Resource pricing games on graphs: existence of Nash equilibria

Optimization Letters (Impact Factor: 1.65). 01/2011; 7(2):1-10. DOI: 10.1007/s11590-011-0411-2

ABSTRACT In this letter, we consider a non-cooperative resource pricing game on a graph where sellers (i.e., players) set the prices
for their own resources to maximize the payoffs and buyers migrate to seek the least expensive resources. We present a model
for the resource pricing game and prove the existence of Nash equilibria on regular and hierarchical graphs. The results obtained
are applicable to the study of market economies, social networks and computer networks where individuals trade resources in
a spatially extended environment.

KeywordsResource pricing–Peer-to-peer networks–Mobile agents–Market economies–Game theoretic modeling

  • [Show abstract] [Hide abstract]
    ABSTRACT: We consider a model whereby players compete for a set of shared resources to produce and sell substitute products in the same market, which can be viewed as a generalization of the classical Cournot oligopolistic competition model, or, from a different angle, the Wardrop type routing model. In particular, we suppose that there are K players, who compete for the usage of resources as well as the sales of the end-products. Moreover, the unit costs of the shared resources and the selling prices of the products are assumed to be affine linear functions in the consumption/production quantities. We show that the price of anarchy in this case is lower bounded by 1/K, and this bound is essentially tight, which manifests the harsh nature of the competitive market for the producers.
    Journal of Global Optimization 08/2013; 56(4). · 1.31 Impact Factor