Task #$5.$

Weather is a bit unstable, but John can start thinking about organising a party in his summer cottage$.$

There is a bit of uncertainty regarding the weather, the possible states are: hot, warm, rain, storm. John

can arrange various possible types involving various groups of guests: A$)$ barbecue, B$)$ a party inside the

cottage$,$ C$)$ mud$-$wrestling competition, D$)$ romantic evening. Unfortunately John has got to decide before

he knows the weather for sure. His pay$-$offs are collected in the table below.

A$.$ Make a choice with maximin criterion.

B$.$ Make a choice with maximax criterion.

C$.$ Make a choice with Laplace criterion.

D$.$ Make a choice with Savage criterion.

E$.$ For what values of $$ in Hurwicz criterion D is recommended? Task #$6.$

Robert got bruised one day while on his winter vacation. He is now thinking whether to go on the slope the

next day or rather to take a break. If he chooses to have a break, he can go to the movies, or take a walk.

He can also stay at his hotel room and wait and see whether weather is fine. Obviously he can go skiing in

the morning and optionally return to the hotel should the weather not be too good, but then he will no

longer have time to go to the movies or for the walk.

Weather very often changes in the middle of a day, and so the possible states of the world are: good$/$good$,$

good$/$bad$,$ bad$/$good$,$ bad$/$bad$.$ The table below shows Robert's pay$-$offs depending on the decision alter$-$

native and the state of the world. For example, the pay$-$off resulting from skiing depends on whether the

weather is good $($good visibility, no moguls, he can ski carefully and have fun$)$ or bad $($the possibility of inju$-$

ry and no fun$).$

A$.$ Make a choice with maximin criterion.

B$.$ Make a choice with maximax criterion.

C$.$ Make a choice with Hurwicz criterion depending on $$ parameter.

D$.$ Make a choice with Savage criterion.Task #$4.$

Table below presents pay$-$offs for various alternatives and states of the world.

A$.$ Make a choice with maximin criterion.

B$.$ Make a choice with maximax criterion.

C$.$ Make a choice with Hurwicz criterion depending on $$ parameter.

D$.$ Make a choice with Savage $($minmax regret$)$ criterion.

E$.$ As you know, Savage criterion does not guarantee a coherent choice $($i$.$e$.$ decision can change when

irrelevant alternatives are added$)-$ which alternative $($except for the recommendation made in $D$

above$)$ do we have to remove, in order for the optimal recommendation in D cease to be optimal.