Game Theory. Please do the homework and show work, i will upvote.

Consider the Chomp game version in Wikipedia. $($Click here to see the Wikipedia page$).$

Suppose there are $2$ rows and $2$ columns. Player $1$ first chooses among $4$ actions:

$(1,1),(1,2),(2,1),$ and $(2,2).$ Here $($i$,$ j$)$ refers to the cell in row i and column j$.$ If

player $1$ loses $($by choosing $(1,1)),$ then player $1$s payoff is $-1$ and player $2$s payoff is

$1.$ If player $2$ loses, then player $2$s payoff is $-1$ and player $1$s payoff is $1.$

$($a$)$ Draw the extensive form game $($game tree$)$ of this game.

$($b$)$ Find all SPNE $($subgame perfect Nash equilibria$)$ in pure strategies by

using backward induction.

$($c$)$ Show that in every SPNE that you found in $($a$),$ player $1$ wins.