Advanced Game Theory, Matrix Analysis, and Optimization Techniques1)How do you determine the eigenvalues and eigenvectors in a given matrix? What steps areinvolved in approximating the eigenvector, and how are Shapley values used torationalize thepayoff in a multi-player scenario?A and B are definitions.The first step in C is to find the real eigenvalues. There is only one. Because we used anapproximate value for the eigenvalue, our eigenvector will not be perfect.As a first approximation, notice that 34/18 = 17/9, so choose x3= 9From the second row, this makes x2= 17From the first row, this makes x1= 48Normalizing this eigenvector gives the weightsD is a rationalization involving Shapley value calculations. It should be obvious that eachminer will have the same value and payoff.2)How does Floyd’s algorithm work, and what are the steps for applying it in the currentassignment? How do you present the results of this method and discuss the implications of thefindings?A is just references.B uses Floyd’s method exactly like the first assignment.Preview Mode
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