The reaction function summarizes the follower’s best response to each possible choice by the leader. The leader uses this relationship when selecting a quantity, price, or another strategic variable, rather than optimizing without considering the second move. This anticipatory step links the two decisions and determines how the follower’s expected response shapes the leader’s eventual outcome.
Backward induction begins with the follower’s decision and works backward to the leader’s choice. First, the follower’s best response is identified for possible leader actions. The leader then selects the action that accounts for that response. This procedure supports a subgame-perfect equilibrium, because the predicted behavior remains optimal at the relevant stages of the sequential interaction.
A first-mover advantage can arise because the leader commits to a strategic choice before the follower acts. That commitment gives the leader an opportunity to shape the follower’s response and influence output or profit differences. The advantage is not automatic, however; it depends on how the follower responds and on the strategic variable selected by the leader.
The key difference is the information available when decisions are made. In sequential competition, the follower observes the leader’s action and chooses a response, so the leader can incorporate that response into the initial decision. In a simultaneous-move model, neither decision-maker conditions the choice on an observed action, producing a different strategic analysis and potentially different outcomes.
A typical solution first specifies the leader’s and follower’s strategic variables, such as quantity or price. Next, the follower’s best response is derived as a reaction function. The leader then evaluates possible choices using that response and selects an optimal action. Substituting the leader’s choice back into the follower’s response yields the sequential outcome and associated profit or output comparisons.
This framework is useful when one firm, participant, or contracting party makes a decision before another can respond. In microeconomics, it can analyze market power, output and profit differences, entry deterrence, and supply-chain contracting. Its value lies in connecting the timing of decisions with strategic responses, helping explain how order of action affects market outcomes.