1993), Feichtinger and Wirl (1993), Wirl (1996), Piga (2000), Ihori and Itaya (2001), Rubio and Casino (2002), Wirl and Feichtinger (2002), Benchekroun and Long (2008), Fujiwara (2008Fujiwara ( , 2009Fujiwara ( , 2010, Fujiwara and Matsueda (2009). A list of papers belonging to the second stream of the literature includes: Wirl (1994), Wirl and Dockner (1995), Shibata (2002), Rubio and Casino (2003), Wirl (2007).…”

The Free Rider Problem: A Dynamic Analysis

“…See, among others,Rosenthal [1984] and,Bergstrom, Blume and Varian [1985].4 See, for example,Itaya and Shimomura [2001],Yanase [2006],Fujiwara and Matsueda [2009].5 Work has been done to study non-Markov equilibria. See, for example,Dutta and Sundaram [1993], andGaitsgory and Nitzan [1994] Gaitsgory an Nitzan [1994].…”