In strategic situations, actors are mutually anticipating the actions their 
counterparts will take, and then acting according to their own preferences.
This anticipation leads to points of mutual understanding in which all 
players have no incentive to adjust their plans, because they are all 
already doing the best they can given what they anticipate others will do.

## Example: Rock-Paper-Scissors
Everyone knows the rules. If you think the other person will throw Rock, you
throw Paper. If they think you will throw Paper, they throw Scissors. That back
and forth means any fixed choice can be exploited. The balance is to make your
choice in a way that cannot be predicted. When both people reach that balance,
no one can do better by changing their choice on their own.

![Mutual anticipation diagram](/images/docs/mutual_anticipation.jpeg)

In Rock-Paper-Scissors, the equilibrium is both actors choosing Rock, Paper, and
Scissors with equal probability. Any bias, even a small one, can be anticipated
and taken advantage of, so the only stable choice is to be unpredictable.

## The Definition

A Nash equilibrium is a strategy profile — one strategy for each player — where
no player can improve their outcome by unilaterally changing their own strategy.
Each player's strategy is already a *best response* to the strategies the others
are actually playing.

This single condition — mutual best response — carries a powerful implication:
the strategy profile is *self-consistent*. If you told each player exactly what
everyone else was going to do, no one would want to change their plan. There are
no surprises and no regrets.

In practice, people rarely discover an equilibrium through introspection alone.
Algorithms like Counterfactual Regret Minimization (CFR) can compute equilibrium
strategies directly, even in games far too complex for human intuition.

## See also
- [What is Abstraction?](/docs/what-is-abstraction)
- [What is Thinking?](/docs/what-is-thinking)