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4. Consider the following strategic setting involving a cat named Baker, a mouse namedCheezy, and a dog named Spike. Baker’s objective is to catch Cheezy while avoidingSpike; Cheezy wants to tease Baker but avoid get- ting caught; Spike wants to rest andis unhappy when he is disturbed. In the morning, Baker and Cheezy simultaneouslydecide what activity to engage in. Baker can either nap (N) or hunt (H), where huntinginvolves moving Spike’s bone. Cheezy can either hide (h) or play (p). If nap and hideare chosen, then the game ends. The game also will end immediately if hunt and playare chosen, in which case Baker captures Cheezy. On the other hand, if nap and playare chosen, then Cheezy observes that Baker is napping and must decide whether tomove Spike’s bone (m) or not (n). If he chooses to not move the bone, then the gameends. Finally, in the event that Spike’s bone was moved (either by Baker choosing tohunt or by Cheezy moving it later), then Spike learns that his bone was moved butdoes not observe who moved it; in this contingency, Spike must choose whether topunish Baker (B) or punish Cheezy (J). After Spike moves, the game ends. In thisgame, how many information sets are there for Cheezy? How many strategy profilesare there in this game?
QuestionBaker the cat wishes to catch Cheezy the mouse while avoiding Spike to dog; Cheezy wishesto tease and dodge Baker; and Spike wishes to rest undisturbed. In the morning, Baker andCheezy…