Subadditivity is a property of a set function where the function's value at the union of two sets is less than or equal to the sum of its values at each set individually, reflecting a form of diminishing returns. This concept is crucial in various fields, including economics, information theory, and probability, where it helps in understanding cost functions, entropy, and risk aggregation, respectively.
A concave function is one where, for any two points on the graph, the line segment connecting them lies below or on the graph, indicating a 'bowl-down' shape. This property is crucial in optimization problems, as it guarantees that any local maximum is also a global maximum, simplifying the search for optimal solutions.
Superadditivity is a property of a function where the value of the function at the sum of two inputs is greater than or equal to the sum of the function's values at those inputs individually. This concept is often used in economics, game theory, and cooperative scenarios to describe situations where collaboration or combination yields greater benefits than individual efforts.