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The expected utility of the above bet (with a 50% chance of receiving 100 and a 50% chance of receiving 0) is = (() + ()) /, and if the person has the utility function with u(0)=0, u(40)=5, and u(100)=10 then the expected utility of the bet equals 5, which is the same as the known utility of the amount 40. Hence the certainty equivalent is 40.
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. [ 1 ] [ 2 ] [ 3 ] This concept first arose in calculus , and was later generalized to the more abstract setting of order theory .
In mathematics, a homothetic function is a monotonic transformation of a function which is homogeneous; [2] however, since ordinal utility functions are only defined up to an increasing monotonic transformation, there is a small distinction between the two concepts in consumer theory. [1]: 147
In mathematics, a supermodular function is a function on a lattice that, informally, has the property of being characterized by "increasing differences." Seen from the point of set functions , this can also be viewed as a relationship of "increasing returns", where adding more elements to a subset increases its valuation.
For every utility function v, there is a unique preference relation represented by v. However, the opposite is not true: a preference relation may be represented by many different utility functions. The same preferences could be expressed as any utility function that is a monotonically increasing transformation of v. E.g., if
A differentiable function f is (strictly) concave on an interval if and only if its derivative function f ′ is (strictly) monotonically decreasing on that interval, that is, a concave function has a non-increasing (decreasing) slope.
In economics, utility is a measure of a certain person's satisfaction from a certain state of the world. Over time, the term has been used with at least two meanings. In a normative context, utility refers to a goal or objective that we wish to maximize, i.e., an objective function.
Zero-sum games and particularly their solutions are commonly misunderstood by critics of game theory, usually with respect to the independence and rationality of the players, as well as to the interpretation of utility functions [further explanation needed]. Furthermore, the word "game" does not imply the model is valid only for recreational games.