Commentary for Arakhin 8:2

אָמַר אֶחָד, הֲרֵי הִיא שֶׁלִּי בְעֶשֶׂר סְלָעִים, וְאֶחָד אוֹמֵר בְּעֶשְׂרִים, וְאֶחָד אוֹמֵר בִּשְׁלשִׁים, וְאֶחָד אוֹמֵר בְּאַרְבָּעִים, וְאֶחָד אוֹמֵר בַּחֲמִשִּׁים. חָזַר בּוֹ שֶׁל חֲמִשִּׁים, מְמַשְׁכְּנִין מִנְּכָסָיו עַד עָשֶׂר. חָזַר בּוֹ שֶׁל אַרְבָּעִים, מְמַשְׁכְּנִין מִנְּכָסָיו עַד עָשֶׂר. חָזַר בּוֹ שֶׁל שְׁלשִׁים, מְמַשְׁכְּנִין מִנְּכָסָיו עַד עָשֶׂר. חָזַר בּוֹ שֶׁל עֶשְׂרִים, מְמַשְׁכְּנִים מִנְּכָסָיו עַד עָשֶׂר. חָזַר בּוֹ שֶׁל עֶשֶׂר, מוֹכְרִים אוֹתָהּ בְּשָׁוְיָהּ וְנִפְרָעִים מִשֶּׁל עֶשֶׂר אֶת הַמּוֹתָר. הַבְּעָלִים אוֹמְרִים בְּעֶשְׂרִים, וְכָל אָדָם אוֹמְרִים בְּעֶשְׂרִים, הַבְּעָלִים קוֹדְמִים, מִפְּנֵי שֶׁהֵן מוֹסִיפִין חֹמֶשׁ:

If one said: “I will acquire it for ten selaim” and another, “[for] twenty”, and another “for thirty”, and another “for forty”, and another “for fifty” - if he [that bid] fifty reneged, they take pledges from his property up to ten selaim. If he [that bid] forty reneged, they take pledges from his property up to ten selaim. If he [that bid] thirty reneged, they take pledges from his property up to ten selaim. If he that bid twenty reneged they take pledges from his property up to ten selaim. If he that bid ten reneged they sell [the field] for what it is worth, and collect what remains from him who bid ten. If the owner bid twenty and any other man bid twenty, then the owner comes first, because he must add one fifth.

Bartenura on Mishnah Arakhin

ממשכנין מנכסיו עד עשר וכו' (they exact a surety from his property for ten) – and these words are when they retracted one after the other. But if they retracted all of them together, they divide in thirds between them equally. How so. If the first said: “This is mine for ten,” and the second said: “[this is mine] for twenty” and the third said:” [this is mine] for twenty-four, and the second and third [individuals] retracted as one, they give it to the first [individual] for ten, and exact a surety from the property of the second for seven and from the property of the third for seven, and it is found, that what is given in dedication to the Temple collects twenty four. And similarly, if all three of them retracted as one (i.e., at the same time), and the object was sold from that which was dedicated to the Temple to all three, they exact a surety from the properties of each one of the three [individuals] seven Sela. And such is the manner forever.

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English Explanation of Mishnah Arakhin

If one said: I will acquire it for ten selas, and another, [for] twenty, and another for thirty, and another for forty, and another for fifty, If he [that bid] fifty reneged, they take pledges from his property up to ten selas. If he [that bid] forty reneged, they take pledges from his property up to ten selas. If he [that bid] thirty reneged, they take pledges from his property up to ten selas. If he that bid twenty reneged they take pledges from his property up to ten selas. If he that bid ten reneged they sell [the field] for what it is worth, and collect what remains from him who bid ten.
In this imaginative scenario there is initially a bidding war for the field, each person upping the previous bid by ten selas. Finally, the bid is won by the person who bid 50 selas. Then all of the bidders begin to renege. The mishnah delineates how the Temple deals with this situation. Notethe idea is that the Temple should collect the highest bid, but that all of those who bid should have to pay something. Basically the Temple takes a pledge from each person equivalent to the amount that he upped the previous bid ten selas. When they get to the last person, they simply sell the field and then take from him the difference between ten and the sale price. In this way, the Temple collects fifty selas, but no more than fifty selas.

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English Explanation of Mishnah Arakhin

If the owner bid twenty and any other man bid twenty, then the owner comes first, because he must add one fifth.
If the owner and another person put forth the same bid, the owner's bid is accepted because he must add an extra fifth. In this way the Temple maximizes its profits.

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