Superadditiivisuus

Superadditiivisuus, the Finnish term for superadditivity, refers to a property of a function or a system in which the whole is greater than the sum of its parts. In mathematical terms a function f is superadditive over a domain if for any two elements x and y in that domain the inequality f(x + y) ≥ f(x) + f(y) holds. The concept appears in a variety of fields, most notably in economics where the combined value of two firms can exceed the sum of their individual values, in game theory where a coalition’s joint payoff is more than the sum of what its members could achieve separately, and in combinatorics where the union of sets can have properties surpassing what each set alone provides.

Superadditiivisuus is the counterpart of subadditivity, in which the inequality is reversed. In linguistics the term is sometimes used to describe the phenomenon of idiomatic expressions whose meaning cannot be deduced from individual words, an effect that is stronger than the additive contributions of its parts. In probability and statistics the concept underlies correlations that cause joint events to be more likely than the product of individual probabilities. In signal processing it describes non-linear systems where combining inputs yields an output whose magnitude exceeds the linear sum of each input’s output.

The study of superadditiivisuus informs the design of cooperative strategies, optimization algorithms and the analysis of systems where synergy plays a crucial role. Because of its wide applicability the concept is frequently highlighted in introductory texts on optimization, cooperative game theory and statistical mechanics.