Editing Nash Equilibrium (section)

== <span style="color: #FFFFFF;">Understanding</span> ==
Nash Equilibrium is understood through '''Mutual Best Response''' and '''Stability'''.

'''1. The Logic of "Best Response"''':
Imagine you are playing a game. You look at what your opponent is doing and ask: "Is there anything I could do differently to get a better result?"
* If the answer is "No," you are at a best response.
* If *every* player in the game says "No" at the same time, you have reached a '''Nash Equilibrium'''.

'''2. Stability vs. Optimal Results''':
The most important (and counter-intuitive) thing about Nash Equilibrium is that it is often **Not** the best possible outcome for the group.
* '''Example''': In the Prisoner's Dilemma, the best outcome is for both to stay silent.
* However, the Nash Equilibrium is for both to "Betray" each other.
* Why? Because if you stay silent, your opponent has an incentive to betray you to get a better deal. To protect yourself, you betray them too. You both end up in a stable but "Bad" outcome.

'''3. Multiplicity''':
Some games have zero Nash Equilibria (in pure strategies), while others have many.
* '''Coordination Games''': If we both want to meet up, but don't care where, both "Meeting at the Coffee Shop" and "Meeting at the Library" are Nash Equilibria. The challenge is picking the same one.

'''John Nash's Proof''': He proved that in any game with a finite number of players and actions, there is *always* at least one Nash Equilibrium (though it might involve "Mixed" random strategies).
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