## 1 Introduction  
In the research of multi-agent simulations, several types of auction mechanisms have been investigated extensively to solve large-scale distributed resource allocation problems [1] and several applications have been proposed in different kinds of markets [2; 3; 4]. In the auctions, resources are generally supposed to have clear capacity limitations, and in some cases they also have explicit temporal limitations on their value [5]. In other words, the resources are modeled to be _perishable_ in some problem settings. This study discusses the problem of trading perishable goods, such as fish and vegetables, in a market. Several enterprises produce perishable goods or services and make profits by allocating them to dynamic demand before they deteriorate. In the services industries, _revenue management_ techniques [6] have been investigated. Their objective is to maximize the revenues of a single seller because revenue management is typically practiced by the seller for its own profit. Therefore, it is difficult to apply those techniques to the markets, in which perishable products of multiple sellers must be traded in a coordinated manner to maximize social utility. Agricultural and marine products are usually traded at _spot markets_ (The opposite of spot markets are _forward markets_, which trade goods before production.) that deal in already-produced goods because their quantity and quality are highly uncertain in advance of production. Hence, their production costs are _fixed_ in the markets. Their _salvage value_ is zero because they perish when they remain unsold in the markets. Therefore, their production costs are _sunk_ and sellers' marginal costs are zero in the traditional one-shot markets for perishable goods. This justifies extensive use of one-sided auctions, in which only buyers submit bids, for deciding allocations and prices of perishable goods in fresh markets [7]. However, in such markets, sellers cannot straightforwardly influence price making to obtain fair profits [8]. In _double action_ (DA) markets [9], both buyers and sellers submit their bids and an auctioneer determines resource allocation and prices on the basis of their bids. Recent studies [10; 11; 12] have applied multi-attribute double auction mechanisms to perishable goods supply chain problems using mixed integer linear programming. Although their approach is powerful in dealing with idiosyncratic properties of perishable goods, such as lead time and a shelf life, they have not considered the fluctuating nature of perishable goods markets, where supply and demand change dynamically and unpredictably. To solve the problem, we develop an _online DA_ market, in which multiple buyers and sellers dynamically tender their bids for trading commodities before their due dates. Our online DA market is developed as an instance of a _call market_, which collects bids continuously and clears the market periodically using predetermined rules. Since bids in the call market have multiple matching chances, the perishable goods in the call market can hold certain salvage values until their time limits. Therefore, sellers can participate in the price-making process of the online DA market, in which their reservation prices are equal to remaining values of the goods. However, since values of the perishable goods decrease progressively, sellers have an incentive to discount their price for fear of spoiling unsold goods. Taking advantage of such an incentive of the sellers, buyers can increase their surplus by bidding a lower price. Nevertheless, buyers need to bid a moderate price for securing the goods before time limits for procurement. Related ResearchUntil recently there has been little research undertaken on the online DA. As a preliminary study for an online DA, an efficient and truthful mechanism for a static DA with temporally constrained bids was developed using weighted bipartite matching in graph theory [13].