Describing Resource Allocation to Dynamically Formed Groups with Grammars

In this paper we model dynamic group formation and resource allocation with grammars in order to gain a deeper understanding into the involved processes. Modelling with grammars allows us to describe resource allocation and group formation as generative processes that provide, at any given time, information about at what stage the process of group formation and resource allocation is. We divide our model into four phases: (1) resource supply, (2) candidate group formation, (3) final group formation, and (4) resource distribution. In particular, we show that we can use permitting random context grammars to describe the first two phases. For the third phase we introduce an algorithm that determines based on a resource allocation strategy the final group to which resources are distributed. The last phase is described with random context grammars under a specific leftmost derivation mode. Our model shows that if information about the available resource and candidate group formation is distributed and kept separate, then the synchronisation of this information at a later stage (i.e. resource distribution phase) needs a more powerful grammar model.