Abstract
A new model of strategic networking is developed and analyzed, where an agent’s investment in links is nonspecific. The model comprises a large class of games which are both potential and super- or submodular games. We obtain comparative statics results for Nash equilibria with respect to investment costs for supermodular as well as submodular networking games. We also study supermodular games with potentials. We find that the set of potential maximizers forms a sublattice of the lattice of Nash equilibria and derive comparative statics results for the smallest and the largest potential maximizer. Finally, we provide a broad spectrum of applications from social interaction to industrial organization.
Highlights
Models of strategic network formation typically assume that each agent selects his direct links to other agents in which to invest
We focus on nonspecific networking, meaning that an agent cannot select a specific subset of feasible links which he wants to establish or strengthen
By Proposition 2, if in addition to satisfying (A) and (C), a networking game is a potential game, the set of potential maximizers forms a nonempty sublattice of the set of equilibrium points
Summary
Models of strategic network formation typically assume that each agent selects his direct links to other agents in which to invest. We obtain a weak monotonicity result by applying an earlier result of Milgrom and Roberts [30]: Proposition 6 Consider a family of networking games Gτ satisfying (A) and (C) which differ in the marginal cost parameters τ = By Proposition 2, if in addition to satisfying (A) and (C), a networking game is a potential game, the set of potential maximizers forms a nonempty sublattice of the set of equilibrium points. Because Gθ and Gθ are potential games and the payoff function of each player i satisfies increasing differences on Si ×Θ, it is the case that s ≥ s0 and θ ≥ θ implies.
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