Flashcards in 01 - Static Games of Complete Information Deck (29)

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1

## What is normal-form representation?

### display a game as static game in matrix. some information-loss compared to extensive-form representation.

2

## What does complete information mean?

### all players’ available actions and utilities from various outcomes are common knowledge

3

## What is the problem for players in normal-form representation?

### strategic uncertainty - problem of predicting how others will behave, in order to figure out what is best

4

## What is strategy space Sᵢ?

### set of strategies available to player i

5

## What is a strategy profile?

###
a combination of strategies

s = (s₁, . . . , sₙ) ∈ S,

where S := S₁ × · · · × Sₙ

6

## What is a payoff function uᵢ?

###
uᵢ: S -> R specifies player i’s utility uᵢ(s₁, . . . , sₙ) for

every possible strategy profile (consequence).

7

## What is the prisoner's dilemma?

###
2 players, finite strategy spaces

Bonnie & Clyde committed crime, face prison sentence

best pay-off for both together: when both do not confess

individually best pay-off: confess while other does not confess

bad pay-off: when both confess

8

## What is the outcome of the prisoner's dilemma?

### both will confess, because for both player it is individually strictly better to confess than not to confess (rationality & strict dominance)

9

## What is a strictly dominant strategy?

###
a strategy sᵢ ∈ Sᵢ is a strictly dominant strategy for player i if for all sᵢ′ ≠ sᵢ,

uᵢ(sᵢ, s₋ᵢ) > uᵢ(sᵢ′, s₋ᵢ) for all s₋ᵢ ∈ S₋ᵢ.

10

## What is a strictly dominated strategy?

###
a strategy sᵢ ∈ Sᵢ is a strictly dominated strategy for player i if there is another strategy sᵢ′ ∈ Sᵢ,

uᵢ(sᵢ', s₋ᵢ) > uᵢ(sᵢ, s₋ᵢ) for all s₋ᵢ ∈ S₋ᵢ.

11

## What is IESDS?

### Iterated Elimination of Strictly Dominated Strategies

12

## What is the idea behind IESDS?

###
- rational player never plays strictly dominated strategy

- all players know this and can thus eliminate those strategies from the game

- repeat reasoning on resulting smaller game

13

## What are the epistemic foundations of IESDS?

###
- all players are rational

- rationality is common knowledge (i.e. everyone knows that they know etc etc that all players are rational)

14

## Do you need specific epistemic foundations for strictly dominant strategies?

### No, because they do not require any knowledge about the other players, only about their own payoffs

15

## What is weak domination?

###
a strategy sᵢ ∈ Sᵢ is a weakly dominated strategy for player i if there is another strategy sᵢ′ ∈ Sᵢ, such that

uᵢ(sᵢ', s₋ᵢ) >= uᵢ(sᵢ, s₋ᵢ) for at least one s₋ᵢ ∈ S₋ᵢ.

16

## What could be problematic with weak dominance?

### Strategies that are only weakly dominated cannot be ruled out based solely on rationality.

17

## What is problematic with IEWDS?

### outcome depends on order of elimination and on whether all or only some weakly dominated strategies are eliminated in each step

18

## What is a Nash equilibrium?

### A Nash equilibrium is a strategy profile with the property that no player can gain by unilaterally deviating from it.

19

## When must an outcome be a Nash equilibrium?

### If a game has a unique predicted outcome. Otherwise rational players (knowing the prediction) would deviate.

20

## What does "Nash equilibrium as a self-enforcing agreement" mean?

### nonbinding communication among players prior to playing until they can all trust it

21

## What does "Nash equilibrium as a stable social convention" mean?

###
• If game is played repeatedly, a particular way of playing may arise over

time,

• Nash equilibrium as steady state of dynamic adjustment process

22

## What is BRᵢ(s₋ᵢ)?

### the set of all best responses against s₋ᵢ

23

## How do IESDS and Nash equilibrium relate?

### If IESDS results in a unique strategy profile, then this is the unique Nash equilibrium of the game.

24

## How do IEWDS and Nash equilibrium relate?

### Weakly dominated strategies can be part of a Nash equilibrium. There are Nash equilibria that do not survive IEWDS.

25

## How do you practically do IESDS?

### look for strategies that a player would never play (which are strictly dominated) and eliminate them from the game. turn to the other player and do the same.

26

## What if there are two solutions in strictly or weakly dominant strategies?

### Then there is no solution (because not unique)

27

## Can there be two solutions in IESDS?

### yes, but they would be called "strategies surviving IESDS"

28

## Does a Nash equilibrium need to be strictly dominant?

### No, it is sufficient if there is no incentive to deviate (i.e. weakly dominant)

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