Stable
Solutions (Saddle Point)
A game is said to have a stable solution if playing safe
results in an equilibrium where it isn’t advantageous for the players to change
their strategy. In a zero sum game there will only be a stable solution if the
row maximin equals the column minimax.
|
4
|
-1
|
2
|
3
|
-1
|
|
4
|
6
|
3
|
7
|
3
|
|
1
|
2
|
-2
|
4
|
-2
|
|
4
|
6
|
3
|
7
|
|
As we can see in the example above A would play row 2 (as
this is the maximin) and win 3 and B would play column 3 (as this is the
minimax) and would result in a loss of 3. In this case the row maximin = the
column minimax hence there is equilibrium.
If there isn’t a stable solution then it A or B could profit
by playing a different strategy (i.e. not play a safe strategy).
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