A two-firm pricing game and collusion
| English | Español |
|---|---|
| interdependence/ˌɪntədɪˈpendəns/ | interdependence |
| dominant strategy/ˈdɒmɪnənt ˈstrætədʒi/ | dominant strategy |
| Nash equilibrium/næʃ ˌiːkwɪˈlɪbrɪəm/ | Nash equilibrium |
| cartel/kɑːˈtel/ | cartel |
| price leadership | price leadership |
A decision you can investigate
- Two firms could both earn more by keeping a high price, yet each can gain by cutting while the other stays high.
- Check the incentives cell by cell before predicting the outcome.
Build the explanation
- Interdependence 相互依赖 means a firm’s payoff depends on both its choice and its rival’s. In a simple simultaneous two-firm game, identify each firm’s best response to each possible rival choice. A dominant strategy 占优策略 is best against either rival choice; a Nash equilibrium 纳什均衡 has no profitable unilateral deviation. Do not confuse the highest combined payoff with individually stable choices.
- A cartel 卡特尔 coordinates decisions such as output or prices; members can have incentives to cheat. Price leadership 价格领导 means others follow a leading firm’s price changes and is not by itself proof of an agreement. Price wars are repeated competitive cuts, possibly eroding margins. Collusion may seek higher profit and reduced uncertainty; non-collusion can reflect entry, different costs/objectives, cheating incentives and restrictions on coordination. Repeated interactions and credible responses can alter incentives, but cannot be inferred from a one-round table.
Work through the evidence
- Use fictional profits in order(A,B). If both choose High, payoffs are(8,8); A Low/B High gives(12,2); A High/B Low gives(2,12); both Low gives(4,4). Against B High, A prefers12 to8; against B Low, A prefers4 to2. B has the symmetric comparisons, so Low is dominant for both and(Low,Low) is a Nash equilibrium. Both High yields combined16 rather than8, but each can gain from deviating when the other stays High.
- A coordinated high-price outcome may benefit producers through margins and predictability, but consumers can face higher prices, less output and choice. Workers may gain stable employment or face reduced output/investment; government may receive higher taxable profit but face enforcement costs and welfare losses. The table’s profit total is not social welfare: consumer surplus, resource costs and external effects are not shown.
Against B High, what is A’s best response?
Compare A’s first payoff12 with8.
Which cell is stable against unilateral deviation?
At Low/Low, changing alone lowers own payoff4→2.
Following a leading firm’s price is sufficient evidence of an explicit cartel agreement.
Similar responses can have other causes; conduct and agreement require evidence.
Test the limits
- The game assumes known payoffs, two specified choices and one simultaneous round; it is not a complete model of every oligopoly. Do not select a cell using only the first payoff or assume that both firms maximize the sum. In repeated markets, monitoring, punishment, demand changes and entry can matter; the one-shot result remains conditional.
- Parallel prices can follow similar costs or demand without an agreement. Coordination can reduce waste or uncertainty but can also restrict rivalry; actual rules and evidence vary. This lesson diagnoses incentives and stakeholder effects, not instructions to coordinate real pricing. Profit gains for firms do not by themselves establish benefits for consumers or workers.
What does combined profit16 at High/High establish?
The table omits consumer and external effects and each firm has a deviation incentive.
Apply and explain your answer
- Why is(High,High) not stable in the one-shot table despite a larger combined profit?
- Either firm can increase its own payoff8→12 by choosing Low while the other stays High.
Match the terms to their meanings.
Use each term for its stated economic relationship.
Use the terms precisely
- interdependence: A firm’s outcome depends on its decisions and the anticipated responses of significant rivals.
- Nash equilibrium: A combination of choices where no player can improve its payoff by changing only its own choice.
- dominant strategy: A choice giving a player its highest payoff for every stated rival choice.
- cartel: A group coordinating decisions such as prices or output.
- price leadership: A pattern where other firms follow a leading firm’s price changes.
Use fictional profits in order(A,B). If both choose High, payoffs are(8,8); A Low/B High gives(12,2); A High/B Low gives(2,12); both Low gives(4,4). Against B High, A prefers12 to8; against B Low, A prefers4 to2. B has the symmetric comparisons, so Low is dominant for both and(Low,Low) is a Nash equilibrium. Both High yields combined16 rather than8, but each can gain from deviating when the other stays High. A coordinated high-price outcome may benefit producers through margins and predictability, but consumers can face higher prices, less output and choice. Workers may gain stable employment or face reduced output/investment; government may receive higher taxable profit but face enforcement costs and welfare losses. The table’s profit total is not social welfare: consumer surplus, resource costs and external effects are not shown.
The game assumes known payoffs, two specified choices and one simultaneous round; it is not a complete model of every oligopoly. Do not select a cell using only the first payoff or assume that both firms maximize the sum. In repeated markets, monitoring, punishment, demand changes and entry can matter; the one-shot result remains conditional. Parallel prices can follow similar costs or demand without an agreement. Coordination can reduce waste or uncertainty but can also restrict rivalry; actual rules and evidence vary. This lesson diagnoses incentives and stakeholder effects, not instructions to coordinate real pricing. Profit gains for firms do not by themselves establish benefits for consumers or workers.
Interdependence means a firm’s payoff depends on both its choice and its rival’s. In a simple simultaneous two-firm game, identify each firm’s best response to each possible rival choice. A dominant strategy is best against either rival choice; a Nash equilibrium has no profitable unilateral deviation. Do not confuse the highest combined payoff with individually stable choices.