Market Structures, Costs and Revenue: Question 8

Worked solution

Setting out the game

The payoff table gives each firm’s own profit as the first-named figure in each cell, and the rival’s profit as the second-named figure, for every combination of the two firms’ choices:

Part (a): Two specific payoffs for NovaChem

If both firms restrict output (top-left cell), NovaChem earns $40m.

If NovaChem maximises output while PolyForge restricts (bottom-left cell), NovaChem earns $55m.

Part (b): Why maximising output is NovaChem’s dominant strategy

A dominant strategy is one that gives a firm its best outcome no matter what the rival chooses. Checking both of PolyForge’s possible choices from NovaChem’s point of view:

• If PolyForge restricts output: NovaChem earns $40m by also restricting, but $55m by maximising. Maximising is better ($55>40$).
• If PolyForge maximises output: NovaChem earns $10m by restricting, but $25m by maximising. Maximising is still better ($25>10$).

Since maximising output gives NovaChem a strictly higher profit than restricting output regardless of what PolyForge decides, maximising output is NovaChem’s dominant strategy. (By the same reasoning applied to the columns of the table, maximising output is also PolyForge’s dominant strategy.)

Part (c): The Nash equilibrium

A Nash equilibrium is an outcome where neither firm can raise its own profit by unilaterally changing its own choice, given the other firm’s choice. Since maximising output is a dominant strategy for both firms, both firms maximising output is the Nash equilibrium of this game: at (Maximise, Maximise), NovaChem cannot do better by switching to restricting output (its profit would fall from $25m to $10m), and the same is true for PolyForge.

Combined annual profit at this outcome: $25 + 25 = 50$

This is $50m combined. Lower than the $80m the two firms would earn together ($40+40$) if both had restricted output instead, which is exactly what makes this a Prisoner’s Dilemma: the individually rational outcome for each firm leaves both firms worse off than if they had cooperated.

Part (d): Can NovaChem and PolyForge sustain collusion?

In the single-period version of this game shown by the payoff table, both firms have a clear private incentive to cheat on any agreement to restrict output, since Part (b) shows that maximising output raises each firm’s own profit whichever choice the rival makes. If the game were played only once, this incentive to cheat would be expected to break any collusive agreement, pulling the outcome down to the lower joint-profit Nash equilibrium of $25m each rather than the $40m each available through cooperation.

In reality, however, NovaChem and PolyForge are likely to interact repeatedly over many years rather than just once, and this repetition changes the incentives considerably. If one firm cheats by secretly maximising output, the other firm can observe the resulting fall in price or its own lost sales and retaliate in future periods, for example, by permanently reverting to maximising output itself, or by starting a price war. The threat of this future retaliation can make honouring the agreement more profitable overall than the short-term gain from cheating, supporting more stable collusion than the one-off payoff table alone would predict.

Several other factors also affect how stable this particular duopoly’s collusion is likely to be. Because there are only two firms, each can monitor the other’s output relatively easily, making cheating harder to hide than in a market with many firms. A homogeneous, easily comparable product such as an industrial resin also makes any secret price-cutting or extra output easy for the rival to detect. High barriers to entry would help protect the higher cartel price from being undercut by new entrants attracted by the higher profits. Against this, unstable or falling demand for the resin, or the risk of investigation and prosecution given that cartels are illegal in most countries, would both tend to weaken the firms’ willingness to sustain a formal agreement.

Overall, while the one-off game predicts collusion should collapse, the repeated nature of the firms’ real relationship, combined with there being only two easily-monitored firms and high barriers to entry, means sustained collusion is a realistic possibility, though it remains fragile, since each firm always retains a short-term incentive to cheat.

Final answers

• (a) Both restrict $\Rightarrow$ NovaChem earns $40m; NovaChem maximises while PolyForge restricts $\Rightarrow$ NovaChem earns $55m
• (b) Maximising output beats restricting for NovaChem against both of PolyForge’s choices ($55m > $40m, and $25m > $10m), so it is NovaChem’s dominant strategy
• (c) Nash equilibrium $=$ (Maximise, Maximise); combined profit $=$ $50m
• (d) Likely unstable in a one-off game, but repeated interaction, easy monitoring between just two firms, and entry barriers can support more stable collusion in practice, though each firm always retains an incentive to cheat