03 - Static Games of Complete Information

Question 1

Are all Nash equilibiria equally likely? What aspects would we consider to answer this question?

Answer 1

• Context and Focal Points
• Robustness against small variations in strategies (! Trembling-hand perfect equilibrium)
• Robustness against small variations in payoffs
• Bounded rationality and dynamic learning process
(! Evolutionary Game Theory)

Question 2

What are focal points?

Answer 2

Some equilibria “appear” much more likely to be played than others. Such equilibria are focal points.
• Players coordinate by using information that is abstracted away by the normal-form representation.

Question 3

What may focal equilibrium points depend on?

Answer 3

Which equilibrium is focal may depend on:
• social conventions and norms,
• players’ cultural background and past experiences,
• structure of game, e.g., equilibrium with most desirable outcome is focal,
• pre-play communication, players may agree on a particular equilibrium that then becomes focal

Question 4

What do “trembling hands” and “trembling hands perfection” mean?

Answer 4

• Suppose players accidentally make mistakes: with some low probability they play a different strategy than intended (“their hands tremble”).
• Trembling-hand perfection is a refinement of Nash equilibrium that requires the equilibrium to be robust against such low probability mistakes.

Question 5

When is an equilibrium for sure trembling-hand perfect?

Answer 5

• totally mixed Nash equilibria

* in a two-player normal-form game if it is not a weakly dominated strategy for any player

Question 6

What do we mean by “assuming ordinal preferences”?

Answer 6

• Any numbers would do as long as the order of the outcomes remains unchanged. -> Preferences are ordinal (completeness and transitivity axioms).

Question 7

Are there limits to merely assuming ordinal preferences?

Answer 7

Yes:
• stochastic outcomes
• mixed strategies

Question 8

What does correlated equilibrium mean?

Answer 8

(Mixed) Nash equilibrium assumes that players use independent randomization.
In correlated equilibrium, players have a signalling randomization device which allows them to reach higher payoffs.

Question 9

How can you calculate whether a strategy is trembling-hand-perfect?

Answer 9

1) is it strictly dominant? yes -> t.h. perfect

2) compare payoffs of either strategy when inserting probabilities (ε, 1-ε) for the other player`s strategies