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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 (2015).

In this paper, we present a general statistical framework within which we can draw a new interpretation of the Laakso-Taagepera effective number of parties fragmentation index. With the particular method of sampling with probability proportional to the party sizes, we show that the Laakso-Taagepera effective number of parties is the inverse of the size biased version of the traditional expected party size in shares. Further, we provide an axiomatic definition of the Laakso-Taagepera effective number of parties., Nous présentons dans cet article un environnement statistique général dans lequel nous pouvons donner une interprétation nouvelle du nombre effectif de partis de Laakso-Taagepera comme indice de fragmentation. Grâce à la méthode particulière d'échantillonnage dans laquelle les probabilités sont proportionnelles aux tailles des partis, nous montrons que le nombre effectif de partis de Laakso-Taagepera n'est rien d'autre que la version biaisée par la taille de l'espérance normale de la taille des partis. De plus, nous fournissons une définition axiomatique du nombre effectif de partis de Laakso-Taagepera.