A real-valued set function is supermodular if it satisfies the displayed inequality. Its negative is a submodular set function. Equivalently, the gain from adding an element cannot decrease as the set grows. This is the defining property of a convex cooperative game, and makes coalition marginal allocations lie in the core of a cooperative game.
A set function is submodular if for every pair of subsets. Entropy submodularity is a fundamental example.
Articles by others on the same topic
The term "set function" can refer to different concepts depending on the context, particularly in mathematics, computer science, and programming. Here are a few interpretations: 1. **Mathematical Set Function**: In mathematics, particularly in set theory and measure theory, a set function is a function defined on a collection of sets (often a σ-algebra) that assigns a value (typically a number) to each set.
This section is about functions that operates on arbitrary sets.