Johnson, Cathleen Amanda; PhD
VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY, 2000
ECONOMICS, THEORY (0511)
We introduce a spatial cost topology in the network formation model analyzed
by Jackson and Wolinsky,
<italic>Journal of Economic Theory</italic> <bold> 71</bold> (1996),
44–74. This cost topology
might represent geographical, social, or individual differences. It describes
variable costs of establishing
social network connections. Participants form links based on a cost-benefit
analysis. We examine the
pairwise stable networks within this spatial environment. Incentives vary enough
to show a rich pattern of
emerging behavior. We also investigate the subgame perfect implementation of
pairwise stable and
efficient networks. We construct a multistage extensive form game that describes
the formation of links in
our spatial environment. Finally, we identify the conditions under which the
subgame perfect Nash
equilibria of these network formation games are stable. We analyze the dynamic
implications of learning in
a large population coordination game where both the actions of the players and
the communication
network evolve over time. Cost considerations of social interaction are incorporated
by considering a
circular model with endogenous neighborhoods, meaning that the locations of
the players are fixed but
players can create their own communication network. The dynamic process describing
medium-run
behavior is shown to converge to an absorbing state, which may be characterized
by coexistence of
conventions. In the long run, when mistake probabilities are small but nonvanishing,
coexistence of
conventions is no longer sustainable as the risk-dominant convention becomes
the unique stochastically
stable state. We create and investigate a system that is capable of observing
the accumulation of social
capital and the effect of social capital accumulation on behavior of individually
rational players. In the first
model, we develop a restricted system to show that social capital forms and
is maintained at a steady state
level. The resulting network is the chain. The second model uses a congestion
function in conjunction
with social capital to show a network emerge that contains links that costlier
than those in the chain
network.
Social
Systems Simulation Group
P.O. Box 6904 San Diego, CA 92166-0904 Roland Werner, Principal Phone/FAX (619) 660-1603 |