A small research drug company, labeled 1, has developed a drug. It does not have the resources to get FDA (Food and Drug Administration) approval or to market the drug, so it considers selling the rights to the drug to a big drug company. Drug companies 2 and 3 are interested in buying the rights but only if both companies are involved in order to spread the risks. Suppose that the research drug company wants $1 billion, but will take $100 million if only one of the two big drug companies are involved. The profit to a participating drug company 2 or 3 is $5 billion, which they split. Here is a possible characteristic function with units in billions:
because any coalition that doesn’t include player 1 will be worth nothing.
(a) Find the normalized characteristic function and find the core using the normalized characteristic function.
(b) The least core using normalized allocation is
Find the least core in unnormalized allocations.