## 5 Incremental Improvement of Market Mechanism
### Adjusting Buyers' Penalty Based on Market Condition  
Since buyers are more likely to underbid for increasing their surpluses in the lower-risk markets, as shown in Table 1, larger penalties must be imposed on buyers' trade failures in the lower-risk markets in order to prevent buyers' strategic bidding. For this purpose, we modify the buyer's penalty on matching failures as follows:  
\[\tilde{p}_{j}^{t}=p_{j}^{t}\times 0.5/(1.0-MatchingRate()) \tag{6}\]  
In Equation (6), \(MatchingRate()\) is a function that calculates a current successful matching rate of bids and asks in the market. If the matching rate is above 50%, the market is considered to have a low risk of trade failures and the adjusted buyer's penalty \(\tilde{p}_{j}^{t}\) has a larger value than the original penalty \(p_{j}^{t}\). We call the DA mechanism with the modified penalty an _adaptively penalized DA mechanism_. Table 2 shows the payoff matrix between sellers and buyers in the low-risk market shown in Figure 1c with the adaptively penalized DA mechanism. The table shows that there are three Nash equilibria strategy profiles: (MODE, CONR 0.2), (STEP, CONR 1.0), and (MONO, CONR 1.0). To be noted is that we consider (MONO, CONR 1.0) is a Nash equilibrium because its seller's utility (i.e., 1051) is not significantly smaller than the seller's utility in (STEP, CONR 1.0) (i.e., 1058) based on its standard deviation (i.e., 147). Among them, adopting CONR 0.2 strategy is risky for buyers for the same reason explained in Section 5.2. Therefore, (STEP, CONR 1.0) and (MONO, CONR 1.0) are more feasible strategy profiles to be executed in the low-risk market with the adaptively penalized DA mechanism. From the above equilibrium analysis, it is found out that buyers maximize their profits by truthfully reporting their true valuation and the adaptively penalized DA mechanism achieves quasi incentive compatibility for buyers. The adaptively penalized DA mechanism also succeeds in achieving quasi incentive compatibility for buyers in riskier market conditions, such as Figure 1a,b, as shown in Tables 3 and 4. As explained, the results in the first row of the tables are the same as those of the naive DA mechanism. (MODE, CONR 0.2) is a dominant strategy equilibrium when sellers are not allowed to bid in the naive DA market, which is the case with the conventional perishable goods markets. Therefore, by comparing the results of (MONO, CONR 1.0) strategy profile with those of (MODE, CONR 0.2) strategy profile, we can clarify the effects of applying the adaptively penalized DA mechanism to perishable goods markets. From the abovementioned results, we find that the adaptively penalized DA mechanism increases sellers' utility while it depresses buyers' utility and decreases total utility especially in higher-risk markets. This means the adaptively penalized DA mechanism makes markets fairer, but it also makes markets less efficient in high risk conditions due to low matching rates. However, since the inefficiency of markets largely comes from sellers' loss of perished goods (i.e., 7984 in the high-risk market and 3797 in the medium-risk market), sellers can improve their profits and the market's efficiency by controlling their supplies based on the estimated market condition. In the adaptively penalized DA market, sellers can make a reasonable estimation of the market conditions from their matching rates, which is not possible with the conventional markets in which almost all of the supplies are sold at equally low prices regardless of the market conditions (i.e., 4 in the high-risk market, 5 in the medium-risk market, and 7 in the low-risk market).