BOUDIN, Chief Judge.

Augusta News brought this antitrust case in district court against Portland News, Hudson News, and Hudson-Portland News, LLC (the “LLC”). Augusta alleged violations of both section 2(c) of the Clayton Act, 15 U.S.C. § 13(c), as amended by the Robinson-Patman Act, Pub. L. No. 74-692, 49 Stat. 1527 (1936), and section 1 of the Sherman Act, 15 U.S.C. § l. 1 After discovery was complete, the district court granted summary judgment on all counts for the defendants and Augusta appealed to this court. We begin with a statement of background facts.

Prior to 1995, publishers seeking to sell magazines and newspapers in Maine sold them to local wholesale distributors who then resold the publications to retailers at a discount off the printed cover price. Augusta News and Portland News were two of five local wholesale distributors operating in Maine in late 1995; the others were Magazines, Inc., Winebaum News and Maine Periodical Distributors. Each wholesaler served a de facto exclusive territory and operated as the sole supplier of periodicals to all retailers within that locale.

In late 1995, this system began to change in Maine (and elsewhere) at the insistence of the large retail chains like Wal-Mart, which comprised much of the distributors’ sales. Rather than deal with numerous distributors, the large multi-lo-cation retailers sought to consolidate regionally their purchasing of publications and obtain from the chosen regional distributor lower prices, centralized billing, *43 and improved service. In response to such retailer demands, two distributor entities began to compete for chain business on a regional basis in New England in 1995.

The first, Retail Product Marketing (“RPM”), was formed in September 1995 by fifteen independent wholesale distributors in New England, including two in Maine: Portland and Magazines, Inc. Although Augusta was offered the opportunity to join RPM, it declined to do so. RPM members agreed to bid for large retail chain contracts exclusively through RPM. When an RPM bid was successful, RPM says that it would then determine which RPM member or members would service the retailer’s various locations throughout New England, based on retailer preference and other considerations such as the location of individual RPM members.

The second entity — -which became the primary competitor to RPM for regional business — was Hudson, a wholesale distributor based in New Jersey with operations in New York and parts of New England. In November 1995, Hudson signed a contract to supply all Wal-Mart stores in the Northeast, including four stores previously serviced by Augusta accounting for about 10 percent of Augusta’s business. In December 1995, Hudson won a bid against RPM to supply all of Hannaford’s 80 stores in the Northeast, including 11 stores previously serviced by Augusta representing 40 percent of Augusta’s business.

In late December 1995, Hudson formed a joint venture with Portland (the Hudson-Portland LLC) under which Portland would service all of Hudson’s customers in Maine, including customers acquired after the agreement. Thereafter, Hudson prevailed over RPM in bidding to supply K-Mart’s Northeast stores (March 1996) and Cumberland Farms’ New England stores (late July 1996); Portland serviced these accounts. However, Portland remained a member of RPM, eligible for any business RPM won in competition with Hudson.

Like Hudson, RPM was successful in obtaining region-wide business. In March 1996, it won a bid to supply 100 Shaw’s Supermarkets locations throughout New England, two of which were in Augusta’s formerly exclusive territory. In April, RPM won over all of Christy’s stores in New England, including eight locations previously served by Augusta, and- all of CVS’s stores in Maine, four of which had been serviced by Augusta. In July, RPM secured the contract for Rite Aid stores in Maine, some of which had been serviced by Augusta.

RPM and Hudson each offered large upfront per-store fees to the chain retailers. For example, Hudson paid Hannaford $1,000 per store and K-Mart between $1,000 and $5,000 per store to secure exclusive contracts. RPM paid from $667 per-store for each existing CVS location to $15,000 per-store for each Rite Aid location. The amounts were sometimes paid annually and sometimes spread over the life of the- contract. Some retailers demanded the fees; one, Wal-Mart, declined to accept them. Under the RPM charter, the fees were paid by the member which serviced the store. Under the Hudson-Portland LLC agreement, Portland agreed to pay the fees for every store it serviced.

Augusta, which refused to offer retailers up-front fees, rapidly lost its chain store customers. Augusta says that it thought such payments were illegal and unprofitable. Augusta also chose not to service customers on a regional level, bidding only for the local or state-wide business of the chains. In July 1996, concluding that it could not stay in business without the retail chain stores that it had lost to Hudson and RPM, Augusta closed its doors.

