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Flashcards in Game Theory Deck (9)
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1
Q

What is a pay-off matrix?

A

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

2
Q

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

A

The row player.

3
Q

What is a zero-sum game?

A

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

4
Q

What does it mean if a player is playing safe?

A

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

5
Q

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

A
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.
6
Q

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

A

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.

7
Q

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

A

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

8
Q

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

A

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

9
Q

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?

A

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