Public Goods in Networks with Constraints on Sharing

Abstract

This paper considers incentives to provide goods that are partially excludable along social links. Individuals face a capacity constraint in that, conditional upon providing, they may nominate only a subset of neighbours as co-beneficiaries.Our model has two typically incompatible ingredients: (i) a graphical game (individuals decide how much of the good to provide), and (ii) graph formation (individuals decide which subset of neighbours to nominate as co-beneficiaries).

Exact capacitated domination: on the computational complexity of uniqueness

“…In the rest of this section, we provide two simple assumptions for the rest of the paper which will allow to simplify some of our proofs. We also provide a proof of the above-mentioned theorem of Gerke et al [6] to make this paper self-contained. In both assumptions, (G, κ) is a capacitated graph.…”

“…Variants and extensions of the algorithm have been applied to a wide variety of assignment problems in economics including college admissions, the market for kidney donors, and refugee resettlement (see [12] for a survey). 6 The assignment problem that motivates our study arises in the provision of local public goods. The story is as follows.…”

“…Since H is a bipartite graph, we will write it as the triple (X, Y ; E), where X, Y are D-set and Pset of H, respectively, and E is the edge set of H. A vertex set B is a D-set of (G, κ) if (G, κ) has a DP -Nash subgraph in which B is the D-set. Gerke et al [6] proved that every capacitated graph has a DP -Nash subgraph implying that every capacitated graph has a D-set (below we provide a slightly modified version of this proof, see Theorem 1).…”

“…Theorem 1 below means that all Netflix Games introduced in [6] have pure strategy Nash equilibria; see Section 2 for a brief discussion of Netflix Games and their relation to DP -Nash subgraphs and D-sets in capacitated graphs. As explained in Section 2, there are two natural problems of interest in economics.…”

The Effect of Social Distancing on the Reach of an Epidemic in Social Networks

“…We do not mean individuals maintaining a predetermined physical distance throughout an encounter. Our measure is adapted from the gametheoretic model of Netflix Games (Gerke et al, 2019;Gutin et al, 2020). There, the purchaser of a product may only share with a limited number of friends.…”