# Tacit collusion

Tacit collusion occurs where firms undergo actions that are likely to minimise a response from another firm, e.g. avoiding the opportunity to price cut an opposition. Put another way, two firms agree to play a certain strategy without explicitly saying so. Oligopolists usually try not to engage in price cutting, excessive advertising or other forms of competition. Thus, there may be unwritten rules of collusive behavior such as price leadership (tacit collusion). A price leader will then emerge and sets the general industry price, with other firms following suit. For example see the case of British Salt Limited and New Cheshire Salt Works Limited.[1]

## Duopoly example

Tacit collusion is best understood in the context of a duopoly and the concept of game theory (namely, Nash equilibrium). Let's take an example of two firms A and B, who both play an advertising game over an indefinite number of periods (effectively saying 'infinitely many'). Both of the firms' payoffs are contingent upon their own action, but more importantly the action of their competitor. They can choose to stay at the current level of advertising or choose a more aggressive advertising strategy. If either firm chooses low advertising while the other chooses high, then the low-advertising firm will suffer a great loss in market share while the other experiences a boost. However if they both choose high advertising, then neither firms' market share will increase but their advertising costs will increase, thus lowering their profits. If they both choose to stay at the normal level of advertising, then sales will remain constant without the added advertising expense. Thus, both firms will experience a greater payoff if they both choose normal advertising (however this set of actions is unstable, as both are tempted to defect to higher advertising to increase payoffs). A payoff matrix is presented with numbers given:

Firm A normal advertising Each earns $50 profit Firm A:$0 profit
Firm B: $80 profit Firm A aggressive advertising Firm A:$80 profit
Firm B: $0 profit Each earns$15 profit

Notice that Nash's equilibrium is set at both firms choosing an aggressive advertising strategy. This is to protect themselves against lost sales. Note also that this game is an example of a prisoner's dilemma.

In general, if the payoffs for colluding (normal, normal) are greater than the payoffs for cheating (aggressive, aggressive), then the two firms will want to collude (tacitly). Although this collusive arrangement is not an equilibrium in the one-shot game above, repeating the game allows the firms to sustain collusion over long time periods. This can be achieved, for example if each firm's strategy is to undertake normal advertising so long as its rival does likewise, and to pursue aggressive advertising forever as soon as its rival has used an aggressive advertising campaign at least once (see: grim trigger) (this threat is credible since symmetric use of aggressive advertising is a Nash equilibrium of each stage of the game). Each firm must then weigh the short term gain of $30 from 'cheating' against the long term loss of$35 in all future periods that comes as part of its punishment. Provided that firms care enough about the future, collusion is an equilibrium of this repeated game.

To be more precise, suppose that firms have a discount factor $\delta$. The discounted value of the cost to cheating and being punished indefinitely are

$\sum_{t=1}^{\infty}\delta^t 35=\frac{\delta}{1-\delta}35$.

The firms therefore prefer not to cheat (so that collusion is an equilibrium) if

$30<\frac{\delta}{1-\delta}35\Leftrightarrow\delta>\frac{6}{13}$.

## Forms

Classical (economic theory) holds that price stability is ideally attained at a price equal to the incremental cost of producing additional units. Monopolies are able to extract optimum revenue by offering fewer units at a higher cost.

An oligopoly where each firm acts independently tends toward equilibrium at the ideal, but such covert cooperation as price leadership tends toward higher profitability for all, though it is an unstable arrangement.

In barometric firm price leadership, the most reliable firm emerges as the best barometer of market conditions, or the firm could be the one with the lowest costs of production, leading other firms to follow suit. Although this firm might not be dominating the industry, its prices are believed to reflect market conditions which are the most satisfactory, as the firm would most likely be a good forecaster of economic changes.