Advanced Game Theory And Network Optimization: Algorithms, Strategies, And Applications

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Advanced Game Theory and Network Optimization: Algorithms, Strategies, and Applications 1) A) Definitions for the first three parts Part iv is finding the Shapley value as in previous exercises B) Again definitions for the first three parts. Part iv uses Johnson’s algorithm 2) Reduce the matrix by domination. Find conditions on probabilities and solve for column player. Then find row player strategy that creates equilibrium. B) Reduce the game to 2x2. Now there is a saddle point in the 2x2 matrix C) This one is discussed in the file. 3) Already worked 4) First part is a definition Second part uses Dijkstra’s method Third part uses Floyd’s method. Numbers that change are circled. Fourth part finds maximum flow and minimal cut. Remember that a cut must separate the network into two disjoint subsets. Fifth part is to find maximum spanning tree. All nodes must be visited. 1) A) First three are definitions. Fourth part has a saddle point B) First three are again definitions. Fourth part is minimum spanning tree
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