All questions
Question 1
In an infinitely repeated game, two firms can either compete aggressively (A) or accommodate (C). Per-period payoffs are: (A,A) = (2,2), (A,C) = (6,1), (C,A) = (1,6), (C,C) = (4,4). Using a trigger strategy where firms accommodate until someone deviates, then compete aggressively forever, what is the minimum discount factor required to sustain accommodation?
- δ≥0.5, because the short-term gain from deviation must be offset by the long-term loss from punishment (correct answer)
- δ≥0.67, because the present value of cooperation must exceed the one-time deviation benefit plus discounted punishment
- δ≥0.75, because the sustainability condition requires that future cooperation benefits outweigh immediate defection gains
- δ≥0.8, because trigger strategies require a high discount factor to make the infinite punishment threat credible
Explanation: The sustainability condition compares cooperating forever (getting 4 each period) versus deviating once (getting 6) then being punished forever (getting 2 each period). Cooperation gives: 1−δ4. Deviation gives: 6+1−δ2δ. Setting cooperation ≥ deviation: 1−δ4≥6+1−δ2δ. Multiplying by (1−δ): 4≥6(1−δ)+2δ=6−6δ+2δ=6−4δ. So 4δ≥2, thus δ≥0.5. Choices B, C, and D use incorrect calculations of the sustainability condition or misunderstand the trigger strategy payoffs. Question 2
Two firms are considering whether to enter a new market. If both enter, each loses $2 million. If only one enters, it gains $5 million while the other gains $0. If neither enters, both gain $0. Which of the following best describes the Nash equilibrium outcome and its efficiency?
- Multiple pure strategy equilibria exist, and the outcome is Pareto efficient since no player can improve without harming the other
- A unique mixed strategy equilibrium exists where each firm enters with probability 0.4, resulting in expected payoffs of $0 for both firms
- Two pure strategy Nash equilibria exist where exactly one firm enters, and both equilibria are Pareto efficient compared to mutual entry (correct answer)
- No pure strategy equilibrium exists, and the mixed strategy equilibrium yields expected payoffs of $1 million for each firm with entry probability 0.2
Explanation: This is a coordination game with two pure strategy Nash equilibria: (Enter, Stay Out) and (Stay Out, Enter). In each equilibrium, one firm gets $5M and the other gets $0, totaling 5M.TheseareParetoefficientcomparedtomutualentry(−2M each = -4Mtotal)andtheno−entryoutcome(0 total). Choice A is wrong because multiple equilibria exist but the reasoning about Pareto efficiency is incomplete. Choice B incorrectly calculates the mixed strategy probabilities. Choice D has wrong probability and payoff calculations for the mixed strategy equilibrium. Question 3
In a finitely repeated prisoner's dilemma game played for exactly 10 rounds, Player A discovers that Player B is using a "tit-for-tat" strategy (cooperate first, then copy opponent's previous move). If both players cooperate, each gets 3 points per round. If both defect, each gets 1 point per round. If one cooperates and one defects, the defector gets 5 points and the cooperator gets 0 points. What is Player A's optimal strategy?
- Cooperate for all 10 rounds to maximize the total joint payoff and encourage continued cooperation from Player B
- Defect in round 10 only, since Player B cannot retaliate, but cooperate in all previous rounds to maintain mutual cooperation
- Defect in rounds 9 and 10, since Player B's retaliation in round 10 will occur regardless of Player A's round 9 action
- Defect in all rounds from round 8 onward, since backward induction shows cooperation cannot be sustained in the final periods (correct answer)
Explanation: By backward induction, in round 10, Player A should defect regardless of history since there's no future retaliation. Knowing this, in round 9, Player B (using tit-for-tat) will defect in round 10 if Player A defects in round 9, but Player A should still defect in round 9 since the round 10 outcome is already determined. This logic unravels backward: Player A should defect starting from some early round. Given the payoff structure, defecting from round 8 onward is optimal. Choice A ignores the finite horizon problem. Choice B fails to account for the unraveling effect. Choice C partially recognizes unraveling but doesn't go far enough backward.
