What are the best non-cooperative game models for analyzing strategic interactions in oligopolies?

The Cournot model named after the French economist Antoine Augustin Cournot is one of the foundational models for analyzing strategic interactions in oligopolies. In the Cournot model, firms compete on the quantity of output they decide to produce. Each firm makes an output decision based on the assumption that its rivals' output levels will remain constant. The equilibrium in this model is reached when each firm's output decision is optimal given the output levels of its competitors. This leads to a Nash equilibrium where no firm can increase its profit by unilaterally changing its output. The Cournot model is particularly useful for industries where firms produce homogeneous goods and have significant control over their production levels.

The Bertrand model, developed by Joseph Bertrand, focuses on price competition rather than quantity competition. In this model, firms choose the price of their products simultaneously, assuming their competitors' prices will remain unchanged. The Bertrand model predicts that, in the case of homogeneous products, firms will undercut each other's prices until they reach the marginal cost, resulting in a perfectly competitive outcome with zero economic profits. The Bertrand model highlights the intensity of price competition in oligopolistic markets and is especially relevant in industries where products are highly substitutable.

The Stackelberg model, named after Heinrich von Stackelberg, extends the Cournot model by introducing a leader-follower dynamic. In this model, one firm (the leader) sets its output level first, and the other firms (the followers) then choose their output levels based on the leader's decision. This sequential decision-making process leads to a Stackelberg equilibrium, where the leader typically enjoys a strategic advantage and earns higher profits compared to the followers. The Stackelberg model is useful for analyzing markets where one firm has a dominant position or significant first-mover advantages, such as through superior technology, better information, or brand recognition.

The kinked demand model is used to explain price rigidity in oligopolistic markets. Proposed by Paul Sweezy, this model suggests that an oligopolist faces a demand curve that is more elastic for price increases and less elastic for price decreases. This kinked demand curve implies that firms expect rivals to match price decreases but not price increases, leading to a discontinuity in the marginal revenue curve and resulting in stable prices even in the face of cost changes. The kinked demand model is particularly relevant for markets characterized by few firms and where price wars are costly and undesirable.

The contestable market model, developed by William Baumol and his colleagues, suggests that the threat of potential entry can discipline the behavior of incumbent firms in an oligopoly. According to this model, even if a market is concentrated, the absence of barriers to entry and exit can lead to outcomes similar to those in competitive markets. Incumbent firms are constrained by the possibility of new entrants undercutting them, leading to competitive pricing and efficient production. The contestable market model is particularly useful for analyzing industries where technological advancements or regulatory changes lower entry barriers. It highlights the importance of potential competition in shaping market behavior and outcomes.

When analyzing strategic interactions in oligopolies, it is important to consider several additional factors beyond the traditional non-cooperative game models. One crucial aspect is the role of repeated interactions and long-term relationships among firms. Repeated games can lead to different outcomes compared to one-shot games, as firms may adopt cooperative strategies to sustain long-term profitability. The concept of tacit collusion, where firms implicitly coordinate their actions without explicit agreements, becomes relevant in this context. Another important consideration is the presence of product differentiation and its impact on competition.