Three gunmen face each other in a duel. All are excellent marksmen so it is not

Question

Three gunmen face each other in a duel. All are excellent marksmen so it is not reasonable to assume any will miss their target. Each one has one gun and the option to shoot one of the other two gunmen, or do not shoot.
What is their best strategy?

After an initial presentation to these riddles, two replies are common:

The problems are not realistic and the solutions given by Game Theory are perhaps interesting and clever, but not practical.

The use of mathematics seems to be unnecessary to understand these problems.

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Explanation / Answer

What is their best strategy?

Dilemma:

So to be alive its bettter not to fire. So all three gun man should not fire and hence system is in equilibria.

The use of mathematics seems to be unnecessary to understand these problems.

We can also consider other ways of attacking, like economic sanctions, each with a different cost. To find the best strategy for each one of the players, the equilibrium points, and the conditions when these points are lost in these more complex models, the use of sophisticated mathematics is required.

Each gunman can use this situation as an excuse to get another gun, starting an arms race; or they can decide to drop their guns wisely at the same time, and look for another way to solve their differences, thereby signing a disarmament agreement. In this sense, Game Theory is a valuable tool that brings clarity to the situation. This clarity is useful to each party in the conflict and can inform their decision.

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