## Madman Strategy and its Applications to Game Theory

Surprisingly, Game Theory and Politics might go hand in hand. It is posited that Donald Trump is pulling off the madman strategy, coined by Richard Nixon back in the 1960’s, in an effort to placate North Korea and their Nuclear efforts. Nixon utilized the madman strategy in his first term in the Oval Office to solve the problem of the Vietnam War. His aim was to appear to be irrational and unstable, enough to convince Russia that he was moments away from pulling the trigger that would lead to an all-out Nuclear War. If his tactic succeeded, Nixon hoped that Russia would pressure the Vietnamese to capitulating. It is believed that with tensions rising in North Korea, Trump is pulling out the madman chip at the bargaining table. Although some people cite his prior experience as a business man that would make him well-versed in such a strategy, others believe that Trump is simply insane.

Ignoring the political side, we can rephrase the madman situation to a classic game theory perspective. Recall the Prisoner’s Dilemma, however, instead of prisoner’s and jail time, we utilize world leaders and nuclear war. Without loss of generality, let us denote Trump as World Leader A and
Kim Jung Un as World Leader B. In this “game” (we treat the politics as a simplified game for argument sake), each world leader has two moves — hold their ground or fold. We can recreate the Payoff matrix below (notice the similarities to the Prisoner’s Dilemma).

(H, H): Leads to war. Payoff of (-20, -20) for both players.
(F, H): Leads to World Leader B Victory. Payoff of (-30, 0)
(H, F): Leads to World Leader A Victory. Payoff of (0, -30)
(F, F): Leads to compromise. Payoff of (-10, -10) for both players.

Here, H stands for Hold Ground and F stands for Fold. The first element refers to the strategy of World Leader A and the second element refers to the strategy of World Leader B. We note that, similar to Prisoner’s Dilemma, the only Nash Equilibrium is both leaders holding their ground. How does the madman strategy lead to countries preferring the (F, F)
option? It might be possible with the following logic. W.L.O.G. let World Leader A be the one employing the madman strategy. Because he now appears to be irrational and unstable, World Leader B might think that going to war will actually lead to even worse payoffs. With World Leader A acting like a madman, World Leader B might belive
that the (h, H) strategy will now have a -100 payoff for both players. This might be because with World Leader A being especially insane, much more damage will be
done if war happens. Thus, the new Nash Equilibrium becomes (F, F). This shows how, in theory, the madman strategy might lead to peace. Unfortunately, it did not work for Nixon, but one can only hope history will not repeat itself.