Let L be a finite distributive lattice. Coxeter groups, polytopes, simplicial complexes, and matchings arise. Abstract A non-cooperative model of network formation is developed. Agents form links with others based on the cost of the link and its assessed benefit. Link formation is one-sided, i.e., agents can initiate links with other agents without their consent, provided the agent forming the link makes the appropriate investment.
Information flow is two-way.
The model builds on the work of Bala and Goyal, but allows for agent heterogeneity. Whereas they permit links to fail with a certain common probability, in our model the probability of failure can be different for different links. We investigate Nash networks that exhibit connectedness and super-connectedness. We provide an explicit characterization of star networks and examine some other types of common network architectures. Efficiency and Pareto-optimality issues are discussed through examples.