Networking - Home Work - Tragedy of the Commons Consider same example, Tragedy of the Commons for Single Network Resource, with the following change: latency function, l (f) = 1 / (C-f), where f = {sxs , total used bandwidth on link Hence, net utility of user r, ir (tr) = xr - Xr/ (C - f) Social Welfare, W = Er Mr (xr) S S (1) Solve Selfish Optimization to obtain xe, and resulting Social Welfare, W ( xe) (2) Solve for Efficient Allocation, obtain x *, and Social Welfare, W(x *) r (3) Obtain Efficiency Loss (4) Show that Social Welfare from Efficient Allocation does not depend on R, whereas it does with Selfish Optimization (5) Show that Efficiency Loss -> 100% as R -> ~ Networking - Home Work - Tragedy of the Commons Consider same example, Tragedy of the Commons for Single Network Resource, with the following change: latency function, l (f) = 1 / (C-f), where f = {sxs , total used bandwidth on link Hence, net utility of user r, ir (tr) = xr - Xr/ (C - f) Social Welfare, W = Er Mr (xr) S S (1) Solve Selfish Optimization to obtain xe, and resulting Social Welfare, W ( xe) (2) Solve for Efficient Allocation, obtain x *, and Social Welfare, W(x *) r (3) Obtain Efficiency Loss (4) Show that Social Welfare from Efficient Allocation does not depend on R, whereas it does with Selfish Optimization (5) Show that Efficiency Loss -> 100% as R -> ~