Flashcards in 03 - Static Games of Complete Information Deck (9)

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1

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

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• 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)

2

## What are focal points?

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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.

3

## What may focal equilibrium points depend on?

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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

4

## What do "trembling hands" and "trembling hands perfection" mean?

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• 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.

5

## When is an equilibrium for sure trembling-hand perfect?

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• totally mixed Nash equilibria

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

6

## What do we mean by "assuming ordinal preferences"?

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

7

## Are there limits to merely assuming ordinal preferences?

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Yes:

• stochastic outcomes

• mixed strategies

8

## What does correlated equilibrium mean?

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(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.

9