Start by holding the rival’s action fixed, then identify the choice that gives the firm its highest payoff, such as profit. Repeating this optimization for different rival choices produces an equation or curve linking the rival’s decision to the firm’s best response. This relationship reveals how the firm’s preferred action changes across possible competitive situations.
Strategic complements describe decisions that tend to move together: a change in one firm’s action is associated with a best response in the same direction. Strategic substitutes describe responses that move oppositely, so a larger action by one competitor corresponds to a smaller preferred action by the other. This distinction helps interpret the direction of competitive interaction.
The intersection identifies a combination of choices at which each firm is responding optimally to the other firms’ decisions. Because neither firm benefits from changing its own action alone at that point, the intersection represents a Nash equilibrium. Examining how nearby choices affect incentives also helps researchers assess whether the predicted outcome is stable under unilateral adjustments.
Researchers first specify the firms’ strategic choices and the payoff each firm seeks to maximize. They then determine each firm’s best response while treating competitors’ choices as given, express those responses as equations or curves, and compare them graphically or analytically. The resulting intersection provides the predicted equilibrium for the selected market model.
Costs and demand shape the payoff associated with each possible strategic choice, so they can alter the action a firm prefers for any given rival decision. A change in either condition may therefore shift the relevant equation or curve and change where firms’ responses intersect. Reaction functions provide a way to trace how these economic conditions affect competitive outcomes.
They are useful when firms compete over output, price, or another strategic decision and the analyst wants to compare the resulting outcomes. By changing the decision being modeled or the market structure, researchers can examine differences in best responses, equilibrium choices, and incentives to adjust. This makes the framework relevant to broader microeconomic analysis of strategic competition.