Strategic competition and collusion

1. Strategic competition and collusion Oligopolists need to ensure that they all restrict output – collusion is sustained AND (in the same way as monopolists) they also need to deter entry of new firms

2. Sustaining collusion – not so easy in a prisoners’ dilemma • Revision of prisoners’ dilemma generally and in an oligopoly context

3. The prisoners’ dilemma • The payoffs are years in prison • Use the underlining method to find the Nash Equilibrium

4. The Nash equilibrium The Nash equilibrium is also a dominant strategy equilibrium. So game theorists believe that the predicted outcome is very convincing; confession is a dominant strategy for both players and yet…..

5. The equilibrium of the prisoners’ dilemma • The equilibrium is {confess, confess} • But both would be better off if neither confessed • The dilemma for the prisoners’ is that they would both be better off if they co-operated with each other (by not confessing) but it is individually rational for them both to confess • in any other strategy combination there is an incentive for one of the prisoners to deviate

6. A more general interpretation of the prisoners’ dilemma • Confess implies cheating on (or defection from) some mutually beneficial, but not necessarily explicit agreement (to deny): non-cooperation • To deny implies some kind of working together or collusion or cooperation between the players

7. The generalised PD problem c > a > d > b What is the dominant strategy equilibrium (DSE)?

8. The generalised PD problem Since c> a and d > b the DSE is: {not cooperate, not cooperate} But both players would be better off cooperating since a > d Remember that c > a > d > b

9. GENERALISATION • Any game with this payoff structure is a Prisoners’ Dilemma • The players do not have to be prisoners

10. SMALL GROUP WORK • Discussion questions on the Prisoners’ Dilemma • Why does the group think so much attention has been given to the prisoners’ dilemma in (i) economics and (ii) the social sciences more generally? • Describe three or more examples of a prisoners’ dilemma that is faced by real people (acting individually or in groups) in real life. • How, if at all, are the prisoners’ dilemma problems described in (2) above resolved? If they are not resolved in practices how might they be resolved?

11. The prisoners’ dilemma and cooperation/collusion between 2-firms in an Oligopoly (Duopoly) • Alpha and Beta are two oil producers who share the market. • Each firm has two possible strategies: • 1. High output –Lower price • Low output – higher price • Each chooses its strategy without knowing what strategy the other has chosen • (equivalent to simultaneous or hidden moves)

12. Prisoners’ dilemma and oligopoly • four possible outcomes: • Both produce a high output • OK profits (1 billion) • Both produce a low output – collusive agreement. • E.g. by forming a cartel: Arrangements entered into voluntarily which restrict firms’ future actions (Alpha and Beta each agree to restrict output to keep prices high). • High profits (2 billion) • Beta produces low output but Alpha produces high output. • Beta has very low profits (0), Alpha very high profits (3) • Alpha produces low output but Beta produces high output. • Beta has very high profits (3), Alpha very low profits (0)

13. The Prisoners’ Dilemma and oligopoly collusion Beta’s Strategy Compete on price: high output Don’t compete on price: low output Alpha’s Strategy Compete on price: high output 1 1 3 0 Don’t compete on price: low Output 0 3 2 2 Both firms would improve profits if they colluded to form a cartel in which each agreed to limit price competition and restrict output. But what is the likely outcome (the Nash Equilibrium) of this strategic game?

14. The Prisoners’ Dilemma and oligopoly collusion Beta’s Strategy Don’t compete on price: low output Compete on price: high output Alpha’s Strategy Compete on price: high output 1 1 0 3 Don’t compete on price: low Output 2 0 3 2 Although both firms would have higher profits if they colluded to restrict output there is an incentive for each to cheat because each firm could increase its profits by increasing its output as long as the other firm keeps to the agreement and keeps its own output low. The likely outcome is that they both produce high output.

15. Implications • Collusion between oligopolists is undesirable but it is also unlikely to be stable • firms are likely to be involved in a ‘prisoners’ dilemma’ – especially given that collusion is illegal and subject to punishment • they can agree to collude BUT this still leaves problem of enforcement. • So regulators don’t have to worry? • Depends - how realistic is the analysis?

16. Test your understanding • Collusion: Explain why game theorists predict that collusion between oligopolists is likely to be fragile

17. Exercise on oligopoly