Question 4
An established firm in a market with significant economies of scale wants to prevent a potential competitor from entering. The established firm sets its output level higher than what would maximize its short-run profit, leading to a market price that is below the monopoly price but above its own average cost. The price is low enough that a new entrant could not cover its average costs. This strategy is best described as:
- predatory pricing.
- limit pricing. (correct answer)
- a Cournot-Nash equilibrium.
- price discrimination.
Explanation: This scenario describes limit pricing. Limit pricing is a strategy where an incumbent firm discourages entry by charging a price lower than the monopoly price. The price is set at a level that is unprofitable for potential entrants, typically because the entrant would capture too small a market share to take advantage of economies of scale. It is distinct from predatory pricing, which involves setting prices below cost to drive existing competitors out of the market, not to deter potential ones.
Question 5
Two firms, Innovate Inc. and TechCorp, produce slightly differentiated smartphones and compete on price. Both firms have identical cost structures. If this market evolves from simultaneous price-setting (Bertrand competition) to a sequential price-setting model where Innovate Inc. acts as the price leader, what is the most likely outcome?
- Innovate Inc. will gain a first-mover advantage and earn higher profits than TechCorp. (correct answer)
- TechCorp will benefit from a second-mover advantage, allowing it to earn higher profits than Innovate Inc.
- Both firms will earn higher profits than in the simultaneous game due to the established price leadership.
- The market price will fall to marginal cost for both firms, and profits will be zero.
Explanation: In sequential price competition with differentiated products (a Stackelberg model of price leadership), there is a first-mover advantage. The leader (Innovate Inc.) anticipates the follower's (TechCorp's) reaction to its price. It then chooses a price that maximizes its own profit, given this reaction. This allows the leader to secure a more favorable market position and earn higher profits than it would in a simultaneous-move (Nash) equilibrium. The follower is forced to react and typically earns lower profits than in the simultaneous game.
Question 6
Two airlines, FlyHigh and JetSet, form the dominant duopoly on a popular route. They face a classic prisoner's dilemma regarding pricing each month. A collusive high-price strategy is profitable for both, but each has an incentive to undercut the other. Under which condition is their tacit collusion least likely to be sustainable over time?
- The market is experiencing rapid, unpredictable fluctuations in demand. (correct answer)
- Both airlines have adopted a clear 'price-matching' guarantee in their advertising.
- The CEOs of both airlines are known to be patient and prioritize long-term gains.
- The industry is heavily regulated, making it extremely difficult for a new airline to enter the route.
Explanation: Tacit collusion is difficult to sustain when it is hard to detect cheating. Rapid and unpredictable fluctuations in demand make it difficult for a firm to know whether a drop in its sales is due to its rival cheating (cutting prices) or due to a general market downturn. This uncertainty makes it harder to implement punishment strategies, thus making collusion less stable. The other options all facilitate collusion: price-matching guarantees create an automatic punishment for defectors, patience (a low discount rate) makes future collusive profits more valuable, and high barriers to entry ensure the game remains between the same players for the long run.
Question 7
An oligopolistic firm operating under the assumptions of the kinked demand curve model currently produces at the 'kink.' The firm's marginal cost curve shifts upward due to a new industry-wide tax, but the new MC curve still passes through the gap in the marginal revenue curve. What is the predicted response of the firm?
- The firm will increase its price and decrease its quantity.
- The firm will keep its price constant but decrease its quantity.
- The firm will keep both its price and quantity constant. (correct answer)
- The firm will decrease its price to gain market share and offset the tax.
