L4 - Rationality Flashcards
What is a “Belief”?
A belief is a probability distribution, just like a mixed strategy profile. A mixed strategy is a belief in which every strategy is independently chosen.
When is a strategy “rationalizable”?
We say a strategy is rationalizable if there exists a belief over the opponent’s strategy such that this strategy is a best response. Another way of saying this, When is a strategy rational? - Whenever this strategy gives you the highest payoff possible conditional on your beliefs over what your opponent is going to do. I.e., the strategy is a best response.
What is the solution concept rationalizability?
The solution concept rationalizability, is the set of strategies $R$ that is rationalizable.
The set of rationalizible strategies $R$ is the largest best reply set there is.
The set of rationalizable strategies is the set of strategies that survive the iterated elimination of strictly dominated strategies, i.e., strategies that are never a best response.
How do we find R?
We find this by:
- Eliminating the never best responses, or
- Unionizing all the best reply sets.
“Essentially, we can also find R by eliminating all strategies that are never best
responses. That is, we know players are rational and never play strategies that
are never best responses. We eliminate those strategies and then check if any
other strategies are never best responses etc” L4
What are correlated vs indipendent strategis?
If we independently choose our strategies, non of us are communicating in any way when we are playing the game. If we communicate, then our strategies are instead correlated.
What does a Best reply set include?
Best reply sets include only strategies which are best responses under some beliefs.
Every think in a best reply set is a…..
best response.
When is strategies that survies I.E.D.S R?
Turns out if you allow for correlated beliefs (or have 2 players) the set which survives I.E.S.D =$R$. This is however not true with independent believes and/or more than two player.
What is a never best response?
A never best response is equivalent to a strictly dominated strategy. Only true with correlated believes and/or more than two players.
What is the difference between dominance and best response?
A strategy is dominated if there exists a single strategy that is better than this strategy for all my opponents strategies!
A strategy is a best response if it is better than all the other strategies I have given by opponents strategies.
