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agents allocation assignment assume Bayesian bidders Bikhchandani bundle selection bundles to bid calculate chapter combinatorial auctions consider constraint cost function defined denote discuss distribution economies of scope edge owners edge-ordered edge-owners equation equilibrium price vector example expected profit extensive form game Figure final price formulation fraction game theory lane bundle lane ij lanes or bundles learning algorithms maximize maximum MCST method minimum spanning tree mixed strategy MPST multi-round Nash equilibrium NETRAM mechanism nodes normal form game number of bundles number of lanes number of rounds parameters participating players pricing equilibrium private information probability of winning pure strategy select bundles seller set of edges set of lanes shipper solution solving spanning tree networks Step strategy profile subgame perfect equilibrium synergy Theorem total cost transportation service procurement trucks update utility valuation Vickrey Walrasian equilibrium winning a bundle winning bid winning price