Strictly Dominant

When the payoff of one strategy offers a higher payoff regardless of what the other player plays.
Never Play a strictly dominated strategy.

Rationality

Rational outcomes can lead to outcomes that suck, prisoners dilemma- where playing dominant selfish strategy leads to a worse outcome than cooperating. Suggests not playing a dominated strategy

Weakly dominant

Same outcomes, bar one which offers a higher payoff for a specific strategy of the other player

Co-ordination problem

No dominant strategy

Common knowledge

Known of rules and the payoffs of each situation, each others utility functions

Best Response

Strategy that offers a better payoff to a specific strategy of player 2.
To find best response - draw diagram
Never play a best response that is strictly dominated
If no domination check mixed strategy.

Rationalizable

Nash Equilibrium

Best Response Condition 1

A strictly dominated strategy will never be BR

Best response condition 2

A strategy that is never BR doesn't mean it is strictly dominated

Nash Equilibrium

Mutually best response, just because BR for one Strat doesnt necessarily mean it's NE.
No willing deviation
x is as good to y as strategies goes

Nash Equilibrium (Weakly dominated)

A Nash equilibrium can be weakly dominated however not strictly dominated.

Iteration Deletion

Can delete some Nash equilibriums but not all. Gets rid of all weak NE

Taxpayer Game

Direct and strategic effects

Mixed Strategy

Randomisation of strategies. If never play one make sure to put in 0.
If mixed stat Nash equilibrium then, pure strategies should be also, will never offer a higher payoff.

Guess and Check Method

Some NE converge, segregated and mixed. Communication can help

Candidate problem

Best to enter if no one. If one other candidate, enter if equidistant to one another. If 3 not profitable to run.

Stable and Unstable

Segregated and mixed & integrated

Strict NE

No deviation makes better off. Change one players actions

Weak NE

Equal to another swap of them

ESS

Symmetric- won't be taken over by mutant population

Nature

In nature isn't efficient - cooperation

Strictly dominated strategy in ESS

won't be an ESS as will never be NE

If s' is a successful mutation doesn't mean that it will be ESS itself

...

Mixed Strat in ESS

Check condition 3

Best response and NE

Has to be mutually best response to be in NE

BR cannot be dominated

However there could be strategies that are not BR but doesnt have to be dominated.

BR and weak dominance

Can be weakly dominated

If s is evolutionary stable, cannot be dominated

However there can exist another pure strategy that is not weakly dominated by ESS

ESS always?

No sometimes there could be ESS

If asking for mixed strategy in 3

Decide how to delete one

Something that has survived deletion of dominated strategies

Doesn't mean its a best response , this is because there can be a strategy that is not best response but not dominated .

Common knowledge

suggests that no player will play a dominated strategy