Potential games in volatile environments

Abstract

This paper studies the co-evolution of networks and play in the context of finite population potential games. Action revision, link creation and link destruction are combined in a continuous-time Markov process. I derive the unique invariant distribution of this process in closed form, as well as the marginal distribution over action profiles and the conditional distribution over networks. It is shown that the equilibrium interaction topology is an inhomogeneous random graph. Furthermore, a characterization of the set of stochastically stable states is provided, generalizing existing results to models with endogenous interaction structures.

Nestedness in networks: A theoretical model and some applications

“…13,14 12 f (t) = o(g(t)) as t → ∞ if lim t→∞ f (t)/g(t) = 0. 13 In a similar way, Staudigl (2011) assumes that the linking activity levels of agents depend on their relative marginal payoffs. Snijders (2001) and Snijders et al (2010) introduced exponential link update rates, which "depend on actor-specific covariates or on network statistics expressing the degree to which the actor is satisfied with the present network structure."…”

“…Snijders (2001) and Snijders et al (2010) introduced exponential link update rates, which "depend on actor-specific covariates or on network statistics expressing the degree to which the actor is satisfied with the present network structure." See also (3.4) in Staudigl (2011) and Section 7.1 in Snijders (2001).…”

Evolution of social networks

“…Theorem 4.6 (Staudigl (2011),Staudigl (2012). The unique invariant distribution of the coevolutionary process {X ε,τ N (t)} t≥0 is the Gibbs measure The Gibbs measure (9) is defined by a function µ ε,τ 0,N capturing the effect of the network -31-formation process, and a function depending on the potential function ρ, which can be interpreted as a welfare function.…”

Evolution of Social Networks

“…Theorem 4.6 (Staudigl (2011),Staudigl (2012). The unique invariant distribution of the coevolutionary process {X The Gibbs measure (9) is defined by a function µ ε,τ 0,N capturing the effect of the network -31-formation process, and a function depending on the potential function ρ, which can be interpreted as a welfare function.…”