At this stage of the epidemic, we have increasing numbers of coronavirus infections, due to seasonality of the virus and slack on the epidemic control, both from the policy side and from the citizen side. At the same time, vaccination campaigns have become, and will eventually extinguish the virus, provided no new surprises pop up.
It is tempting to vaccinate as fast as possible, and almost at all costs. However, as firms are profit maximizing agents, production capacity is limited. If they were not, the recipe for coronavirus vaccines would be available at market prices to any market player willing to produce it. This would be welfare optimal. Now suppose firms wouldn't care about profits and countries were valuing lives saved infinitely more than the realisation of monetary added value in the pharmaceutical sector, then the vaccine recipe would be available for free. Of course, this is not the case, although the University of Oxford has convinced its producing partner AstraZeneca (which has little experience making vaccines) to sell coronavirus vaccines at cost price, and the Pfizer-BioNTech and Moderna vaccines have a similar pricing to influenza viruses - which is about ten times the Oxford-AstraZeneca price, begging the question whether the market is competitive. Probably not.
Either way, countries have put their bids for the coronavirus vaccines, and we are now seeing the winners and losers from this bid. Some countries are quick to approve the vaccines and pay higher prices than others. Rushing through procedures (at a potential cost in safety) and paying a premium price boil down to the same thing. It appears that rich countries that have individually negotiated prices, have faster access, but at a higher cost. Poorer countries without bargaining leverage would have slow access, at a high cost. Examples are Israel and the UK. Countries that group their purchases, notable the European Union, have lower costs, but slower access. There is little internal inequality between the countries from the EU. This means for Bulgaria or Portugal, it is undoubtedly interesting to join the coordinated purchase, but countries like Germany, Sweden, and the Netherlands may wonder whether it wouldn't have been more advantageous to order separately.
This is a game theoretical bidding problem. To begin with, assume demand for the vaccine is inelastic: any country wants it at almost any price. The propensity to pay is equal to the cost of a raging coronavirus epidemic. Supply, on the other hand, has a normal, upward slope. In absence of competition, the producer will be able to set prices far above the market equilibrium price. In itself, such disproportionate producer surpluses are not problematic, but the resulting inequality and the inability to share the welfare that has been generated, is. To play the game, suppose that countries can either put a low bid (L) at the equilibrium price, or a high bid (H) at a level above equilibrium. In absence of perfect competition, in order to avoid inequalities, the first-best solution would be to ensure countries bargain collectively and put low bids. However, single countries putting a high bid could undercut this strategy and leave the rest of the world at a massive disadvantage, as the the high-bidding country would be the only one disposing of full production capabilities. As a result, without coordination, countries will put high bids and will benefit from it individually, but if all countries do so, we end up in a second-best equilibrium.