Test 2 Flashcards
What is meant by sequential rationality?
A player is sequentially rational if and only if he will maximise his expected utility conditional on the fact that he is at that node even if this node is precluded by his own strategy.
If sequential rationality is used to solve a game, what is the outcome called? Give an example.
In a finite game of perfect information common knowledge of sequential rationality means there will be a ‘backwards induction’ outcome.
An example of the game would be entry game I.
Solve an say that Pepsi is sequentially rational.
How do you solve an imperfect information game?
- Compute the Nash of the equilibrium of the subgame.
- Fix the equilibrium actions as they are.
- Take the equilibrium payoffs as the payoffs for entering the subgame.
- Then compute a nash for the remaining game.
What are the assumptions for a subgame perfect nash?
(i) Player 1 is rational
(ii) player 2 is sequentially rational.
(iii) at the node he moves, p2 knows (i).
(iv) Player 1 knows (ii) and (iii)
if Player 1 can choose between L and R after player 2 has chose l or r, how many choices do they have.
How does this change with imperfect information?
They will have four choices.
With imperfect information, they will only have two choices. This is because they regard the node with imperfect information as one choice, because they do not know what decision went before that.
When is a Nash Equlibria Subgame perfect?
A nash equilibrium is subgame perfect if the player’s strategies constitute a nash in every subgame.
This means that the nash will be subgame perfect if you divide the game into each subgame and the strategy is still a Nash into each of these subgames.
How to determine the number of subgames within a game?
A subgame is a subset of any game with an initial node and all successfor nodes.
The subgame must be so that the initial node is independent from any information set.
What is an information set?
An information set is a set of nodes.
The player who plays at the information set is technically playing at every node within the information set.
When the play of the game reaches a node in the information set, the player with the move does not know which node in the information set has and has not been reached.
Why can’t a subgame start at an information set.
Because a subgame starts at a single decision node.
And information sets actually contain more than a single decision node.
What is meant by sequential rationality?
A player will exhibit sequential rationality if it maximises his or her expected payoff conditional on every information set at which they have their move.
Player i’s strategy should specify an optimal action at each of player i’s information sets, even the information sets that player i does not believe he will reach in the game.
When is a strategy profile rationalizable?
1) Every player’s strategy is consistent with their own rationality. This means that they must maximise their own payoff with respect to the strategies of other players.
2) The conjectures made must be consistent with other player’s rationality.
So if i thinks j will play sj, then sj must maximise j’s payoff with respect to conjectures that J has made about other players strategy.
AD INFINITUM
How can you construct the prisoner’s dilemma game for repeated game scenarios?
CC=(0,0) CD=(7,-2) DC(-2,7) DD(5,5)
Remember in this game, the lower the payoff the better.
How can you determine the total payoff from a finitely repeated game for say four years?
Just add the single Nash equilibrium payoff together for the four years.
e.g if the Nash is (57,57), the payoff would be 57+57+57+57,
which equals 228.
How to find the subgame perfect equilibrium of a finite repeated game.
If the game has a unique Nash or a sequential move game has a unique subgame perfect equilibrium, then this equilibrium will also be the unique subgame perfect equilibrium.
How to prove the derivation of the discount factor?
S = sig+sig2+sig3 = sig(1+sig+sig2) Ssig=sig2+sig3+sig4= sig(sig+sig2+sig3)
S-Ssig=1
s(1-sig)=1
therefore s= 1/(1-sig)
