Consider the selfish load balancing scenario of m equispeed machines (all speeds equal to 1) and...

 

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Consider the selfish load balancing scenario of m equispeed machines (all speeds equal to 1) and n selfish users (user i = 1,..., n) with integer weights W, W2...., Wn. User i has to choose a single specific machine to allocate her weight, w. The cost of user i, provided that she chooses to allocate her load w, to machine j, is exactly the sum of all loads that are allocated to machine j. For any particular allocation A of weights to machines as described above, let (A) be the (total) load of machine j. Consider the function: m F(A) = R(A) ju1 (5 marks) Is this function a potential of the load balancing game considered? Please answer with a YES or NO. If you answered YES, then what type of potential is it? (15 marks) Justify your answer to (a). (5 marks) Does this game have pure Nash Equilibria ? Please answer with a YES or NO. Consider the selfish load balancing scenario of m equispeed machines (all speeds equal to 1) and n selfish users (user i = 1,..., n) with integer weights W, W2...., Wn. User i has to choose a single specific machine to allocate her weight, w. The cost of user i, provided that she chooses to allocate her load w, to machine j, is exactly the sum of all loads that are allocated to machine j. For any particular allocation A of weights to machines as described above, let (A) be the (total) load of machine j. Consider the function: m F(A) = R(A) ju1 (5 marks) Is this function a potential of the load balancing game considered? Please answer with a YES or NO. If you answered YES, then what type of potential is it? (15 marks) Justify your answer to (a). (5 marks) Does this game have pure Nash Equilibria ? Please answer with a YES or NO.