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In Cournot competition, two or more firms decide on the amount of output they will produce, and they make these decisions simultaneously without knowing the choices of the other competitors. Here, each firm considers the output level of its competitor as given and then decides its production quantity to maximize its own profit.
This competition model is characterized by the **interdependence** of firms, making strategic thinking essential. When one firm decides to increase its output, the market supply goes up, causing a decrease in market prices. This ultimately reduces potential profits for all players involved. Consequently, **reaction functions** are crucial, helping each firm determine its best course of action in response to competitors. Firm B's strategy to reduce its production will naturally follow if Firm A increases production, stabilizing the market conditions and maintaining profitability.

In stark contrast to Cournot competition, Bertrand competition involves firms competing on price rather than quantity. Within this framework, each firm independently chooses a product price, with the primary objective of capturing a greater market share. The assumption here is that consumers gravitate towards the cheaper option among comparable products, pushing firms towards aggressive price setting strategies.
If Firm A decides to lower its price, it effectively attracts a larger customer base due to its more attractive pricing. Firm B, seeking to stay competitive, is prompted to lower its price as well, leading to the proverbial price war. Consequently, **reaction functions** in Bertrand models revolve around price adjustments rather than output changes, stressing adaptability in pricing to capture and sustain consumer interest. This highlights the firm's focus not just on its production volumes but more significantly on its price positioning to outmaneuver its competitors.

Reaction functions represent the strategic moves firms make in response to competitors' actions, playing a vital role in competitive scenarios. In Cournot competition, a firm's reaction function will define the quantity it believes it should produce based on the quantity produced by its competitor. This forms a feedback loop where each firm adjusts to the other's output, keeping market equilibrium and ensuring firms aim towards maximizing profits while suppressing excessive market supply.
In Bertrand competition, reaction functions are centered around pricing. When one firm changes its price, the reaction function dictates how the competitor will alter its own prices to remain viable in the marketplace. Both competition models illuminate different facets of strategic decision-making: one skews towards optimizing production quantities, while the other leans heavily on pricing tactics to remain consumer-relevant. Recognizing these action-reaction dynamics is key in studying game theory and understanding how distinct competitive landscapes shape business strategies.