Safe bidding policies for multi-input producers in arbitrary networks

Determine whether there exists a producer bidding policy for the SAMP-SB simultaneous ascending (M+1)st-price auction protocol that is safe for producers with multiple complementary inputs in arbitrary task dependency networks—i.e., guarantees that no producer obtains negative surplus in quiescence—and, if such a policy exists, construct it; otherwise, prove impossibility under the protocol’s rules.

Background

The paper defines the SAMP-SB auction protocol and studies its convergence and efficiency properties. A producer bidding policy is termed “safe” if it prevents producers from ending quiescence with negative surplus. The authors introduce a variant, safe SAMP-SB, and prove it ensures 2-δ-competitive equilibrium for networks without input complementarities (single-input producers).

However, for producers with multiple complementary inputs in arbitrary task dependency networks, the authors cannot guarantee safety and explicitly note that they do not know of any safe producer bidding policy beyond degenerate choices. This leaves open whether such a policy can be devised or must be shown impossible within the protocol’s constraints.