Game Theory

Question 1

What is a pay-off matrix?

Answer 1

A table showing the outcomes of a two-person game.

Question 2

Whose perspective is the pay-off matrix always written from?

Answer 2

The row player.

Question 3

What is a zero-sum game?

Answer 3

A game in which any win for player A corresponds to an equal loss for player B.
=> therefore collaboration is never beneficial.

Question 4

What does it mean if a player is playing safe?

Answer 4

Each player looks for the worst-case scenario of each play, then picks the least worst option

Question 5

How can you determine if a stable solution (saddle point) exists?

Answer 5

If max(row min)=min(col. max)
then there is a saddle point and therefore a stable solution.
If there is no stable solution, the players must play a mixed strategy.

Question 6

What does it mean if one row(or column) dominates another?

Answer 6

The dominating row is always a better option for a player than another row.
The dominated row can be DELETED to REDUCE the pay-off matrix.

Question 7

In what case will the optimum solution for a game need to be solved using the simplex algorithm?

Answer 7

If the pay-off matrix is 3x3 or larger and cannot be reduced by dominance, and there is no stable solution.

Question 8

What is the first step in converting a game to a linear programming problem?

Answer 8

Determine no strategies are dominated and there is no saddle point (stable solution).
Then modify the pay-off matrix by adding the constant that will make all of the entries in the matrix positive and non-zero.
V=v-a where a is the constant added
v is the value of the modified matrix
V is the value of the original matrix

Question 9

When using the simplex algorithm to solve a game theory problem, the initial tableau will not have a pivot row as all ratios are zero, where should you start?

Answer 9

Let the pivot row be the first non-objective row.