Summary
Duopolies are commonly used when explaining sequential games, because they model the interdependence between two firms. We learn in this Learning Path how duopolists react to each other’s actions, how collusions work and how repeated sequential games may change the essence of a game.Basic definitions:
Duopolies and collusions:
- Cournot duopolies
- Stackelberg duopolies
- Collusion
Repeated games:
Collusion makes allusion to the cooperation between different firms. This cooperation leads to a restrain of market competition, in any of its forms, which translates into higher profits for the firms in detriment of consumer’s welfare. A cartel is an example of firms belonging to the same industry structure which collude to some degree in setting prices and/or output levels. Agreements which have as their object or effect the prevention, restriction or distortion of perfect competition are prohibited. Such agreements include, but are not restricted to, activities such as:
-fixing purchase or selling prices or any other trading condition, directly or indirectly;
-controlling or limiting production levels, markets, technological advances or investments;
-sharing markets or resources supplies.
Legislation in different countries may consider different scenarios and penalties for such agreements, but the main idea is clear: firms behaviour shall not affect the correct functioning of market forces.
A clear example is to consider an industry where there are only two firms (duopoly). Both firms will set their levels of output and prices with the objective of maximizing their joint profits. Many strategies can be used in order to maximize profits which would lead to a multiple Nash equilibria solution. As seen in the figurebelow, collusion maximises aggregate profits for both firms, since the isoprofit curves are tangent. It’s a better equilibrium than the one in Cournot duopolies or Stackelberg duopolies.
However, cartels are not stable. There will always be incentives for each firm to trick the other, and change their output and/or price level in such a way, that they’ll increase their own profit in detriment of the other’s. To avoid this practice, any deviation by any party should be instantly punished; this is known as a trigger strategy. James W. Friedman demonstrated in his paper “A Non-cooperative Equilibrium for Supergames”, 1971, that in this context of infinite interactions, it is possible that collusion occurs due to this punishment strategy. That is, the cartel may endure as long as punishment strategies are so devastating that the benefits derived form deviation would end up being smaller than the benefits of keep colluding. J. W. Fridman put this idea in what is known in game theory as Folk theorem:
The sustainability of the equation will depend mainly in two factors: the credibility of the threat of punishment, and the discount factor. The former is easily understood as a credible threat will ensure no deviations are made, and the latter is related with how much does each party value the profits obtained from the results of following a collusive strategy, compared to the possible profits of changing their strategy.
Factors that guarantee collusion stability:
There are number of factors that affect this collusive equilibrium, such as:
-Number of firms in the market: the higher the degree of concentration in a market the higher the incentives to collude. Firms in highly concentrated markets will tend to collude since all the profits will be distributed amongst fewer firms.
-Multimarket contact: if firms compete in more than one market, the collusive agreement will be more stable. Firms that compete with other firms over many markets can establish trigger strategies that can be applied in all these markets, which will create a more devastating punishment strategy.
-Market transparency: the more transparent a market is, the easier it is to ensure that every firm is following the same strategy and is not deviating from the deal. Collusion will be more difficult in industries where it is harder to detect changes in firm’s prices or output.
-Asymmetry between firms: the bigger the asymmetry between firms, the harder it is for collusion to take place. If firms have different cost structures, the one with the lowest costs will be incentivised to lower its prices, and thus cause the other firm to have to exit the market.
Collusion agreement games:
In game theory, collusion agreements can be described using the extensive form, as depicted in the adjacent game tree. In this case, two firms share the market, already colluding and maintaining high prices. Each firm can decide to stop colluding and start a price war, in order to increase their market share, even force the other to quit the market. Firm 1 can either keep colluding with firm 2, or start a price war. If firm 1 decides to keep colluding, firm 2 will need to make a decision. If they both agree to collude, they will get 5,5. However, if one of them decides to start a price war, the set of payoffs will be either 4,3 or 3,4, depending on which one starts the war (and therefore acquires a greater market share). It’s easy to see that collude-collude is both the Nash equilibrium and a Pareto optimum situation. This result may change when considering repeated games, as seen before.
