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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.

Left Center Right
Up 3, 5 7, 3 1, -1
Middle -2, 1 1, 4 9, 0
Down -5, 2 6, 8 4, 5
$\beta$ $\gamma$ $\delta$

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?


i and iii


i, ii and v


ii, iii and iv


ii, iii and v


iii and v

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