*44 In June 1999, Augusta filed this suit in the federal district court in Maine. Augusta’s complaint claimed that up-front fees paid by Hudson and Portland violated section 2(c) of the Clayton Act, as amended by the Robinson-Patman Act, and section 1 of the Sherman Act. In addition, Augusta charged that Hudson and Portland (and possibly RPM’s other members) had agreed to divide the Maine market, in violation of section 1 of the Sherman Act.

Soon after the present suit was brought, Hudson merged operations with RPM to form Hudson-RPM. Allegedly, it is now the only regional distributor servicing large retail chains in Maine. The new entity also stopped offering up-front fees to retailers on new contracts.

After discovery was complete, Hudson and Portland moved for summary judgment. In a careful opinion, the magistrate judge recommended granting the motion, finding that the up-front fees were price concessions, rather than brokerage payments, and therefore not covered by section 2(c), and that Augusta’s section 1 claim lacked merit because Augusta had failed to show injury to competition. In a brief order, the district court affirmed the recommendation and entered judgment for defendants. This appeal followed.

We begin with Augusta’s claims under the Robinson-Patman Act: one, set forth in the complaint and resolved adversely to Augusta in the district court, is that the up-front fees paid by Hudson and Portland were brokerage fees or other concessions forbidden by section 2(c); the other is a claim that these payments violated section 2(a)’s restriction on price discrimination, a claim that Augusta belatedly sought to introduce into the case after the magistrate judge’s recommended decision. The relationship between the two Robinson-Patman provisions is relevant.

As adopted in 1914, the original section 2 of the Clayton Act simply prohibited sellers from discriminating in price among purchasers of commodities “where the effect of such discrimination may be to substantially lessen competition or tend to create a monopoly” — subject to a cost defense and a meeting competition defense. Pub. Law No. 63-212, 38 Stat. 730-31 (1914). When section 2 was revised in 1936 by the Robinson-Patman Act, this anti-discrimination ban was re-designated as section 2(a) (with a portion re-located into section 2(b) and elaborated in certain respects not pertinent here).

At the same time, Congress added section 2(c) as a new and more rigid ban on certain brokerage or other payments. The full text of section 2(c) is as follows:

It shall be unlawful for any person engaged in commerce, in the course of such commerce, to pay or grant, or to receive or accept, anything of value as a commission, brokerage, or other compensation, or any allowance or discount in lieu thereof, except for services rendered in connection with the sale or purchase of goods, wares, or merchandise, either to the other party to such transaction or to an agent, representative, or other intermediary therein where such intermediary is acting in fact for or in behalf, or is subject to the direct or indirect control, of any party to such transaction other than the person by whom such compensation is so granted or paid.

15 U.S.C. § 13(c).

This convoluted paragraph has bewildered lawyers and judges ever since, but its history provides some enlightenment. The Robinson-Patman Act, unlike the ordinary antitrust laws, was designed less to protect competition than (in the midst of the Great Depression) to protect small businesses against chain stores. A partic *45 ular target were the discounts that manufacturers furnished to large chain stores. The revamped section 2(a) directly addresses such discounts; and the protective purpose accounts for certain anti-competitive rigidities in judicial interpretation of what might otherwise appear to be a conventional antitrust statute. 2

Section 2(c) was intended to close firmly a potential loophole in the new regime. Sellers often employ brokers, who are paid a commission, to seek out and arrange sales; one of the ways that chains obtained discounts was through the seller’s payments to the buyer, or to an agent of the buyer, for brokerage services not actually furnished or through a reduction in the selling price purportedly furnished in lieu of brokerage. With certain qualifications, section 2(c) sought to ban outright both such brokerage payments from seller to buyer and reductions in the selling price in lieu of brokerage; the ban covers other variations as well but “the seller to buyer” payment ban is the one pertinent here. 3

If section 2(c) were limited to brokerage payments or reductions in lieu of brokerage, then Augusta’s claim would be facially silly. The up-front payments in question have no relationship to traditional brokerage services at all: they do not purport to be for the sellers’ performance of brokerage services nor are they even claimed to correspond to amounts previously paid by the sellers to independent brokers to secure sales for the publishers. Robinson v. Stanley Home Prods., Inc., 272 F.2d 601, 604 (1st Cir.1959). The payments are simply price reductions offered to the buyers for the exclusive right to supply a set of stores under multi-year contracts.

Augusta makes no effort to identify any link between the up-front payment and brokerage. Nor does it say that it will offer evidence that such a link exists but has been concealed. Rather, at least in this court, it relies on the fact that section 2(c) itself speaks not solely of brokerage but of “commission, brokerage, or other compensation.” Ambitiously, Augusta suggests that any payment from seller to buyer is within the ban.