Explanation: The kinked demand curve model assumes that rivals will match price cuts but not price increases. This creates a 'kink' in the firm's demand curve at the current price, which in turn creates a vertical discontinuity or 'gap' in the marginal revenue (MR) curve. The profit-maximizing rule is to produce where MR = MC. As long as the marginal cost (MC) curve intersects the MR curve in this vertical gap, even if MC shifts up or down, the profit-maximizing price and quantity (corresponding to the kink) will not change. Therefore, the firm will absorb the cost increase and keep its price and quantity constant.
Question 8
A duopoly has formed a cartel and is maximizing joint profits by producing the monopoly output level, with each firm producing half of that quantity (q1=q2=QM/2). The market price is the monopoly price, PM. For an individual firm in this cartel, the incentive to cheat by increasing its own output exists because, at its assigned quota:
- its marginal cost is equal to the market price PM.
- the other firm is likely to cheat first, so it is better to be the first to defect.
- its average total cost is at a minimum, allowing for profitable expansion.
- the market price PM is greater than the firm's marginal cost. (correct answer)
Explanation: A cartel maximizes joint profit by producing where the cartel's marginal revenue equals marginal cost (MRcartel=MC). At this total output level, the market price PM is determined by the demand curve, and PM>MRcartel. Since each firm has the same MC, for an individual firm at its quota, PM>MC. This means that if the firm produces one more unit, the revenue it gets from that unit (the price PM) is greater than the cost of producing it (MC). This creates a powerful incentive to cheat on the cartel agreement by producing more than its quota. Question 9
Two firms, A and B, produce an identical product and compete on price. Firm A has a constant marginal cost of $10, and Firm B has a constant marginal cost of $12. There are no fixed costs. In the unique Bertrand-Nash equilibrium, what is the market price?
- $10.00
- $12.00
- A price just below $12.00 (correct answer)
- A price equal to the monopoly price for Firm A
Explanation: In Bertrand competition with asymmetric costs, the low-cost firm (Firm A) has a strategic advantage. Firm B cannot set a price below its marginal cost of $12. Firm A can capture the entire market by setting a price just below Firm B's marginal cost. For example, by setting a price of $11.99, Firm A ensures that Firm B cannot profitably match or undercut it. This price is above Firm A's own marginal cost of $10, so Firm A earns a positive profit on every unit sold. This is a stable equilibrium because Firm A has no incentive to raise the price (it would lose the market to B) or lower it further (it would reduce its own profit margin unnecessarily).
Question 10
Consider two duopoly markets, Market A and Market B. Both markets have identical demand and cost conditions. However, the firms in Market A produce identical, homogeneous products, while the firms in Market B produce differentiated products. If firms in both markets compete on price (Bertrand competition), which of the following is the most likely difference in outcomes?
- Prices and profits will be higher in Market A than in Market B.
- Firms in Market A will earn positive profits, while firms in Market B will earn zero profit.
- The outcomes in both markets will be identical, with prices equal to marginal cost.
- Prices and profits will be higher in Market B than in Market A. (correct answer)
Explanation: When you encounter Bertrand competition questions, focus on how product differentiation affects firms' pricing power and ability to maintain profits above marginal cost.
In Bertrand competition with homogeneous products (Market A), firms compete solely on price since consumers view the products as identical. This creates intense price competition where any firm charging above a competitor's price loses all customers instantly. The result is a "race to the bottom" where firms undercut each other until price equals marginal cost, eliminating economic profits entirely.
However, when products are differentiated (Market B), firms gain some monopolistic power over their specific product variants. Consumers may prefer one firm's product features, quality, or branding, making them less sensitive to small price differences. This consumer loyalty allows firms to charge prices above marginal cost without losing all their customers, enabling positive economic profits.
Option A is backwards—homogeneous products create more intense price competition, not less. Option B incorrectly suggests that homogeneous product firms earn positive profits when they actually face the most severe price competition. Option C ignores the crucial distinction that product differentiation creates: while homogeneous Bertrand competition does drive prices to marginal cost, differentiated products allow prices above this level.
