Monotone Comparative Statics in Games with both Strategic Complements and Strategic Substitutes

This paper analyzes games with both strategic substitutes and strategic complements. Such games may behave differently from either games with strategic complements or games with strategic substitutes. In such games, equilibria do not decrease as the parameter increases. Moreover, natural conditions are presented to guarantee that an increase in the parameter leads to an increase in the equilibrium: in other words, conditions to guarantee monotone comparative statics. These conditions are based on intuitive tradeoffs between direct parameter effects and indirect strategic effects. These conditions are needed only for players with strategic substitutes; no conditions are imposed on players with strategic complements. Several examples highlight the results.