Admittedly, some courts have read the statute to apply to outright commercial, bribery whereby one party to the transaction corrupts an agent of the other. 4 This view builds on, but obviously goes somewhat beyond, a statement by the Supreme Court that congressional debates on section 2(c) show it to proscribe “other practices such as the ‘bribing’ of a seller’s broker by a buyer.” FTC v. Henry Broch & Co., 363 U.S. 166, 169 n. 6, 80 S.Ct. 1158, *46 4 L.Ed.2d 1124 (1960). Yet, a buyer might perform numerous legitimate services for a seller—advertising, special shelf space, warranty repairs—and the courts have never read section 2(c) as a general ban on seller-to-buyer payments without regard to purpose.

In this case, there is no link to brokerage payments, nothing was disguised, and Augusta does not claim that any agent was bribed or corrupted. All that we have is a payment—effectively a price reduction to the buyer—that was openly made for the exclusive right to supply specific buyer stores for a specific period. The antitrust laws are not automatically hostile to price reductions or to exclusive dealing. Section 2(c) remains a ban directed to a particular evil; it is not a mechanical prohibition on all price reductions cast in the form of one-time payments. See Zeller Corp. v. Federal-Mogul, 173 F.3d 858 (6th Cir.1999) (unpublished opinion).

A reduction in price to less than all customers may, of course, violate section 2(a), if the required effect on or threat to competition can be shown by the plaintiff and if the defendant cannot make out one or more of the defenses allowed by the statute. Augusta did not allege a violation of section 2(a) in its complaint. Discovery was conducted, and the summary judgment motions were filed and contested, on the assumption that section 2(a) was not part of the case. After the magistrate judge’s recommended decision, Augusta for the first time sought to proffer a claim under section 2(a).

It did so by suggesting, in its objections to the magistrate judge’s recommended decision, that the district court should allow an amendment to the complaint. The district court did not comment on the suggestion. In this court, Augusta says again that an amendment to the complaint should have been allowed. Appellees respond that Augusta did not properly raise the issue in the district court by filing a motion to amend and that no claim of error can be based on the failure to grant a motion that was never made. In any event, say appellees, the refusal of the suggestion was not error.

We will assume arguendo that Augusta’s desire to amend was made clear to the district court even if no formal motion was ever filed. But a plaintiffs request to add a new claim to the case after full discovery and after the grant of summary judgment to the defendants on all existing claims would require remarkable justification. See Hayes v. New England Millwork Distr., Inc., 602 F.2d 15, 19-20 (1st Cir.1979). Nothing remotely close to a good excuse for failure to make the motion earlier is provided by Augusta. Augusta’s suggestion that defendants would not be prejudiced by the need now to try the section 2(a) claim is not sufficient. 5

Independent of the Robinson-Patman Act claims, Augusta charged in its complaint that the defendants had violated section 1 of the Sherman Act, which in essence forbids agreements in restraint of trade. The magistrate judge recommended dismissal bf this claim as well on the ground that Augusta’s evidence did not establish a triable issue as to injury to *47 consumer welfare, e.g., through higher prices or reduced consumer choice among publications stocked in retail stores.

On appeal, Augusta’s principal argument is that no such evidence of injury to consumer welfare was required because the facts made out, or at least provided a basis for trial on, two different “per se ” theories. Specifically, Augusta says that “the agreements to pay up-front fees” were illegal and that the defendants, although competitors, agreed to “a horizontal division of markets.” Augusta also says that it made a showing of injury to consumer welfare even though this is unnecessary for a per se violation.

The premise from which Augusta departs is correct, but only the premise. Almost any agreement that affects or has the potential to affect interstate commerce is potentially within the reach of section 1; but the legality of most kinds of agreements (e.g., R & D projects, information sharing, distribution contracts) is tested by the rule of reason. Under that rule, adverse effects on consumer welfare are an important part of the equation. U.S. Healthcare, Inc. v. Healthsource, Inc., 986 F.2d 589, 595 (1st Cir.1993); California Dental Ass’n v. FTC, 224 F.3d 942, 958 (9th Cir.2000). The evaluation is not wholly ad hoc—there is a good deal of doctrine as to specific practices—but it is hard to imagine a rule of reason violation absent a potential threat to the public.

