On the Expressiveness of Assignment Messages
Maximilian Fichtl
TL;DR
This paper demonstrates that the class of valuation functions representable through integral assignment messages is a strict subset of strong substitutes valuations, indicating some strong substitutes valuations cannot be expressed with assignment messages.
Contribution
It establishes a formal separation showing that not all strong substitutes valuations are representable via integral assignment messages.
Findings
Integral assignment messages do not capture all strong substitutes valuations.
Strong substitutes valuations form a broader class than those representable by assignment messages.
The paper provides a theoretical proof of the subset relationship.
Abstract
In this note we prove that the class of valuation functions representable via integral assignment messages is a proper subset of strong substitutes valuations. Thus, there are strong substitutes valuations not expressible via assignment messages.
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