Strategic Interaction and Networks

Abstract

Geography and social links shape economic interactions. In industries, schools, and markets, the entire network determines outcomes. This paper analyzes a large class of games and obtains a striking result. Equilibria depend on a single network measure: the lowest eigenvalue. This paper is the first to uncover the importance of the lowest eigenvalue to economic and social outcomes. It captures how much the network amplifies agents' actions. The paper combines new tools--potential games, optimization, and spectral graph theory--to solve for all Nash and stable equilibria and applies the results to R&D, crime, and the econometrics of peer effects

Risk taking under heterogenous revenue sharing

“…Ballester et al (2006) renewed the idea in the field of economics. Some additional insights in the theory are given in Ballester and Calvó-Armengol (forthcoming) and Bramoullé et al (2010). 8 That risk taking decisions can be lowered under increased insurance can also admit different explanations.…”

“…Heterogenous sharing on the two-link network.15 Bramoullé et al (2010) use a similar potential function to characterize uniqueness in terms of the minimal modulus of eigenvalues of the network of interaction.16 When λ ii ≥ 1 2 for all i, the matrix Λ ρ is diagonal dominant. Combined with the fact that its diagonal is positive, this implies that all eigenvalues are positive.17 When the economic application requires x HOS (λ 0 ) ≤ 1, a sufficient condition is written hb 1 + ρ 2 .…”

Action, Inaction, Trust, and Cybersecurity's Common Property Problem

“…From the point of view of interdependent security 8 we view a network as a mechanism that adjusts the probabilistic outcomes for the various nodes. The recent work of 9 and 10 have looked at optimal decision making (in an abstract setting) when agents are arranged in fixed networks, when an individual agents (acting as a node) actions affect the costs of others. Similarly to the single firm decision making example we outlined previously and the empirical evidence on the lazy attacker the impact of fixed adjustment costs is considerable within the network.…”

Effect of local information within network layers on the evolution of cooperation in duplex public goods games

“…Public goods game (PGG), which is a multi-person Prisoner's Dilemma, is often employed as a typical model for studying grouped cooperation in the society [1][2][3][4][5][6]. In a traditional PGG, agents choose whether to invest in a public pool, then the total contributions in the public pool are multiplied by an enhancement factor, and finally the obtained payoffs will be divided equally to all the participants irrespective of their contributions [7].…”