Main.NashEquilibrium History
Hide minor edits - Show changes to output
Changed line 5 from:
* The Dominant strategy for a player of a game = a strategy that the player would not change no matter what.
to:
* The Dominant strategy for a player of a game = a strategy that a rational player would not change no matter what.
Changed lines 1-4 from:
!!!Brief notes on Nash equilibrium
2.2003
to:
!Brief notes on Nash equilibrium
Notes taken from a HKU talk in 2.2003
Changed line 16 from:
[[Category.Logic and Maths]
to:
[[Category.Logic and Maths]]
Added lines 1-16:
!!!Brief notes on Nash equilibrium
2.2003
* The Dominant strategy for a player of a game = a strategy that the player would not change no matter what.
* If all players of a game has a dominant strategy, then the outcome of a game can be predicted. The outcome is called the "solution" of the game.
* Example : "confess" is the dominant strategy of 1 2-person prisoners' dilemma.
* But not all games have a solution in the above sense.
* Nash's contribution #1 : defined a more general concept of a solution (Nash equilibrium).
* Nash equilibrium : a decision matrix where each player will not change its decision provided that the other player do not change theirs.
* Example : In a boring lecture, every student wants to leave, but they also don't want to be the first to leave. So they all end up staying.
* Mixed Nash equilibrium : Nash equilibrium when it comes to mixed strategies e.g. 70% of the time decision A and 30% of the time decision B in repeated games.
* Nash's contribution #2 : (won the Nobel prize for) proving that every finite n-player non-cooperative game has a mixed Nash equilibrium.
* Proof : (i) existence of M.N.eq. for a game corresponds to the existence of a fixed point in some polynomial eqt that corresponds to the game. (ii) Applies fixed point theorem to show that there is a fixed point for the polynomial for every game.
[[Category.Logic and Maths]