Based on Brams and Taylor (2000). Suppose that Eli Lilly and Pfizer are going to merge. Merger negotiations must settle the following issues:
■ What will the name of the merged corporation be?
■ Will corporate headquarters be in Indianapolis (Lilly wants this) or New York (Pfizer wants this)?
■ Which company’s chairperson will be chairperson of the merged corporation?
■ Which company gets to choose the CEO?
■ On the issue of layoffs, what percentage of each company’s view will prevail?
Brams developed a remarkably simple method for the two adversaries to settle their differences. (This same method could be used to settle differences between other adversaries, such as a husband and wife in a divorce, Arab and Israel in Middle East, and so on.) Each adversary allocates 100 points between all of the issues. These allocations are listed in the file P04_84.xlsx. For example, Lilly believes headquarters is worth 25 points, whereas Pfizer thinks headquarters is only worth 10 points. Layoffs may be divided (for example, Lilly might get 70% of the say in layoffs and Pfizer 30%), but on all other issues, only one company gets its way. The adjusted winner procedure says that the best way to make decisions on each issue is to:
■ give each adversary the same number of points;
■ ensure that each company prefers its allocation to the allocation of its opponent;
■ maximize the number of points received by either participant.
Such a solution is equitable (because each party receives the same number of points) and is envy-free (because neither side prefers what its opponent receives to what it receives). It can also be shown that the adjusted winner procedure yields a Pareto optimal solution. This means that no other allocation can make one player better off without making the other player worse off. Find the adjusted winner solution to the merger example. Also show that the adjusted winner solution for this example is Pareto optimal.