## Politics as Nash bargaining

In our previous post, we presented this beautiful essay by Avinash Dixit and David McAdams, who use game theory to analyze the year-long political impasse over the U.S. Supreme Court. We now wish to say a few more words about Dixit and McAdams’s model. In essence, they model the standoff between the President and the Senate as a Nash bargaining game. In the simplest version of this game, there are two players (let’s call them Player 1 and Player 2), and each player requests a portion of some good, such as a fixed amount of money x (or a Supreme Court justice with liberal or conservative political views). If the total amount requested by both players is less than x (or if the proposed Supreme Court justice has political views acceptable to both players), then both players get their request. If, however, their total request is greater than x, neither player gets their request. (As an aside, notice that a bargaining game can also be modelled as an equilibrium selection problem, since many bargaining situations have multiple equilibria with varying payoffs for each player.) So, how much should a player request in this game? x/2? What if you don’t know the value of ahead of time? The answers to these questions depend in large part on the disagreement points or outside options of the players: d1 for Player 1 and d2 for Player 2. In brief, the respective disagreement points of the players are the amounts (i.e. some fraction of x) either player can expect to receive if they are unable to reach an agreement. In the case of Justice Scalia’s replacement, however, the outside options of the parties depend on who wins the election in November (Clinton or Trump) and on whether the Republicans will retain control of the Senate, and these events, in turn, are purely probabilistic ones.