## 1 Introduction
In addition, for online DAs, some studies have addressed several important aspects of the mechanism, such as design of matching algorithms with good worst-case performance within the competitive analysis framework [14], construction of a general framework that facilitates a truthful dynamic DA by extending static DA rules [15], and an application to electric vehicle charging problems [16]. Although these research results are innovative and significant, we cannot directly apply their mechanisms to our online DA problem because their models incorporate the assumption that trade failures never cause a loss to traders, which is not true in perishable goods markets. It is demonstrated that no efficient and Bayesian-Nash incentive compatible exchange mechanism can be simultaneously budget balanced and individually rational [17]. For a static DA mechanism with temporal constraints, it is shown that the mechanism is dominant-strategy incentive compatible (or strategy-proof) if and only if the following three conditions are met: (1) its allocation policy is _monotonic_, where a buyer (seller) agent that loses with a bid (ask) \(v\), arrival \(a\) and departure \(d\) also loses all bids (asks) with \(v^{\prime}\leq v\) (\(v^{\prime}\geq v\)), \(a^{\prime}\geq a\) and \(d^{\prime}\leq d\) (When we must distinguish between claims made by buyers and sellers, we refer to the _bid_ from a buyer and the _ask_ from a seller. ); (2) every winning trader pays (or is paid) her _critical value_ at which the trader first wins in some period; and (3) the payment is zero for losing traders [13]. In the perishable goods market, the third condition cannot be satisfied because losing sellers have to give up the value of their unsold goods. Even when buyers bid truthfully, the sellers have a strong incentive to discount their valuation when their departure time is approaching and their goods remain unsold. With the knowledge of the sellers' incentive to discount their goods, buyers have an incentive to take advantage of sellers' discounts by underbidding. A mechanism that fails to induce truthful behavior in its participants cannot be efficient, because it does not have the information necessary to make welfare-maximizing decisions. In addition, for online DA markets, it is impossible to achieve efficiency because of the imperfect foresight about upcoming bids [18]. Therefore, neither perfect efficiency nor incentive compatibility can be achieved in the online DA market for perishable goods. In order to develop stable and socially profitable marketsfor perishable goods, we need to investigate a mechanism that imposes (weak) budget balance and individual rationality while promoting reasonable efficiency and moderate incentive compatibility. In perishable goods markets, 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. In our previous research [19], we designed a new online DA mechanism called the criticality-based allocation policy. In order to reduce trade failures, the mechanism prioritizes bids with closer time limits over bids with farther time limits that might produce more social surplus. The proposed mechanism achieves fair resource allocation in the computer simulations, assuming that agents report their temporal constraints truthfully. However, in the proposed mechanism, traders have an incentive to bid late in order to improve allocation opportunities by increasing the criticality of their bids. This causes unpredictable behavior of traders and leads to deterioration of market efficiency. In this study, extending our previous research, we incrementally develop a heuristic online DA mechanism for perishable goods with a standard greedy price-based allocation policy and achieve fair resource allocation by penalizing buyers' untruthful bids while maintaining their individual rationality.