Game Theory

Question 1

Basic games

Answer 1

Two person game, zero sum

Pure strategy solution and straddle point

Question 2

Mixed Strategy solutions

Answer 2

2 x n games solved by graphic approach

Question 3

LP approach

Answer 3

generic m x n game problem

Question 4

Gain matrix

Answer 4

A is on the left, B is on the top
Gain for A for each strategy
Loss for B for each strategy

Question 5

Assumptions of basic game

Answer 5

The entire matrix is known in advance by both
Both players are rational and risk averse (try to avoid losses)
No mutual gain/loss - zero sum
Strategies are given in secret

Question 6

Player A (gain)

Answer 6

Maximin Criterion
Pessimistic view: whatever strategy A plays, believes B will play strategy so that As gain will be minimised
Avoid getting the worst case

Question 7

Player B (loss)

Answer 7

Minimax Criterion

Pessimistic view: whatever strategy B plays, believes A will play strategy so that Bs loss will be maximised

Question 8

Mixed Strategies

Answer 8

Used when no saddle point exists
Introduces the probability of each strategy
Ultimate goals still the same but now a function