w3 2 player zero-sum games *study lecture instead* Flashcards
w3 expanded on nash equilibrium and talked about a sub category of games caleld zero sum games where one players winning is equal to someone elses lost, also in this week they continuted w2 bc he ran out of time last time lmao so learnet how to calcualte mix nash equilibrium most of the lecture is just an example please study that instead
what is a two player zero sum game
when one player wins, their gain is equal to the other players loss
P1 +10, P2 -10
ex rock paper scisors
why is it good to recognize a 2 player zero sum game
given the payoff matrices, it can be easy to find a pure nash equilibirum
how can you see if there is a pure nash equilbirum in a 2p zero sum game
Check Saddle Points: A pure Nash equilibrium exists if a payoff is the max in its row (Player 1’s best) and min in its column (Player 2’s best).
Verify Stability: Ensure neither player can improve by unilaterally changing strategies.
No Saddle Point: If none, the game only has a mixed Nash equilibrium.
both player want to maximize their own utility
so max x min y xTAy
so the pure nash equilibrium point is at the cross section of points for both players, the saddle point
trying to find the balance of winning the most and losing the least
t/f is there always a purh nash equilibirum
no
what is the value of a game
the value of the game is the expected payoff a player can guarantee themselves, regardless of the opponent’s strategy
the saddle point between two players,
ie both players best/worst bet is choosing two then the value of the game =2
what does the duality in linear programming imply
in two player zero sum game theres always a pair of x and y such that nash equlibrium is real
