Nash Equilibrium Oligopoly Quiz

Oligopoly markets are defined by strategic interdependence: a firm's profit depends on what rivals choose to do. Nash equilibrium directly models this by identifying strategy profiles where every firm is simultaneously choosing the best response to its rivals. In perfect competition, firms are price-takers with no strategic interaction, and monopolists face no rivals. Only in oligopoly does the mutual best-response logic of Nash equilibrium become the essential analytical framework.

For each firm, High yields 3 against a High rival and 7 against a Low rival. Low yields 1 and 5 respectively. High dominates Low for both firms. The Nash equilibrium is mutual High output at (3,3), even though mutual Low at (5,5) would benefit both. Rational firms, acting in self-interest, choose High regardless of the rival's choice, demonstrating how Nash equilibrium in oligopoly can produce collectively suboptimal outcomes through the Prisoners Dilemma structure.

The Cournot model of duopoly is one of the most important applications of Nash equilibrium in oligopoly theory. Each firm selects its profit-maximizing output taking the rival's output as given. The Nash equilibrium occurs where both firms' best-response functions intersect, meaning each firm is simultaneously producing the best response to the other's output level. At this point, neither firm can improve its profit by changing output alone.

When the payoff structure of an oligopoly game makes mutual high pricing a Nash equilibrium, no individual firm has an incentive to undercut. Each firm is best-responding to rivals' prices by maintaining its own high price. This tacit coordination through Nash equilibrium explains how prices can remain elevated in concentrated markets without explicit collusion. The equilibrium is self-enforcing purely through rational self-interested behavior.

The Bertrand paradox states that when two firms compete by setting prices for identical products, the Nash equilibrium drives prices down to marginal cost, identical to the perfectly competitive outcome. Each firm has an incentive to undercut the rival by a tiny amount to capture the entire market, which continues until price equals marginal cost. Despite the market having only two firms, the Bertrand Nash equilibrium eliminates economic profit, contrasting sharply with the Cournot Nash equilibrium.

Nash equilibrium analysis reveals why collusion is unstable: the jointly optimal collusive outcome is not self-enforcing. Each firm earns even more by secretly cutting price or raising output while the rival maintains the collusive agreement. Because defection is individually rational, the collusive outcome fails the Nash equilibrium condition. The Nash equilibrium instead lands at mutual defection, explaining why antitrust enforcement is needed to prevent the temporary cooperation that causes consumer harm before eventually breaking down.

Cournot and Bertrand models both use Nash equilibrium to characterize stable outcomes in quantity and price competition respectively. Collusion is inherently unstable because each firm individually benefits from defecting, preventing the collusive outcome from satisfying the Nash equilibrium condition. The claim that Nash equilibrium always maximizes joint profit is false: in Prisoners Dilemma structures common in oligopoly, the Nash equilibrium leaves all firms earning less than the cooperative maximum.

The Cournot Nash equilibrium is found at the intersection of both firms' best-response functions. At this point, Firm 1 is producing the profit-maximizing quantity given Firm 2's equilibrium output, and Firm 2 is doing the same given Firm 1's equilibrium output. Neither firm can increase profit by changing output unilaterally. This intersection of best-response functions is the defining geometric and analytical characterization of Nash equilibrium in the Cournot duopoly model.

In repeated games, the threat of future punishment makes defection from cooperation costly. A trigger strategy commits a firm to revert to the competitive Nash equilibrium forever if any rival defects. If the present value of cooperation exceeds the short-run gain from defection plus the long-run loss from triggering punishment, firms maintain cooperation. This Folk Theorem result explains why oligopolists in long-run relationships can sustain outcomes above the single-shot Nash equilibrium without formal agreements.

A Nash equilibrium is confirmed when no firm can improve its payoff by deviating unilaterally. Since Firm A would earn $10M by deviating compared to $12M at the current strategy, deviating would reduce Firm A's payoff. Firm A has no incentive to deviate given Firm B's strategy. If Firm B's strategy also satisfies the same condition, the current profile is a Nash equilibrium. This direct payoff comparison is the standard method for verifying Nash equilibrium in oligopoly models.

In the Stackelberg model, the leader commits to a higher output knowing the follower will best-respond by producing less. The subgame perfect Nash equilibrium involves the leader maximizing profit given the follower's best-response function, resulting in higher leader output and lower follower output than Cournot equilibrium quantities. Total industry output is typically higher than in Cournot, driving prices lower. The first-mover advantage in Stackelberg produces an asymmetric Nash equilibrium unavailable in simultaneous Cournot competition.

The mode of competition dramatically affects the Nash equilibrium outcome. Bertrand competition with identical products drives prices to marginal cost and eliminates economic profit. Cournot quantity competition produces higher prices and positive profits. With differentiated products, Bertrand equilibrium prices exceed marginal cost. These differences arise because the strategic variable, price versus quantity, changes the nature of firms' best-response functions and therefore the location and character of the Nash equilibrium.

Nash equilibrium provides a rigorous explanation for why oligopoly inefficiency is persistent rather than temporary. At the Nash equilibrium, each firm is already maximizing its own profit given rivals' strategies. No single firm benefits from cutting price to competitive levels unilaterally; doing so would reduce its own payoff. The self-enforcing nature of Nash equilibrium means the inefficient outcome is stable and will not be corrected by rational self-interested behavior alone, justifying regulatory attention.

Nash equilibrium is applied across multiple oligopoly models. Cournot equilibrium uses quantity best-response functions. Bertrand equilibrium identifies price competition outcomes. Repeated game analysis explains tacit cooperation through trigger strategies. The claim that Nash equilibrium guarantees perfectly competitive outcomes is false: Cournot equilibrium produces prices above marginal cost and positive profits, and even Bertrand competition with differentiated products does not replicate perfect competition results.

Launching yields $4B if the rival launches and $9B if it does not. Not launching yields $2B and $6B respectively. Since $4B exceeds $2B and $9B exceeds $6B, launching dominates not launching for each firm. Both firms launch in the Nash equilibrium at ($4B, $4B), despite both preferring ($6B, $6B). The Nash equilibrium persists because individual rationality traps both firms in the inferior outcome, a classic Prisoners Dilemma in an oligopoly investment context.