In mathematics, a supermodular function is a function on a lattice that, informally, has the property of being characterized by "increasing differences...

condition (sometimes a function satisfying this condition is called log supermodular) i.e., μ ( x ∧ y ) μ ( x ∨ y ) ≥ μ ( x ) μ ( y ) {\displaystyle \mu (x\wedge...

the game-theoretic analysis of reputation formation, repeated games, supermodular games and learning in games. In an influential 1982 paper with David...

Equivalently, this means that the function Π {\displaystyle \,\Pi } is supermodular. On the other hand, the decisions are strategic substitutes if ∂ 2 Π...

queries. Tarski's fixed-point theorem has applications to supermodular games. A supermodular game (also called a game of strategic complements) is a game...

case. A typical utility function for this case is given at the right. Supermodularity is the opposite of submodularity: it means that "the whole is not less...

In probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual dependence between the two...

game is convex if its characteristic function v {\displaystyle v} is supermodular: v ( S ∪ T ) + v ( S ∩ T ) ≥ v ( S ) + v ( T ) , ∀   S , T ⊆ N . {\displaystyle...

let D {\displaystyle D} be a lattice, and let f {\displaystyle f} be supermodular in x {\displaystyle x} and have increasing differences in ( x , θ ) {\displaystyle...

No-trade theorem, Market design, Reputation effects (game theory), supermodular games, monotone comparative statics, Linkage principle, Deferred-acceptance...

properties of upper-bounded supermodular set functions. In a non-bipartite graph, the deficiency function is, in general, not supermodular. A graph G has the Hall...

both submodular and supermodular. Utility functions on indivisible goods Independent goods Submodular set function Supermodular set function Brandt,...

Non-cooperative game Self-fulfilling prophecy Strategic complements Social dilemma Supermodular Uniqueness or multiplicity of equilibrium "Assurance Game - P2P Foundation"...

other hand, they model notions of diversity, information and coverage. Supermodular function Matroid, Polymatroid Utility functions on indivisible goods...

Substitution effect – Sunk costs – Sunspot equilibrium – Sunspots (economics) – Supermodular function – Supply and demand – Supply-side economics – Surplus value...

complementarity is due to Masahiko Aoki and relies on the theory of supermodular games developed by Paul Milgrom and John Roberts. The basic structure...

November 2025. [00:05:45] Charles: I read that you wrote a dissertation on supermodular games. What was that? [00:05:50] Andrew Strauss: That is, um, why we...

f(x)-f(x\wedge x').} Every supermodular function is quasisupermodular. As in the case of single crossing differences, and unlike supermodularity, quasisupermodularity...

The method uses lattice theory and introduces the notions of quasi-supermodularity and the single-crossing condition. The wide application of monotone...

agents' utilities are superadditive set functions (more general than supermodular), a ( log ⁡ m ) 1 + ϵ m {\displaystyle {\frac {(\log m)^{1+\epsilon }}{m}}}...

that the educations of husbands and wives are complements (exhibiting supermodularity); the surplus is maximized when partners have similar levels of education...

∪ F ) = g ( E ) + g ( F ) . {\displaystyle g(E\cup F)=g(E)+g(F).} ; supermodular if for any E , F ∈ C {\displaystyle E,F\in {\mathcal {C}}} , we have...

lattice-theoretic methods to analyze games of strategic complementarities (or supermodular games), and in general complementarities, in economics. His contribution...

{\displaystyle f(\emptyset )=0} and E P f = E P {\displaystyle EP_{f}=EP} . For a supermodular f one analogously may define the contrapolymatroid { w ∈ R ≥ 0 E   |...

Quanrud, Kent; Torres, Manuel R. (January 2022), "Densest Subgraph: Supermodularity, Iterative Peeling, and Flow", Proceedings of the 2022 Annual ACM-SIAM...

which yields the rule in a Nash equilibrium. Moreover, for monotone and supermodular bilateral principles, every subgame perfect equilibrium is coalition-proof...