Question

Which of the following statements are true? Check all that apply.

In a total conflict game, there can be more than one saddle point.

"Equating the expected values" method can be applied for any 2x2 total conflict game.

When the maximin and minimax values in a total conflict game are same, there is no pure strategy.

"Method of Oddments" can be used for 2x2 total conflict game only if there is no saddle point in pure strategies.

If there are two saddle points in a total conflict game, the two have the same value.

Answer 1

1)TRUE

In a zero-sum matrix game, an outcome is a saddle point if the outcome is a minimum in its row and maximum in its column.If a matrix game has a saddle point, both players should play it.

Rose’s strategy is to select her maximin (the maximum of the row minima), while Colin’s strategy is to select his minimax (the minimum of his column maxima). By doing so, each player has chosen the most cautious strategy, for which in Rose?s case, she can guarantee a payoff of at least her maximin value, and Colin can guarantee a loss of at most his minimax value. Assuming that

minimax(columns) = maximin(rows)

then there exists a saddle point. Notice that if a saddle point exists, it may not necessarily be unique. However, if multiple saddle points exist, then they must be equal in value

3)true

2)TRUE 4)TRUE

FOR 2*2 total conflict game has two players with two strategies several shortcut methods are possible this methods apply only of there is no saddle point in pure strategies that are

1)equate the expected values of opposing playrer strategies

2)Method of Oddments also known as williams method

"Equating the expected values" method can be applied for any 2x2 total conflict game.

5)TRUE

If there are two saddle points in a total conflict game, the two have the same value.IF THE ROW PLAYER and the column player both play strategies containing a saddle point outcome the result will always be a saddle point