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The concept of supermodularity is used in the social sciences to analyze how one [[Agent (economics)|agent's]] decision affects the incentives of others.
Consider a [[symmetric game]] with a smooth payoff function <math>\,f</math> defined over actions <math>\,z_i</math> of two or more players <math>i \in {1,2,\dots,N}</math>. Suppose the action space is continuous; for simplicity, suppose each action is chosen from an interval: <math>z_i \in [a,b]</math>. In this context, supermodularity of <math>\,f</math> implies that an increase in player <math>\,i</math>'s choice <math>\,z_i</math> increases the marginal payoff <math>df/dz_j</math> of action <math>\,z_j</math> for all other players <math>\,j</math>. That is, if any player <math>\,i</math> chooses a higher <math>\,z_i</math>, all other players <math>\,j</math> have an incentive to raise their choices <math>\,z_j</math> too. Following the terminology of Bulow, [[John Geanakoplos|Geanakoplos]], and [[Paul Klemperer|Klemperer]] (1985), economists call this situation [[strategic complements|strategic complementarity]], because players' strategies are complements to each other.<ref>{{cite journal |first=Jeremy I. |last=Bulow |first2=John D. |last2=Geanakoplos |first3=Paul D. |last3=Klemperer |year=1985 |title=Multimarket Oligopoly: Strategic Substitutes and Complements |journal=[[Journal of Political Economy]] |volume=93 |issue=3 |pages=488–511 |doi=10.1086/261312 |citeseerx=10.1.1.541.2368 }}</ref> This is the basic property underlying examples of [[General equilibrium#Uniqueness|multiple equilibria]] in [[coordination game]]s.<ref>{{cite journal |first=Russell |last=Cooper |first2=Andrew |last2=John |year=1988 |title=Coordinating coordination failures in Keynesian models |journal=[[Quarterly Journal of Economics]] |volume=103 |issue=3 |pages=441–463 |doi=10.2307/1885539 }}</ref>
The opposite case of submodularity of <math>\,f</math> corresponds to the situation of [[strategic complements|strategic substitutability]]. An increase in <math>\,z_i</math> lowers the marginal payoff to all other player's choices <math>\,z_j</math>, so strategies are substitutes. That is, if <math>\,i</math> chooses a higher <math>\,z_i</math>, other players have an incentive to pick a ''lower'' <math>\,z_j</math>.
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