Option D correctly identifies that differentiated products (Market B) enable higher prices and profits than homogeneous products (Market A) because differentiation reduces the perfect substitutability that drives Bertrand competition to competitive outcomes.
Study tip: Remember that product differentiation always softens price competition by giving firms some market power over their unique product variants.
Question 11
Consider a duopoly market for a homogeneous good. If the two firms move from a Cournot-Nash equilibrium to a collusive arrangement that successfully maximizes joint profits, what is the effect on consumer surplus and total producer surplus (profits)?
- Consumer surplus increases, and producer surplus increases.
- Consumer surplus decreases, and producer surplus decreases.
- Consumer surplus increases, and producer surplus decreases.
- Consumer surplus decreases, and producer surplus increases. (correct answer)
Explanation: When analyzing oligopoly market structures, you need to understand how different strategic behaviors affect market outcomes. In a duopoly, firms can either compete (Cournot-Nash) or cooperate (collusion), and each choice creates different effects on prices, quantities, and welfare distribution.
In a Cournot-Nash equilibrium, each firm chooses its optimal quantity given the other firm's quantity, leading to competition that benefits consumers through lower prices and higher total output compared to monopoly. When firms move to successful collusion, they coordinate to maximize joint profits by acting like a single monopolist - reducing total market output and raising prices.
This shift from competition to collusion decreases consumer surplus because consumers face higher prices and reduced quantity. Simultaneously, producer surplus (total profits) increases because the firms capture more economic rent by eliminating the competitive pressure that previously drove prices down toward marginal cost.
Looking at the wrong answers: Option A incorrectly suggests both surpluses increase, which violates the zero-sum nature of this transfer - gains must come from somewhere. Option B wrongly claims producer surplus decreases, but collusion specifically aims to increase joint profits by reducing competition. Option C incorrectly suggests consumer surplus increases when collusion actually harms consumers through higher prices.
Remember this pattern: successful collusion always represents a transfer of surplus from consumers to producers. When you see questions about firms moving from competition to cooperation, expect consumer welfare to decrease and producer profits to increase - it's the fundamental trade-off in antitrust economics.
Question 12
An oligopolistic industry has one firm that is recognized as having an excellent reputation for assessing market demand and cost conditions. Other firms in the industry often wait for this firm to announce its price changes and then promptly match them. This practice allows the firms to coordinate their prices without a formal agreement. This market structure is best described as:
- a Stackelberg model.
- dominant firm price leadership.
- a kinked demand curve model.
- barometric price leadership. (correct answer)
Explanation: This question tests your understanding of different types of oligopolistic coordination, specifically the various forms of price leadership that can emerge when firms want to coordinate without explicit collusion.
The scenario describes a firm with an excellent reputation for market assessment that other firms follow when setting prices. This is the defining characteristic of barometric price leadership (D). In this model, one firm acts as a "barometer" of market conditions—not because it's the largest or most dominant, but because other firms trust its ability to read the market accurately. The leadership role stems from superior information or forecasting ability, and followers adopt the leader's prices because they view them as optimal responses to market conditions.
Let's examine why the other options don't fit: (A) The Stackelberg model involves sequential decision-making where a leader firm chooses output first, knowing followers will react—this focuses on quantity competition, not price coordination based on market expertise. (B) Dominant firm price leadership occurs when the largest firm in the market sets prices and smaller firms act as price-takers—size and market power drive leadership here, not reputation for market assessment. (C) The kinked demand curve model explains price rigidity in oligopolies through firms' expectations about rivals' reactions to price changes, but doesn't involve any leadership structure.
Study tip: Remember that barometric price leadership is about information advantage, while dominant firm leadership is about market power. The key signal in questions is whether the leader's role comes from superior market knowledge or from sheer size and dominance.
