Extended abstract of “Optimizing public goods in networks”

Description of the model In this paper we consider an exogenous network in which otherwise homoge-neous players (nodes) play a public good game, as the one defined Best shot game in Galeotti et alii (2008).1 The action of each node i is an effort xi and her payoff will depend on the aggregate effort of herself and her neighbors, minus some cost for her own effort. In particular we will restrict to the two specialized actions: xi ∈ {0, 1}.2 In this way ~x, a vector of specialized actions whose length is given by the number of nodes, will characterize any possible configuration of the system. We will consider any setup of incentives such that, in Nash equilibrium (NE), agent i will play action xi according to the following rule:{ xi = 1 if xj = 0 for any neighbor j of node i; xi = 0 otherwise. (1) We will study all the NE of the game, that is all those actions in which, for any link, no both nodes of the link put effort 1; but at the same time for an