By contrast, a few agreements are deemed so pernicious that they are condemned “per se ” and without regard to the power of the parties to accomplish their aims, regardless of justification, and without any need to show an actual or potential adverse effect on consumer welfare. United States v. Socony-Vacuum Oil Co., 310 U.S. 150, 60 S.Ct. 811, 84 L.Ed. 1129 (1940). The classic cases are agreements to set prices, fix output or engage in horizontal market division. Minimum resale price maintenance remains a per se violation. See Addamax Corp. v. Open Software Found., Inc., 152 F.3d 48, 51 (1st Cir.1998). Concerted refusals to deal may or may not be so classed depending on various circumstances. U.S. Healthcare, 986 F.2d at 593.

The categorical descriptions of per se offenses are quite misleading for anyone not well versed in antitrust. For example, price-fixing in its literal sense is not condemned per se: virtually every sale is an agreement on price. The only price-fixing agreements that are condemned per se, with one narrow exception (minimum resale price-fixing), are agreements (1) between competitors (2) as to competing products or services (3) where, in addition, the agreement is not part of a larger, legitimate economic venture. Broadcast Music, Inc. v. Columbia Broadcasting Sys., Inc., 441 U.S. 1, 99 S.Ct. 1551, 60 L.Ed.2d 1 (1979).

Here, Augusta’s first claim—that “the agreements to pay up-front fees” were unlawful—reflects confusion by Augusta on several levels. Insofar as the agreements were between a legitimate selling entity and a buyer (e.g., between Hudson and K-Mart), the up-front fees were discounts on vertical prices of the kind that are “fixed”—and quite lawfully so—every time a buyer buys something from a seller. An agreement between competing distributors to offer such upfront fees to retailers, unconnected to any joint venture, might be a per se violation; but there is no clear claim by Augusta that this happened, no evidence for it, and no reason why competitors would make such an agreement.

Sellers do need to cooperate to raise or stabilize prices at a supra-competitive level because otherwise a hold-out seller could *48 undercut and defeat an increase. But to lower prices, sellers have no reason to agree; each can implement a decrease independently and the objective is normally to undersell the competitor’s undiscounted price and win the customer. Of course, a competing seller will in the future likely be forced to meet the lower price—which is why RPM and Hudson each made such reductions in the same time frame—and a seller who will not compete (like Augusta) will lose business. But this is not an agreement to restrain trade; it is just competition at work.

Both the existence of RPM and the Hudson-Portland distribution arrangement present more complex situations. In forming RPM, local distributors who were at least potential rivals (until then they had served exclusive territories) combined to seek region-wide customers; and incident to such offers, they might be viewed as acting through RPM to “agree” on upfront payments to the buyers. But it is a standard form of joint venture for local firms to combine to provide offerings— here, one stop service for large buyers— that none could as easily provide by itself, and a joint venture often entails setting a single price for the joint offering. See Rothery Storage & Van Co. v. Atlas Van Lines, Inc., 792 F.2d 210, 229 (D.C.Cir.), cert. denied, 479 U.S. 1033, 107 S.Ct. 880, 93 L.Ed.2d 834 (1986).

In particular cases, such joint ventures may well be unlawful under the rule of reason on any of numerous grounds; for example, the venturers may impermissibly collaborate beyond the necessary scope of the venture, see Addamax, 152 F.3d at 52 n. 5, or impermissibly exclude competitors from joining in the venture, see Northwest Wholesale Stationers, Inc. v. Pacific Stationery & Printing Co., 472 U.S. 284, 295-96, 105 S.Ct. 2613, 86 L.Ed.2d 202 (1985). But Augusta makes no effort to analyze the venture under the rule of reason. Indeed, after asserting that there was a combination to set up-front fees, it scarcely mentions the subject again, turning instead to the charge that the defendants engaged in horizontal market division.

The charge of horizontal market division is equally devoid of support insofar as it claims a per se violation. The basic notion underlying this per se offense is that two competitors may not agree not to compete for customers whether identified individually or by class—for example, that one will serve only customers in Massachusetts while the other will serve only those in Maine. Despite unguardedly broad language in United States v. Topco Associates, Inc., 405 U.S. 596, 92 S.Ct. 1126, 31 L.Ed.2d 515 (1972), it is commonly understood today that per se condemnation is limited to “naked” market division agreements, that is, to those that are not part of a larger pro-competitive joint venture. Addamax, 152 F.3d at 52 n. 5; Rothery, 792 F.2d at 229.

