Consider the following strategic setting involving a cat named Baker, a mouse na
ID: 1197785 • Letter: C
Question
Consider the following strategic setting involving a cat named Baker, a
mouse named Cheezy, and a dog named Spike. Baker’s objective is to catch
Cheezy while avoiding Spike; Cheezy wants to tease Baker but avoid getting
caught; Spike wants to rest and is unhappy when he is disturbed.
In the morning, Baker and Cheezy simultaneously decide what activity
to engage in. Baker can either nap (N) or hunt (H), where hunting involves
moving Spike’s bone. Cheezy can either hide (h) or play (p). If nap and
hide are chosen, then the game ends. The game also will end immediately
if hunt and play are chosen, in which case Baker captures Cheezy. On the
other hand, if nap and play are chosen, then Cheezy observes that Baker is
napping and must decide whether to move Spike’s bone (m) or not (n). If he
chooses to not move the bone, then the game ends. Finally, in the event that
Spike’s bone was moved (either by Baker choosing to hunt or by Cheezy
moving it later), then Spike learns that his bone was moved but does not
observe who moved it; in this contingency, Spike must choose whether to
punish Baker (B) or punish Cheezy (J). After Spike moves, the game ends.
In this game, how many information sets are there for Cheezy? How
many strategy profiles are there in this game?
Explanation / Answer
Ans 1 - In this game there are 4 information sets for Cheezy. Hide or Play & Move or Not Spike's bone.
Ans 2 - There are 8 strategy profiles in the game. 4 for Cheezy and 2 for Baker & Spike each.