US vs. USSR Cold War: Arm Missiles or Disarm?

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    Assume the US and USSR are in the Cold War. Should each country make some nuclear missiles to defend themselves against the other?

    If both the US and USSR disarm they benefit by saving $10 billion each because they do not have to research into new missiles or maintain old missile defence systems anymore. If the US arms itself with missiles but the USSR disarms then the US benefits by $200 billion because they beat the USSR in the Cold War and take over their county, the USSR loses $200 billion because they are invaded by the US Army and vice versa. If both the US and USSR arms themselves with missiles then they will not attack the other due to fear of retaliation, so they have both spent their money on missiles and receive a payoff of $0 each.

    If the US believes the USSR will disarm then the US will want to arm itself to receive $200 billion rather than $10 billion. The USSR will reason the same way. So both the US and USSR will play their dominant strategy and arm themselves with missiles.

    Both the US and USSR disarming means they will each save $10 billion because they do not have to spend money on missiles. So the Nash equilibrium (Arm, Arm) makes the US and USSR worse off than if they both disarm. As long as the US and USSR do not trust each other to disarm, they will both arm themselves with missiles. If the US and the USSR could collude and make an agreement or if they trust each other then they could both disarm.

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