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📗 Consider a state space where the states are positive integers between 1 and . State \(i\) has two neighbors \(i - 1\) and \(i + 1\) (subject to the boundary constraints). State \(i\) has score . If one runs the hill climbing algorithm, which initial states can reach the global minimum? Break tie by moving towards the global minimum. If there are multiple global minima, count all of them.
📗 In GoogSoft, software engineers A and B form a two-person team. Their year-end bonus depends on their relative performance. The bonus outcomes are summarized in the following table. The value of slacking to each person is \(s\) = . The total payoff to each person is the sum of the bonus and the value from slacking. What is the smallest integer value of \(x\) such that both players will work hard in a Nash equilibrium?
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