Make It Go Viral! Rate-optimal Control for Resource-Constrained Branching Processes

Details Make It Go Viral! Rate-optimal Control for Resource-Constrained Branching Processes Make It Go Viral! Rate-optimal Control for Resource-Constrained Branching Processes

2012-03-05

arxiv.org/abs/1203.1072v1

Mathematics

Optimization and Control

Scientific paper

We propose a new class of controlled multi-type branching processes with a per-step linear resource constraint, motivated by applications in quantitative marketing, and study the associated growth-rate maximizing control strategies. We show that the optimal growth rate can be achieved by maintaining a single optimal ratio among different population types, for both deterministic and stochastic branching processes. In the special case of a two-type population and with a symmetric revenue structure, the optimal ratio is obtained in closed-form. As a proof of concept, the methodology is applied to the linkage structure of the 2004 US Presidential Election blogosphere, where the optimal growth rate achieves sizable gains over a uniform selection strategy.

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