Abstract
Bergstrom, Blume and Varian [4] provides anelegant game-theoretic model of an economy with one private good and onepublic good. Strategies of players consist of voluntary contributions of theprivate good to public good production. Without relying on first orderconditions, as in prior literature, the authors demonstrate existence ofNash equilibrium. The assumption of one-private good greatly facilities theresults. We provide an analogue of the Bergstrom, Blume and Varian result ina model allowing multiple private and public goods. In addition, we relatethe strategic market game equilibrium to the private-provision equilibriumof Villanacci and Zenginobuz [17], which provides a counter-part to theWalrasian equilibrium for a public goods economy. To obtain our results weintroduce a model of a strategic market game with public goods. Our approachalso incorporates, into the strategic market game literature, economies withproduction.
Highlights
The elegant model of BBV raises a number of challenges, including the development of a strategic model for the analysis of voluntary contributions equilibrium in situations with multiple private goods and with production of public goods
We show that as the bound on the numbers of units of produced goods goes to zero and M is allowed to go to infinity, there is a sequence of Nash equilibria with corresponding allocations and prices that converge to a private provision equilibrium for the finite economy
Given a finite economy, we formulate a continuum representation of the economy in which the actions of each consumer and each firm are negligible from the viewpoint of other agents but with the property that private goods provision equilibria for the continuum economy generate a private goods equilibrium for the finite economy
Summary
One of the most important papers on public good provision is Bergstrom, Blume and Varian (1986), BBV. This question was addressed by Peck, Shell and Spear (1992) who demonstrate conditions on a private-goods economy under which there are strictly positive equilibrium bids for all goods (and provide an in-depth study of the model).8 We cannot establish such a result and do not aim to do so, given that we wish to allow situations where some consumers do not contribute to public good provision and we allow production, with the possibility that some public goods are not produced. Peck, Shell and Spear consider an ‘inside’ or fiat money, representing the private debt of the consumers with default penalties but, unlike the situation in our continuum game model, there is no bound on consumer debt We require such a bound; otherwise consumer demands would be unlimited and, as DG, we wish to demonstrate that, with many players, price-taking equilibrium outcomes arise as outcomes of strategic behavior.. We refer the reader to Giraud (2003) for a recent review of the literature on strategic market games
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
