A formalization of quantity based double auction mechanism

Auction researches are promising field of applied autonomous agent technologies. In this paper, we formalize a double auction, which uses non-linear value function including divides items trading. In this trading, the valuation of the item is decided by quantum of the trading. In this regard, we consider multiple situations, because buyers' and sellers' value functions are not uniquely decided. In this paper, we give some feature examples, and suggest an analysis method. To solve the discontinuous function problem, we propose supplementation presumption method.