Question 13
In a symmetric Cournot duopoly with linear demand P=100−Q and constant marginal cost MC=20 for both firms, if the firms could perfectly collude to maximize joint profits, by what percentage would total industry output decrease compared to the Cournot equilibrium?
- 25% (correct answer)
- 33.3%
- 50%
- 66.7%
Explanation: In Cournot equilibrium, each firm produces qi=3ba−c=3(1)100−20=380, so total output is QC=3160. Under perfect collusion, firms act as a monopoly: MR=100−2Q=MC=20, so QM=40. The percentage decrease is QCQC−QM=31603160−40=3160340=0.25=25%. Choice B incorrectly uses the monopoly output as the base. Choice C assumes output halves. Choice D incorrectly calculates the ratio of monopoly to competitive output. Question 14
Consider a duopoly with two firms producing a homogeneous product. Firm 1 has a lower marginal cost than Firm 2 (MC1<MC2). If these firms compete by setting quantities (Cournot), what is the relationship between their output levels (q1,q2) and profits (π1,π2) in equilibrium?
- q1=q2 and π1>π2.
- q1>q2 and π1>π2. (correct answer)
- q1<q2 and π1>π2.
- q1>q2 and π1=π2.
Explanation: In the Cournot model, a firm's reaction function shows its profit-maximizing output for any given output of its rival. A firm with a lower marginal cost will have a reaction function that is shifted outward, meaning it will produce a higher quantity for any given output level of its competitor. In the Nash equilibrium, where the reaction functions intersect, the lower-cost firm (Firm 1) will produce a greater quantity than the higher-cost firm (Firm 2). Since Firm 1 produces more output and also has a higher profit margin on every unit sold (because price is the same for both but its cost is lower), its total profit will also be higher. Thus, q1>q2 and π1>π2. Question 15
A duopoly faces a market demand curve of P=120−Q, where Q=q1+q2. Both firms have a constant marginal cost of MC=30 and zero fixed costs. If the firms engage in Cournot competition, what is the total quantity produced in the market (Q)?
- 30
- 45
- 60 (correct answer)
- 90
Explanation: In a Cournot duopoly, each firm chooses its quantity to maximize profit, taking the other's quantity as given. Firm 1's profit is π1=(120−q1−q2)q1−30q1. To find the maximum, we set the derivative with respect to q1 to zero, which is equivalent to setting marginal revenue equal to marginal cost. Firm 1's marginal revenue is MR1=120−2q1−q2. Setting MR1=MC, we get 120−2q1−q2=30, which simplifies to Firm 1's reaction function: q1=45−0.5q2. Since the firms are symmetric, Firm 2's reaction function is q2=45−0.5q1. Solving this system of equations, we substitute one into the other: q1=45−0.5(45−0.5q1), which gives q1=30. By symmetry, q2=30. The total market quantity is Q=q1+q2=30+30=60. Question 16
An Incumbent firm (I) and a Potential Entrant (E) are in a sequential game. First, E decides to 'Enter' or 'Stay Out'. If E stays out, the payoff is (10, 0) for (I, E). If E enters, I then decides to 'Accommodate' or 'Fight'. If I accommodates, the payoff is (5, 5). If I fights, the payoff is (2, -2). What is the subgame perfect Nash equilibrium outcome of this game?
- The Entrant stays out because the Incumbent's threat to fight is credible.
- The Entrant enters, and the Incumbent fights.
- The Entrant enters, and the Incumbent accommodates. (correct answer)
- The Entrant stays out, and the Incumbent earns its monopoly profit.
Explanation: We solve this sequential game using backward induction. First, consider the subgame after the Entrant has chosen to 'Enter'. The Incumbent must choose between 'Accommodate' (payoff of 5) and 'Fight' (payoff of 2). A rational Incumbent will choose to Accommodate, as 5 > 2. The threat to fight is not credible. Now, consider the Entrant's initial decision. The Entrant knows that if it enters, the Incumbent will accommodate, leading to a payoff of 5 for the Entrant. If the Entrant stays out, its payoff is 0. Since 5 > 0, the Entrant will choose to 'Enter'. Therefore, the subgame perfect Nash equilibrium outcome is that the Entrant enters and the Incumbent accommodates.
