w9 extensive form games Flashcards
what is the extensive form game and why do we have them
normal form representations dont include sequential features of some games
so extensive forms make the temporal structure more clear
what are the two variants of extensive form games
perfect information extensive form games
imprefect information extensive form games
what is an extensive form game made up of
so its like a binary tree where
players: are non terminal nodes
game tree: is the order of moves
strategy: is the edge of the game tree
outcomes: is the the terminal node
payoffs: values on the terminal nodes
the i th value represents player i’s payoff
what is in a perfect information extensive form game
each player has all knoweldge about all actions taken by all the players in the game at every decision point
what is an imperfect information extensive form game
one player does not always see the choice of the other
what is an information set in an extensive form game
a set of notes such that each set belongs to one player and when the games reaches that set the player who is about to move cannot differentiate between nodes in the set
what is a pure strategy in an extensive form game
in a perfect information game, a pure startegy is a complete specification of which action to take at each node
how to count the number of pure strategies in an extensive form game
is the cross product of the number of actions it has at each of its nodes
ie if player 1 has 3, 2 ,4 strategies in each node
then 3x2x4 pure strategies
what would a mixed equlibirium be in an extensive form game
a probability distribution over pure strategies
how to convert an extensive form game into normal form game
determine the number of pure strategies for each player
draw the matrix,
put the payoff for each strategy profile
what is a non-credible threat in in an extensive form game
a threat in a sequential game that a rational player would not actually carry out
so sometimes nash eqiulirbium is not a good solution concept
what is a subgame in in an extensive form game
a game that can begin at any node of the tree
what is a subgram perfect equilibrium
A strategy is a subgame perfect equilibrium if it represents a Nash equilibrium in every subgame of the game tree.
This means players make optimal decisions at every point in the game, not just at the start.
SPE eliminates non-credible threats by ensuring rational play throughout the entire game.
for any subgame of the game tree there is always a strategy is a nash equilibrium
is there always a subgame perfect equillibrium in an extensive form game
theroem: for every finite extensive form game with perfect informmation there is a subgame perfect equilibrium
every subgame perfect eqiulbrium is a pure nash equalibrium but not vise versa
