In sequential auctions the phenomenon of declining prices is often observed, which in theory can be represented by a supermartingale. This paper employs the perspective that bidders’ values may change over stages and the common priors are sequentially adjusted by the remaining bidders. It is shown that the declining price sequence can be explained by the adjustment of common priors between auctions. The adjustment of common priors is characterized by stochastic orders. Sufficient and necessary conditions for a supermartingale price sequence are derived. In transactions of the phenomenon of declining prices is often observed, which in theory can be represented by a supermartingale. This paper employs the perspective that bidders’ values ​​may change over stages and the common priors are preformed by the remaining bidders. That the declining price sequence can be explained by the adjustment of common priors between auctions. The adjustment of common prior is is characterized by stochastic orders. Sufficient and necessary conditions for a supermartingale price sequence are derived.