Homework2Solution.pdf - Stat 155 Fall 2019 Homework 2...

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Stat 155 Fall 2019Homework 2: SolutionSolution to Problem 1Supposeai1,j1andai2,j2are saddle points. From the definition of saddle point we getai1,j1ai1,j2ai2,j2ai2,j1ai1,j1(the first and the third inequalities are due to the fact that a saddle point is the smallest element inits row, the other two are due to the fact that a saddle point is the largest element in its column.)Thus,ai1,j1=ai2,j2.Solution to Problem 2First, let’s find all the saddle points.We underscore the maximal elements in each column, andmake the minimal elements in each row bold:Player IIABCDPlayer IA3242B2130C2222One can see that there are 4 bold underscored elements, so there are exactly 4 saddle points inthis game: (A, B), (A, D), (C, B), (C, D).Now we solve the game using dominance:324221302222— The 1st, 2nd and 3rs columns are dominated by the 4th,***2***0***2— The 1st and 2nd rows are dominated by the 3rd,***********2— only 1 by 1 is left.

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