Two‐Aggregate Games: Demonstration Using a Production–Appropriation Model

Abstract

We expand the scope of the two-aggregate method by applying it to a situation in which many heterogeneous players are free to contribute to both aggregates. Such situations naturally arise in various resource allocation problems. Hence, our method is useful in many applications. A production-appropriation model is employed to illustrate how the problem of establishing the Nash equilibrium can be reduced from solving n > 2 best-response functions in n unknowns to solving two consistency conditions in two unknowns. We then conduct a comparative static exercise that the conventional approach could not handle easily, if at all, to demonstrate the power of our method.

Existence, uniqueness, and comparative statics of Nash equilibrium in a game of voluntary public good provision with two public goods

“…1 However, Cornes et al (2019) provide an analytical demonstration of the existence of a unique Nash equilibrium in the so-called conflict model developed by Skaperdas (1992), using the aggregate games approach of Cornes and Hartley (2007). Their model, similar to aggregate games with two public goods, could prove the existence of a unique equilibrium involving a production function of public goods, which is the approach used in the second stream.…”

A subscription vs. appropriation framework for natural resource conflicts

“…6 Our model expands this literature precisely through such endogenization. 7 3 See, for example, Murphy et al [1993], Grossman and Kim [1995], Anderton et al [1999], Noh [2002], Hausken [2005], Caruso [2010], Dal Bo and Dal Bo [2011, 2012, Mitra and Ray [2014], Cornes et al [2019] and Bakshi and Dasgupta [2020]. 4 Contributions include Katz et al [1990], Ursprung [1990], Gradstein [1993], Riaz et al [1995].…”

Aggregative games

“…5, see alsoNocke and Schutz (2018) Dickson (2017). andCornes et al (2019).5 Friedman uses the more general assumption of quasi-concavity of payoffs in own's action.6 In more technical term, profits are a Morse function, i.e., a smooth function with non-degenerate critical points(Christensen 2019, footnote 26).…”