Strategic Buyers in a Sum Bid Game for Flat Networks

This note addresses scenarios of buyers purchasing rate along paths in a nonhierarchical communication network. A sum bid game is proposed in which each buyer submits a bid, also equal to a payment, and the network allocates rate in a weighted proportionally fair fashion, with the bids as the weights. This is in contrast to an itemized bid game, considered recently by Johari and Tsitsiklis, under which a buyer separately bids for rate on each link along a path. Johari and Tsitsiklis show that the worst case efficiency for allocation by strategic buyers is 75% for the itemized bid game. It is argued in this note that the sum bid game captures more fully the interactions among strategic buyers. It is shown in a simple example that the worst case efficiency for the sum bid game is zero, meaning that the cost of strategic behavior on the part of the buyers can approach 100%. It is also shown that Nash equilibria can fail to exist for the sum bid game, and the payoff function of a buyer need not be concave.