In all events, Augusta points to nothing to suggest that there was any agreement among the defendants or the defendants and others to divide markets in the sense of promising not to compete. It is not a per se violation for local competitors to join in providing region-wide service that none alone provided before; nor is it unlawful per se for a local competitor to agree to act as a local distributor for an out-of-state competitor who won the contract to serve a local store. Palmer v. BRG of Georgia, Inc., 498 U.S. 46, 111 S.Ct. 401, 112 L.Ed.2d 349 (1990), cited by Augusta, was more or less a sham transaction to disguise a naked market division arrangement and did not involve a bona fide joint venture.

It is worth stressing that the RPM joint venture, the Hudson-Portland arrangements, and the final merger of RPM and *49 Hudson may all have been subject to antitrust attack under section l’s rule of reason or, at least in the last instance, possibly under section 7 of the Clayton Act. Furthermore, the up-front payments were part of multi-year exclusive dealing contracts that might in principle be attacked under the rule of reason. Tampa Elec. Co. v. Nashville Coal Co., 365 U.S. 320, 327, 81 S.Ct. 623, 5 L.Ed.2d 580 (1961). But Augusta ignores or fails to develop these possibilities.

There is no reason for us to consider Augusta’s attacks on the finding by the magistrate judge that consumer welfare was not threatened or injured. The per se claims made by Augusta are without basis and, in this court, Augusta does not even attempt to make out a rule of reason case in which competitive effects would be relevant. At most, Augusta suggests that there were or may have been some negative effects on consumer price or choice; its most specific claim is that what were once local de facto monopolies in Maine, capable of fringe competition, have now been replaced by a larger state-wide monopoly.

The short answer is that in a rule of reason case, negative effects or threatened effects on consumer welfare are almost always a necessary element but they are not sufficient. One still has to identify a specific agreement, locate it within some doctrinal framework or body of precedent, and assess the competitive benefits and disadvantages of the agreement (along with the possibility of achieving the former through less restrictive means). See U.S. Healthcare, 986 F.2d at 596-97. This sounds like a difficult task and it usually is, which is why antitrust plaintiffs try to make out per se violations and, in default of them, rely heavily upon experts.

Nothing in Augusta’s appellate briefs develops a rule of reason case. It may well be that somewhere in the record there are facts and expert testimony that could have been used to construct such a case; but it is not the job of appeals courts to rummage unaided through the record, nor can the other side respond to a claim not seriously asserted on appeal. See U.S. Healthcare, 986 F.2d at 595. Absent an organized rule of reason case, it does not matter whether the magistrate judge got right each of the factual points that Augusta disputes.

Affirmed.

. The Maine antitrust statute, 10 M.S.R.A. §§ 1101-09 was also invoked in the complaint. Augusta treats the Maine antitrust claim as co-extensive with its federal claims so we do not address it separately.

. The most notable departure from standard antitrust analysis is the treatment of any economic loss to the customer of a discriminating seller as injury to competition (so-called "secondary line” injury). FTC v. Morton Salt Co., 334 U.S. 37, 46, 68 S.Ct. 822, 92 L.Ed. 1196 (1948). By contrast, where a competing seller is the plaintiff (a so-called "primary line” injury case), evidence of an actual threat to competition — not just economic loss to the disadvantaged seller — is required. Brooke Group Ltd. v. Brown & Williamson Tobacco Corp., 509 U.S. 209, 223, 113 S.Ct. 2578, 125 L.Ed.2d 168 (1993).

. On an initial reading, one might think that section 2(c) banned such brokerage payments only where they were shams, i.e., where they were not "for [brokerage] services rendered....” Case law, possibly based on a misreading of what the quoted phrase modifies, has been less forgiving. See Quality Bakers of America v. FTC, 114 F.2d 393, 398-99 (1st Cir.1940). Compare 14 Hovenkamp, Antitrust Law § 2362(d) (1999). This issue is not presented in this case.

. Bridges v. MacLean-Stevens Studios, Inc., 201 F.3d 6, 11 (1st Cir.2000) (collecting cases). This circuit has never decided whether a claim for commercial bribery is actionable under section 2(c). Id.

. Because the suggestion came too late and without any justification, we need not consider whether it also may be barred because not first presented to the magistrate judge prior to the recommended decision. This court has previously warned against efforts to treat the magistrate judge proceeding as "mere dress rehearsal,” reserving critical claims "for the second round” before the district judge. See Paterson-Leitch Co. v. Mass. Mun. Wholesale Elec. Co., 840 F.2d 985, 991 (1st Cir.1988).