Flashcards in 03 - Static Games of Complete Information Deck (9)
Are all Nash equilibiria equally likely? What aspects would we consider to answer this question?
• 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)
What are focal points?
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.
What may focal equilibrium points depend on?
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
What do "trembling hands" and "trembling hands perfection" mean?
• 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.
When is an equilibrium for sure trembling-hand perfect?
• totally mixed Nash equilibria
• in a two-player normal-form game if it is not a weakly dominated strategy for any player
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).
Are there limits to merely assuming ordinal preferences?
• stochastic outcomes
• mixed strategies
What does correlated equilibrium mean?
(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.