Consider the game below where we will only focus on the column player. The greek letters $\beta$, $\gamma$ and $\delta$ denote the probabilities assigned to each pure strategy Left, Center and Right.
|Up||3, 5||7, 3||1, -1|
|Middle||-2, 1||1, 4||9, 0|
|Down||-5, 2||6, 8||4, 5|
i. $\gamma =0$
ii. $\gamma =1/2,\delta =1/2$
iii. $\beta =1/4,\gamma =3/4,\delta =0$
iv. $\beta =1$
v. $\beta =0,\gamma =1/4,\delta =1/3$
A mixed strategy gives information about the probability with which each pure strategy is played. It is well-defined if each of its components is between zero and one and if all of its components add up to one. In this case, the requirements are $\beta$, $\gamma$, $\delta$ $\in [0,1]$ and $\beta + \gamma + \delta=1$.
Which of the above are well-defined mixed strategies?