Inducing efficiency in oligopolistic markets with increasing returns to scale

We consider a Cournot Oligopoly market of firms possessing increasing returns to scale technologies (which may not be identical). It is shown that an external regulating agency can increase total social welfare without running a deficit by offering to subsidize one firm an amount which depends on the output level of that firm and the market price. The firms bid for this contract, the regulator collects the highest bid upfront and subsidizes the highest bidding firm. It is shown that there exists a subsidy schedule such that (i) The regulator breaks even (ii) The subsidized firm obtains zero net profit and charges a price equal to its average cost (iii) Every other firm willingly exit the market and (iv) Market price decreases, consumers are better off and total welfare improves.