Nash Equilibrium Applied to Monopolies and Collusion
Article: https://www.law360.com/articles/1528513/unitedhealth-deal-is-not-a-merger-to-monopoly-judge-says
Recently, there was a legal case and decision made on UnitedHealth’s 13.8 billion dollar bid for the acquisition of Change Healthcare. The United Department of Justice (DOJ) believed that this merger would result in a monopoly “for health insurance claims processing technology.” But why is a monopoly so bad?
To answer this question, we can look towards the concepts we learned in class of Nash equilibriums. When there are multiple firms in a certain industry selling the exact same product, there is an incentive to price below the competition.
I have attached a chart above to demonstrate how, in a perfect economic bubble, with inelastic demand, the Nash equilibrium will always be to slightly undercut a competitor, leading to both companies offering a lower price. This is applicable to this described transaction as health insurance claim processing will continue to be a necessary service regardless of price (to a reasonable extent). Thus, in the absence of competitors, the corporation in charge will want to charge as high a price as possible since there is nobody there is undercut them. But, the presence of a competitor(s) incentivizes slight undercutting to the point where prices are similar to costs. This is beneficial to the American government because lower prices mean that the dollar has more value, and the American public will have more money to spend on other discretionary purchases, keeping them happy. In addition, the government works for the public, so it would make sense for them to want to help the public by keeping prices for a cost related to health insurance lower.
The article notes the lawyers arguing for the corporation believed that there was no breach of ant-trust/monopoly, and used the argument that there would be a divestiture in the sole overlapping business unit. So why would a company need to go as extreme as divesting from the company compared to simply having two separate business units? The answer to that is collusion. Looking back at the chart above, it is clear that if a single entity stood to gain from both competing firms, they would look towards which strategy would result in the greatest total profit. That would be the bottom right square. This means that if one entity controls both strategies and stands to benefit equally, consumers will be faced with higher prices.
I’ve added a more extreme example below that demonstrates how this could spiral out of control.
In this case, a mixed strategies equilibrium could be used that would include both the upper left corner and bottom right corner. However, a mixed strategies equilibrium is only used when your opponent’s response is unknown. When it is known, the most optimal strategy can be employed, which would be the bottom right corner. Thus, collusion can result in astronomical prices for the US public, which is why it has been illegal for over a century (Sherman AntiTrust + Clayton AntiTrust).