How can an arms race resemble the prisoner’s dilemma?
The normal-form table illustrates the concept of a saddlepoint, or entry, in a payoff matrix at which the expected gain of each participant (row or column) has the highest guaranteed payoff.
In game theory, an arms race is often modeled as a prisoner’s dilemma (PD) because it illustrates how rational individual choices can lead to a collectively disadvantageous outcome.1
In this model, two countries choose between high or low levels of armaments. While both nations would be more secure and save resources if both chose low levels, each country faces a "dominant strategy" to choose high levels to gain a military advantage or avoid being vulnerable. This results in a Nash equilibrium where both players choose high arms, even though this state is worse for both than if they had cooperated.1
This rivalry traps nations in a mutually disadvantageous position. However, because arms races are ongoing, they are often better represented by the "iterated prisoner’s dilemma," where repeated interactions allow for cooperation through strategies like "tit for tat". Additionally, the theory of moves suggests that far-sighted players can escape this dilemma by anticipating the consequences of their actions, provided the game does not begin in a noncooperative state.12