Question: We aring two selfish users i1 and i2. User i1 is carrying a load (weight) w1=1 and user i2 is carrying a load w2=, where

We aring two selfish users i1 and i2. User i1 is carrying a load (weight) w1=1 and user i2 is carrying a load w2=, where >1. We are also given two identical machines M1 and M2. The delay function in each is equal to its load, i.e. dj(x)=x for each machine Mj. Each user can put her load in any of the two machines. Each pure allocation A of loads to the machines (equilibrium or not) has a global costc(A) which is the total load of the machine with the maximum load. (a) (5 marks) Find an optimal allocation OPT with respect to the cost c(). (b) (5 marks) What are the pure equilibria allocations? (c) (10 marks) What are the mixed equilibria of this game? (As probability distributions of each user i ). (d) (5 marks) What is the price of anarchy (PoA) of this game? Reminder: POA=max(OPDE(G(A)) over all equilibria A, where the expectation is calculated ac cording to the equilibrium probability distribution for each user

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