Theory Stuff

Question 1

Common Knowledge of Rationality (CKR)

Answer 1

Everyone is rational, everyone knows everyone is rational, etc.

Question 2

Iterated Strict Dominance (ISD)

Answer 2

Iterated elimination of strictly dominated strategies
* use this to reduce 3x3 matrices
* assumptions: CKR, CK of game

Question 3

Rationalizability

Answer 3

A rational player should never choose a strategy that isn’t a best response. Rationalizable strategies survive iterated removal of non best-response strategies
* more powerful than ISD

Question 4

Equilibrium Knowledge

Answer 4

Players have correct beliefs about other’s strategies. Prevents players from miscoordinating on their beliefs. Can be:
* prescribed by a planner or mediator
* established thru pre-play communication
* learned in repeated interaction

Question 5

Nash Equilibrium (NE)

Answer 5

The central solution concept of game theory. Requires each player
1) to be rational (not enough)
2) to have Equilibrium Knowledge

Question 6

Beliefs

Answer 6

Bayesian rational players form beliefs (μ) about their opponents’ behavior, described by a prob. distribution

Question 7

Pure vs. Mixed Strategy

Answer 7

In pure strategy, rationalizability gives better prediction than ISD. In mixed strategy, they’re the same.

Question 8

Sequential Rationality (SR)

Answer 8

Requires players to choose optimally at every decision node, not just nodes that are supposed to be reached
* in game with no indifferences, SR leads to a unique prediction (BIS)
* stronger than CKR

Question 9

Backward Induction

Answer 9

Process of examining the final point in a series of decisions (terminal node), finding optimal decision for the respective player, and inferring the actions made by the player(s) before to attain optimal utility.
* does NOT require eq’m knowledge (similar to ISD and Rationalizability)

Question 10

Subgame Perfect (Nash) Equilibrium (SPE)

Answer 10

When BI doesn’t lead to unique solution at every node, we use this (more powerful than BIS)
* SR + eq’m knowledge = SPE

Question 11

Info Sets

Answer 11

We form a partition of each player i’s set of decision nodes Di into info sets
* info set h is a subset of Di
* we require that players have the same set of actions available at each node in a given info set (otherwise can distinguish)
* also require perfect recall

Question 12

Weak Sequential Equilibrium (WSE)

Answer 12

a pair (σ,μ), consisting of a strategy profile σ & belief profile μ, is a WSE if:
1) σ is sequentially rational given μ
2) μ is Bayesian given σ (eq’m knowledge assumption)