The US elections: the games politicians play
For a long time, game theory has analyzed the process of voting and political strategies. One of the best-known examples of game theory in politics is the Median Voter Theorem, in which political parties gravitate toward the ideology of the median voter. Politicians know that, when placed on a spectrum, voters are likely to vote for whoever is closer to them on the spectrum. Thus, it is good practice for a politician to position themselves close to their opponents, and vice versa. After many iterations, a Nash Equilibrium occurs and this occurs at the center of the spectrum where the votes can be split. Neither party can do better by deviating from this strategy.
In the recent election, instead of deviating toward the center, both parties polarized themselves to either pole of the spectrum. This caused a decrease in the amount of money they would have to spend to attract voters than if they were in the middle. Thus, they both benefitted greatly from polarizing, and in this case the Nash Equilibrium occurs when they both deviate, instead of converge. In this particular case, either party cannot position themselves in another spot to pick up more votes, without an inherent cost. Thus, this election went against the well-known Median Voter Theorem, but nonetheless, still had an important Nash Equilibrium other than what the theory stated.
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