Collective Profitability of DAG-Based Selling-Buying Intermediation Processes

Optimal Semi-Competitive Intermediation Networks

“…Parameter represents the number of participant agents. It also gives the number of terms of the sum defining the Nash social welfare function (see (5)). Parameter represents the number of transactions.…”

“…. Observe that if graph is collectively profitable then is well defined by (5), as logarithm is defined for positive real numbers and utilities are positive for all = 1, 2, … , (assuming that log 0 = −∞). Let ∈ ℝ ×1 be the vector of signed limit prices, defined by: (6) = { − ∈ , ∈ ℬ, 0 ∈ ℐ.…”

“…In our recent research work we are interested in the modelling and analysis of such complex business processes as semi-competitive intermediation networks. Our results on this subject are presented in papers [4,5] and synthesis paper [12] and refer to the following aspects of the problem: i) the introduction of a domain-independent process model, grounded on Directed Acyclic Graphs (DAG hereafter), and ii) the development of necessary and sufficient conditions that guarantee profitable pricing strategies of involved actors in the intermediation process.…”