➩ A-K (expected 237 students): (1180 Observatory Dr) SOC SCI 6210

➩ L-R (expected 136 students): (455 N Park St) HUMANTITIES 2650

➩ S-Z (expected 143 students): (1101 University Ave) CHEM S429

➩ Consider a search graph with \(7\) states \(\left\{1, 2, ..., 7\right\}\). For every \(1 \leq i < j \leq 7\), there is a directed edge from \(i\) to \(j\) with an edge cost of \(i + j\). The initial state is \(1\) and the goal state is \(7\). What is an example of an admissible heuristic?

➩ Consider the same search problem as in the previous question, what is an example of an admissible heuristic that dominates \(h\left(s\right) = 7 - s\)?

➩ Two players simultaneously offer \(x_{1}\) and \(x_{2}\) dollars to buy \(7\) dollars from the auctioneer. The player who offer the higher dollar amount will receive the \(7\) dollars, and the other player will receive \(0\) dollars. Break ties by giving the \(7\) dollars to player \(1\). The players' rewards are given by the money received minus the money offered. What are some pure strategy Nash equilibria of the game?

➩ Consider a zero-sum sequential game where the max player chooses one of \(7\) actions, and after the max player chooses any action, the min player chooses one of \(7\) actions. During the Alpha Beta pruning process, what is the maximum number of actions of the min player that can be pruned (assuming actions can be reordered)?

➩ Consider the MDP (Markov Decision Process) with two states \(1\) and \(2\) and two actions "stay" \(s\) and "move" \(m\). Staying in state \(1\) gives reward \(r\) and staying in state \(2\) gives reward \(0.5\). Moving gives reward \(0\). With discount factor \(\beta = 0.7\), what it the minimum reward value of \(r\) (between \(0\) and \(1\)) from staying in state \(1\) so that the policy \(\pi^\star\left(1\right) = s\) is the optimal policy?

➩ When using Genetic Algorithm, suppose the current population contains \(4\) states \(\begin{bmatrix} 1 \\ 0 \\ -2 \end{bmatrix} , \begin{bmatrix} 2 \\ 0 \\ -1 \end{bmatrix} , \begin{bmatrix} 1 \\ 0 \\ -1 \end{bmatrix} , \begin{bmatrix} -1 \\ 0 \\ 1 \end{bmatrix}\). The fitness function is \(f\left(\begin{bmatrix} x_{1} \\ x_{2} \\ x_{3} \end{bmatrix}\right) = \left(x_{1} + x_{2} + x_{3}\right)^{2}\). What are some possible states in the population in the next generation after single-point cross-over without mutation?