Path Auction Games When an Agent Can Own Multiple Edges

We study path auction games in which multiple edges may be owned by the same agent in this paper. The edge costs and the set of edges owned by the same agent are privately known to the owner of the edge. We show that in this setting, given the assumption the losing agent always has 0 payoff, there is no individual rational strategyproof mechanism in which only edge costs are reported. If the agents are asked to report costs as well as ownership, we show that there is no efficient mechanism that is false-name proof. We then study a first-price path auction in this model. We show that, in the special case of parallel-path graphs, there is always a purestrategy 2-Nash equilibrium in bids. We show that this result does not extend to general graphs: we construct a graph in which there is no such 2-Nash equilibrium.