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Respond to the question: Twist to the Lion sheep puzzle?

06/20/2017 03:14 AM by koreangametheory; Twist to the Lion / sheep puzzle
Hi I'm dealing with a problem that has a slight twist to the lion and sheep problem. The problem is as follows
Lions - (1,2 ....K)
Sheeps - (1,2 ....K-1)
Lion choose to ( Eat, not eat) sheep
If k-th lion choose to eat, he becomes sheep for k+1th lion
pay off : lions gains positive payoff from eating but not at a cost
of being eaten

What is the Subgame perfect equilibrium for this problem?

My initial answer to this was (1,2.....K-1 lion choose not eat / K lion choose to eat), but other people have been telling me that the answer
is identical to the original typical lion-sheep problem
where the number of sheep is fixed at 1

but my thought is that, for starters, the answer to the original
problem says the equilibrium changes for odd/even number of lions
that is clearly not a subgame perfect equilibrium. In that it is not
the equilibrium realized in every subgame.

Sorry for the broken english, as english is not my first language
can anyone help?
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