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I am drawing this question from Berkeley's AI course (also not sure if it is the correct place to ask, so I apologize ahead of time) https://inst.eecs.berkeley.edu/~cs188/pacman/course_schedule.html

Currently, I am working on section 3's Homework.

My question is: the question (Part 1, question 6). Why is it that we can only guarantee that if the Min agent acts suboptimally, the best we can hope for is the following enter image description here

It seems that we can put any arbitrary value for the second node e.g. whey does it have to be -Episolon. It could be any range of values, e.g. Epsilon, in which case we would have optimised the Player A

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  • $\begingroup$ Try to summarize your research question;please! $\endgroup$
    – quintumnia
    Jan 23 '17 at 8:19
  • $\begingroup$ The question is very simple - why does A's outcome on the second branch have to be minus epsilon? Couldn't it be any random number? $\endgroup$ Jan 23 '17 at 8:48
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(using X for epsilon because keyboard)

This is just a hypothesis, but if you have a maximising agent and a minimising agent, then the optimal outcome for A (maximising) is to sweep the board (X,0), while the optimal outcome for B (minimising) is (-X,0) because B is minimising A's score, not their own.

A's optimal outcome is then complicated by the factor for sub-optimality, which we then imagine approaches zero.

There seem to be a bunch of assumptions that are not articulated, though, if this hypothesis is true.

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