Probabilistic Interaction Networks

Dr. Rudolf Kulhavý
29 April 2009
There is a common perception in todays business that the world around us becomes less hierarchical and more networked and flat. While the shift towards a networked and decentralised business environment generally creates more freedom to act, it does not increase automatically the chances of success. Understanding the dynamics of networked systems — in particular the interplay between the performance of an individual node and of the entire network, and the importance of effective bonding for the well-being of an organisation — becomes a critical skill. Replacing mental models with a formal, quantitative model can improve such understanding and ultimately allow for systematic network optimisation. To this end, we propose to combine stochastic system dynamics modelling of individual nodes with probabilistic graphical modelling of a network configuration. The latter is closely related to theoretical constructs such as the Ising model in statistical mechanics or Markov random fields in image analysis. Modelling of value networks in business turns out to be even more complex because of the random structure of a network. In this talk, we discuss the economic substance and mathematical representation of node-to-node bonds, formulate a general Bayesian solution to the problem of estimating unknown state and parameter values in the resulting model, and discuss its Markov chain Monte Carlo implementation. To illustrate the concepts introduced, we revisit Clayton Christensens qualitative model of the dynamic behaviour of new entrants versus incumbents when dealing with sustaining and disruptive innovation — and consider its reformulation as a probabilistic interaction network. We conclude by looking outside business for other instances of value networks.
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