Coordination, Local Interactions and Endogenous
Neighborhood Formation
Giorgio Fagiolo
fagiolo@sssup.it
Paper URL: http://www.sssup.it/~lem/WPLem/files/2001-15_0.pdf
The details of the process governing the co-evolution
of expectations formation, individual choices and interaction structure can
crucially affect the long-run social structure emerging in coordination games
repeatedly played in large populations. To investigate this issue, we present
a model of local coordination in which agents can simultaneously choose both
stage-game strategies and the partners with whom to play the game. We consider
a population of myopic (adaptive) individuals with fixed geographical locations
(i.e. located on a one-dimensional lattice without boundaries) who repeatedly
play a pure coordination game with their 'nearest neighbors'. We assume that
holding neighbors is costly and that, from time to time, agents are allowed
to slightly shrink (or enlarge) the 'radius' of their current neighborhood
by maximizing expected net payoffs. We study the behavior of the model in
settings characterized by both positive and negative network externalities.
In particular, we assume that net individual payoff may initially increase
as the number of neighbors increases, but it eventually falls as neighborhood
sizes become very large. After having analytically characterized the set of
steady states and conditions for convergence, we show that both full coordination
and coexistence of conventions may be possible in a steady state. In order
to study the long-run average behavior of the dynamical system as parameters
change we use extended Montecarlo analyses. In particular, we compute average
coordination levels and average neighborhood sizes over large Montecarlo samples.
Computer simulations show that the system is able to reach, on average, very
high long-run coordination levels, together with small average neighborhood
sizes, for a large region of the parameter space. Furthermore, we find that
average coordination increases if the unit cost of holding a neighbor decreases
and that average coordination in presence of a non-zero (although small) frequency
of neighborhood adjustment is higher than if interaction structures were
static. Finally, we introduce alternative neighborhood updating rules characterized
by different levels of individual myopia and we explore their effects
on aggregate coordination.