# Lernkarten

Fabienne Keller
Karten 67 Karten 5 Lernende Deutsch Universität 21.02.2013 / 22.07.2020 Kein Urheberrechtsschutz (CC0)
0 Exakte Antworten 67 Text Antworten 0 Multiple Choice Antworten

Give an example for a game with continuous strategy spaces

- Monopoly

Does Rationality lead to equilibrium play?

not necessarily.

--> we know that rational players will play strategies that survive IESDS. In some cases this leads to a unique profile. (This is then the unique NE of the game)

Definition of Nash Equilibrium

A NE is a list of strategies, on for each player, such that no player can get a better payoff by switching to some other strategy that is available to her while all the othere players adhere to the strategies specified for them in the list.

What's a...

a) strict NE

b) not strict NE

a) a NE where the payoffs of both players are strictly larger than any other payoff in their row/column

b) a NE where at least one of the players could give another answer and would get the same payoff

What's a mixed strategy NE?

a mixed-strategy profile in a finite normal-form game is a mixed NE if and only if, for each player i...

- the expected payoff to every action to which the profile assigns positive probability is the same

- the expected payoff to every action to which the profile assigns zero probability cannot be larger than the payoff of any action to twich the profile assigns positive probability

- each player's expected payoff in an equilibrium is the expected payoff to any of the actions that is used with positive probability. Simplifies the calculation.

Is it possible to play weakly dominated strategies in a NE?

Yes

What's a subgame?

- begins at a decision node x that is a singleton

- includes all decision and terminal nodes following x in the tree.

- it cannot cut any information set

--> The whole game is a subgame!

What's a subgame perfect NE?

A NE is subgame perfect if the players' strategies constitute a Nash equilibrium in every subgame

--> no matter what has happenend before, players must play a NE in the remaining game.

--> at any point in the game players believe that all will behave rationally in the remaining game

--> in games of perfect information, the SPE are the solutions found using backward induction