01 - Static Games of Complete Information

Question 1

What is normal-form representation?

Answer 1

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

Question 2

What does complete information mean?

Answer 2

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

Question 3

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

Answer 3

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

Question 4

What is strategy space Sᵢ?

Answer 4

set of strategies available to player i

Question 5

What is a strategy profile?

Answer 5

a combination of strategies
s = (s₁, . . . , sₙ) ∈ S,
where S := S₁ × · · · × Sₙ

Question 6

What is a payoff function uᵢ?

Answer 6

uᵢ: S -> R specifies player i’s utility uᵢ(s₁, . . . , sₙ) for
every possible strategy profile (consequence).

Question 7

What is the prisoner’s dilemma?

Answer 7

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

Question 8

What is the outcome of the prisoner’s dilemma?

Answer 8

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

Question 9

What is a strictly dominant strategy?

Answer 9

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.

Question 10

What is a strictly dominated strategy?

Answer 10

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.

Question 11

What is IESDS?

Answer 11

Iterated Elimination of Strictly Dominated Strategies

Question 12

What is the idea behind IESDS?

Answer 12

• 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

Question 13

What are the epistemic foundations of IESDS?

Answer 13

• all players are rational

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

Question 14

Do you need specific epistemic foundations for strictly dominant strategies?

Answer 14

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

Question 15

What is weak domination?

Answer 15

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.

Question 16

What could be problematic with weak dominance?

Answer 16

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

Question 17

What is problematic with IEWDS?

Answer 17

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

Question 18

What is a Nash equilibrium?

Answer 18

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

Question 19

When must an outcome be a Nash equilibrium?

Answer 19

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

Question 20

What does “Nash equilibrium as a self-enforcing agreement” mean?

Answer 20

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

Question 21

What does “Nash equilibrium as a stable social convention” mean?

Answer 21

• If game is played repeatedly, a particular way of playing may arise over
time,
• Nash equilibrium as steady state of dynamic adjustment process

Question 22

What is BRᵢ(s₋ᵢ)?

Answer 22

the set of all best responses against s₋ᵢ

Question 23

How do IESDS and Nash equilibrium relate?

Answer 23

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

Question 24

How do IEWDS and Nash equilibrium relate?

Answer 24

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

Question 25

How do you practically do IESDS?

Answer 25

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.

Question 26

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

Answer 26

Then there is no solution (because not unique)

Question 27

Can there be two solutions in IESDS?

Answer 27

yes, but they would be called “strategies surviving IESDS”

Question 28

Does a Nash equilibrium need to be strictly dominant?

Answer 28

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

Question 29

What needs to be included in normal-form representation?

Answer 29

define:
- players N = {player 1, player 2}
- strategy spaces Sᵢ
- payoffs uᵢ