An allocation rule for dynamic random network formation processes

Abstract

Most allocation rules for network games presented in the literature assume that the network structure is fixed. We put explicit emphasis on the construction of networks and examine the dynamic formation of networks whose evolution across time periods is stochastic. Time series of networks are studied that describe processes of network formation where links may appear or disappear at any period. Moreover, convergence to an efficient network is not necessarily prescribed. Transitions from one network to another are random and ruled by a stochastic process, typically a Markov chain. We propose the link-based scenario allocation rule for such dynamic random network formation processes and provide its axiomatic characterization. By considering a monotone game and a particular (natural) network formation process, we recover the link-based flexible network allocation rule of Jackson (Games Econ Behav 51:128-154, 2005a).

Finding the weakest link(s): Coalition games for decentralized discrete-event control

“…Definition 10: (adapted from [7]) The link-based scenario allocation rule for dynamic network processes, over a finite horizon W , is given by:…”

“…is significantly more complex and requires the computation of a weighted average over the transformation of the non-elementary change to a sequence of elementary changes [7]. The example presented below features scenarios with only elementary changes, and thus we restrict the discussion to the more straightforward version of the allocation rule.…”