Question 17
An incumbent monopolist is facing a potential entrant. The incumbent can threaten a price war (setting price below its average cost) if the entrant comes into the market. From a game-theoretic perspective, this threat is considered credible only if:
- the incumbent makes a binding public commitment to engage in a price war.
- initiating the price war is the incumbent's profit-maximizing response after the entrant has already entered. (correct answer)
- the incumbent has significantly more financial resources than the potential entrant.
- the price war would result in greater losses for the entrant than for the incumbent.
Explanation: In game theory, a threat is credible if and only if it is in the player's best interest to carry out the threat at the time when the action must be taken. This is the principle of subgame perfection. If, after the entrant has entered the market, the incumbent would earn higher profits (or smaller losses) by accommodating the entrant rather than fighting, the threat to fight is not credible. The potential entrant will anticipate this and enter. Public announcements without commitment (cheap talk) or having more resources do not, by themselves, make the threat credible if the action is not optimal in the subgame.
Question 18
A market is served by a single firm, but there are no barriers to entry or exit for new firms. According to the theory of contestable markets, what price will the incumbent firm choose in the long run?
- The monopoly price that maximizes its profits.
- A price equal to its marginal cost.
- A price equal to its average total cost. (correct answer)
- A price below its average total cost to deter entry.
Explanation: The theory of contestable markets posits that even a single firm will be forced to behave competitively if the market is 'contestable,' meaning there are no barriers to entry or exit. If the incumbent firm were to set a price above its average total cost (ATC) to earn economic profits, a new firm could enter, slightly undercut the price, capture the market, and earn a profit. To prevent this 'hit-and-run' entry, the incumbent firm is forced to set its price equal to its average total cost, thereby earning zero economic profit and making entry unattractive.
Question 19
In a repeated oligopoly game, firms might adopt a 'grim trigger' strategy to sustain collusion. This strategy entails:
- cooperating in the first period, and then in every subsequent period, mimicking the other player's action from the previous period.
- cooperating as long as all other players have cooperated, but if any player defects, then defecting in all future periods. (correct answer)
- always defecting, which is the Nash equilibrium of the one-shot game, regardless of the other players' actions.
- alternating between cooperating and defecting, punishing defection with a defection in the next round only.
Explanation: A grim trigger strategy is a punishment mechanism used to sustain cooperation in a repeated game. It is defined by the following rule: Cooperate in the first period and continue to cooperate as long as all other players have cooperated in all previous periods. However, if any player deviates (defects) from the cooperative strategy even once, the grim trigger player will respond by defecting in every period for the rest of the game. The 'grim' part of the name comes from the fact that the punishment is permanent. Choice A describes a Tit-for-Tat strategy.
Question 20
In a duopoly market for a homogenous good with identical firm costs, how does the total market output and price in a Stackelberg equilibrium compare to the Cournot and collusive (monopoly) equilibria?
- Stackelberg output is greater than Cournot output, and the price is lower. (correct answer)
- Stackelberg output is less than Cournot output, and the price is higher.
- Stackelberg output is the same as the collusive output, but profits are lower.
- Stackelberg output is greater than the collusive output, but less than the Cournot output.
Explanation: Market outcomes can be ranked by competitiveness. Collusion (monopoly) results in the lowest output and highest price. Cournot competition is more competitive, with higher output and a lower price. Stackelberg competition, where a leader commits to an output level, is even more competitive than Cournot. The leader produces more than its Cournot quantity, forcing the follower to reduce its output, but the total market output is higher than in the Cournot equilibrium, and thus the market price is lower. The ranking of total output is: Collusion < Cournot < Stackelberg.