too small, it is now possible for non-co-operative collusion to occur. Suppose that firm B plays "trigger" strategy, which is to choose low output in period 1 and in any subsequent period provided that firm A has never produced high output, but to produce high output forever more once firm A ever produces high output. That is B co-operates with A unless A "defects", in which case B is triggered into perpetual non-co-operation. If A were also to adopt the "trigger" strategy, then there would always be collusion and each firm would produce low output. Thus the discounted value of this profit flow is:2+2w+2w^2+2w^3+=2/(1-w) If fact A gets this pay-off with any strategy in which he is not the first to defect. If A chooses a strategy in which he defects at any stage, then he gets a pay-off of 3 in the first period of defection (as B still produces low output), and a pay-off of no more than 1 in every subsequent period, due to B being triggered into perpetual non-co-operation. Thus, A's pay-off is at most3+w+w^2+w^3+=3+w/(1-w) If we will compare these two results, we will get that it is better not to defect so long as W * (or =) ? We can conclude that is the firms give enough weight to the future, then non-co-operative collusion can be sustained, for example, by "trigger" strategies. The "trigger" strategies constitute a Nash equilibrium = self-sufficient agreement. However it is not enough for a firm to announce a punishment strategy in order to influence the behaviour of rivals. The strategy that is announced must also be credible in the sense that it must be understood to be in the firm's self-interest to carry out its threat at the time when it becomes necessary. It must also be severe in a sense that the gain from defection should be less than the losses from punishment. But because it is possible that mistakes will be made in detecting cheating (if, for example, the effects of unexpected shifts in output demand are misinterpreted ...
