Provision of Public Goods on Networks: On Existence, Uniqueness, and Centralities

Abstract

We consider the provision of public goods on networks of strategic agents. We study different effort outcomes of these network games, namely, the Nash equilibria, Pareto efficient effort profiles, and semi-cooperative equilibria (effort profiles resulting from interactions among coalitions of agents). We identify necessary and sufficient conditions on the structure of the network for the uniqueness of the Nash equilibrium. We show that our finding unifies (and strengthens) existing results in the literature. We also identify conditions for the existence of Nash equilibria for the subclasses of games at the two extremes of our model, namely games of strategic complements and games of strategic substitutes. We provide a graph-theoretical interpretation of agents' efforts at the Nash equilibrium, as well as the Pareto efficient outcomes and semi-cooperative equilibria, by linking an agent's decision to her centrality in the interaction network. Using this connection, we separate the effects of incoming and outgoing edges on agents' efforts and uncover an alternating effect over walks of different length in the network.

Game equilibria and unification dynamics in networks with heterogeneous agents

“…Writing this relation in detail, we obtain equation 7if agent is unproductive or equation (10) if agent is productive.…”

“…In majority of research on game equilibria in networks, 2,[8][9][10] the agents are assumed to be homogeneous (except their positions in the network), and the problem is to study the relation between the agents' positions in the network and their behavior in the game equilibrium. The models demonstrate that the agents' behavior and wellbeing depend on their position in the network which is characterized by one or another measure of centrality.…”

A variational inequality framework for network games: Existence, uniqueness, convergence and sensitivity analysis

“…This may be overly restrictive since taking the absolute value loses structural properties associated with games of strategic substitutes. Naghizadeh and Liu (2017b) studies public good network games by using linear complementarity problems (which are a subclass of variational inequalities). We remark that variational inequalities have been used to study specific network economic models such as spatial price equilibrium models, traffic networks, migration models and market equilibria, as reviewed for example in Nagurney (2013); Facchinei and Pang (2003).…”

Game Equilibria and Transition Dynamics in Complete Networks and in a Triangle with Heterogeneous Agents

“…Moreover, the solution of each agent is affected by the behavior of his network neighbors. In most studies of game equilibria in networks (e.g., [2,4,11,13]), agents were assumed to be homogeneous, except for their position in the network. In this case, the problem reduces to analyzing the relationship between the agent's position in the network and his behavior in the game equilibrium.…”