L3 - Dominated Strategies

Question 1

Look at a PD.

What is then S (the set of all strategy profiles)

S_i (the set of pure strategies for player i)

Answer 1

Here $S={(C,C)(C,D)(D,C)(D,D) }$, $S_i={C,D}$ is the set of pure strategies for player $i$, $s=(C,C)$ is the strategy profile of the top left cell.

Question 2

What will a rational player never do?

Answer 2

A rational player never plays a strictly dominated strategy!

Question 3

What is a strictly dominant strategy

Answer 3

A strictly dominant strategy is one strategy that dominates every singel strategy.

Note, this is not the same thing as strictly dominant (which a know well).

Question 4

What can be said about orderdependence regarding IESD

Answer 4

⚠️ I.E.S.D is order-independent: we always end up in the same reduced matrix no matter for which player we start eliminating.

⚠️ I.E.W.D is order-dependent!