With the next presidential election coming up, every participating political party has reasons to worry. On the Republican side, the Republican Establishment (core members or anyone who held office) is worried about presidential candidates Trump and Cruz. Both men are extremely popular and at the forefront on the Republican side. The Republican Establishment would like instead either Rubio ,Christie, Kasich or Bush . However, referred to as the “Establishment 4”,these candidates are fighting amongst instead of Trump or Cruz.
Game Theory suggests that the solution to the Republican Establishment’s dilemma would be to have a focal point within the Establishment 4. The idea of having a focal point is that voters would tend towards one of the Establishment 4 due to social awareness or pressure. This would bring a spot light, normally on Trump or Cruz, on one of the Establishment 4 ,thus increasing their chances of competing with Trump or Cruz. The problem is that the Establishment 4 are engaging in an anti-coordination game. In particular, it could be thought of as a “Hawk-Dove” game. If everyone acts passively towards each other, they could evenly divide up the voters that have not sided with Trump or Cruz. If they all act aggressively, they risk leaving those voters confused and unable to decide. This could be thought as killing votes, as the voters cannot decide , therefore, no one gets their votes. The solution the Republican Establishment is looking for in this “Hawk-Dove” is one where a single candidate acts aggressively and the other 3 act passively (ideally drop out).
This solution , however, requires that the Establishment 4 engage in a coordination game where they decide on how to determine who drops out. Of course, this raises the issue of someone in the Establishment 4 to deviate and continue the race despite having agreed to drop out. The fix to this would be to enact penalties , such that the payoff to deviating is less than the payoff of running with two less competitors. All of this , however, is only a theory as it would require the Establishment 4 to act towards social optimality instead of their own optimality.