PROBLEM $(2)$ Suppose there are N possible states of the world $\{$s$1,$ s$2,$ s$3,...,$ sN$\}.$ An act a$=($a$1,$ a$2,$ a$3,...,$ aN$)$ is an action that delivers ai units of utility if si happens to be the state of the world, for each i$=1,..,$N$.$ Suppose the grand set of alternatives $($acts$!)$ X $=\{$a$,$b$,$c$,..,$z$\}.$ When you face a menu $$A $$X$,$ you choose an act in the menu according to: $($i$)$ Maximin criterion, or $($ii$)$ Maximax criterion, or $($iii$)$ Minimax risk $($regret$)$ criterion

$($In the whole question, ignore any considerations about the case of $$ties$$ under any criterion; assume there are never equalities$/$ties that can come up when comparing actions$/$states$...$etc.. so that there are no indifferences in any step of choosing an act under any of the criteria, so that you will never have to break any ties in the process$)$ All parts below are separate question

$($b$)$ Answer part b shown in the pitcure attachted

$($c$)$ answer part c shown in the pitcure attchted

$($d$)$ answer part d shown in the pitcure attchted