Court Opinion

ID: 6336933
Source: CourtListenerOpinion
Date Created: 2022-05-02 15:00:17.282156+00
Date Added: 2024-06-11T09:21:00.482888
License: Public Domain

20-3594-cr
United States v. Aiyer

                         United States Court of Appeals
                                 for the Second Circuit
                           _____________________________________

                                      August Term 2021

                    (Argued: August 27, 2021       Decided: May 2, 2022)

                                       No. 20-3594-cr
                           _____________________________________

                                 UNITED STATES OF AMERICA,

                                           Appellee,

                                           — v. —

                                       AKSHAY AIYER,

                                     Defendant-Appellant.
                           _____________________________________

Before:                   PARKER, BIANCO, and MENASHI, Circuit Judges.

       Defendant-Appellant Akshay Aiyer appeals from the October 2, 2020
judgment entered in the United States District Court for the Southern District of
New York (Koeltl, J.), following a jury trial, convicting him of conspiracy to
restrain trade in violation of Section 1 of the Sherman Act, 15 U.S.C. § 1. More
specifically, Aiyer was convicted for his participation in a conspiracy to fix prices
and rig bids in connection with his trading activity in the foreign currency
exchange market. His primary argument on appeal is that the district court erred
by failing to consider his proffered evidence that the alleged illegal trading activity
lacked anticompetitive effects and had procompetitive benefits and by refusing to
conduct a pre-trial assessment as to whether the per se rule or the rule of reason
applies in this case. Aiyer further contends that the district court abused its
discretion in largely precluding his competitive effects evidence from admission
at trial and in conducting only a limited post-trial inquiry into allegations of juror
misconduct. We hold that the district court was not required to make a threshold
pre-trial determination as to whether the per se rule or the rule of reason applies to
the alleged misconduct in this criminal antitrust case. The grand jury indicted
Aiyer for a per se antitrust violation and the government, which was proceeding
only under that theory, was entitled to present its case to the jury. The district
court properly assessed the sufficiency of the evidence of the alleged per se
violation at the time of Aiyer’s Rule 29 motion after the government rested its case
(which Aiyer renewed after trial), and the sufficiency decision upholding the
verdict is not challenged on appeal. In addition, given that the case was being
tried under the per se rule, the district court acted within its broad discretion in
strictly limiting the admission of Aiyer’s competitive effects evidence at trial to the
issue of intent. Finally, the district court did not abuse its discretion in ending its
post-trial investigation into alleged juror misconduct and concluding there was no
basis to vacate the jury’s verdict where such investigation included interviewing
the accused juror and finding his denial of the allegations credible.

      Accordingly, we AFFIRM the judgment of the district court.

                                              MARY HELEN WIMBERLY (Stratton C.
                                              Strand, Kevin B. Hart, Eric Hoffman,
                                              Philip Andriole, on the brief), United
                                              States Department of Justice, Antitrust
                                              Division, for Richard A. Powers, Acting
                                              Assistant        Attorney      General,
                                              Washington, DC, for Appellee.

                                              MARTIN B. KLOTZ, Willkie Farr &
                                              Gallagher LLP, New York, NY (Joseph
                                              T. Baio, Jocelyn M. Sher, Willkie Farr &
                                              Gallagher LLP, New York, NY, Mark
                                              Stancil, Willkie Farr & Gallagher LLP,

                                          2
                                              Washington, DC, on the brief), for
                                              Defendant-Appellant.

JOSEPH F. BIANCO, Circuit Judge:

      Defendant-Appellant Akshay Aiyer appeals from the October 2, 2020

judgment entered in the United States District Court for the Southern District of

New York (Koeltl, J.), following a jury trial, convicting him of conspiracy to

restrain trade in violation of Section 1 of the Sherman Act, 15 U.S.C. § 1.

Specifically, Aiyer was convicted for his participation in a conspiracy to fix prices

and rig bids in connection with his trading activity in the foreign currency

exchange market. His primary argument on appeal is that the district court erred

by failing to consider his proffered evidence that the alleged illegal trading activity

lacked anticompetitive effects and had procompetitive benefits and by refusing to

conduct a pre-trial assessment as to whether the per se rule or the rule of reason

applies in this case. Aiyer further contends that the district court abused its

discretion in largely precluding his competitive effects evidence from admission

at trial and in conducting only a limited post-trial inquiry into allegations of juror

misconduct. We hold that the district court was not required to make a threshold

pre-trial determination as to whether the per se rule or the rule of reason applies to

the alleged misconduct in this criminal antitrust case. The grand jury indicted

                                          3
Aiyer for a per se antitrust violation and the government, which was proceeding

only under that theory, was entitled to present its case to the jury. The district

court properly assessed the sufficiency of the evidence of the alleged per se

violation at the time of Aiyer’s Rule 29 motion after the government rested its case

(which Aiyer renewed after trial), and the sufficiency decision upholding the

verdict is not challenged on appeal. In addition, given that the case was being

tried under the per se rule, the district court acted within its broad discretion in

strictly limiting the admission of Aiyer’s competitive effects evidence at trial to the

issue of intent. Finally, the district court did not abuse its discretion in ending its

post-trial investigation into alleged juror misconduct and concluding there was no

basis to vacate the jury’s verdict where such investigation included interviewing

the accused juror and finding his denial of the allegations credible.

        Accordingly, we AFFIRM the judgment of the district court.

                                  BACKGROUND

I.    The Relevant Market 1

      This criminal antitrust case arises out of Aiyer’s alleged conduct in—and

corresponding communications relating to—the foreign currency exchange (“FX”)

1 Given that Aiyer appeals from a judgment of conviction entered after a jury trial, “our
statement of the facts views the evidence in the light most favorable to the government,
                                           3
market.    Participants in the FX market buy or sell one national currency in

exchange for another. In other words, FX trading takes place in currency pairs,

where one individual or entity sells a certain amount of one country’s currency to

another individual or entity that purchases that currency with a certain amount of

another country’s currency. See Gov’t Supp. App’x at 3–4 (“[L]et’s take an example

. . . you want to buy [U.S.] dollars in exchange for . . . Canadian dollars . . . . That

exchange . . . between United States dollar and Canadian dollars, that’s called a

currency pair. There are always two currencies because you have got to buy one

and sell the other.”). 2 The mechanism for pricing in the FX market is known as the

“exchange rate,” “rate,” or “price,” which essentially represents the amount of one

specific currency that a market participant can be paid in exchange for another

specific currency. App’x at 33. As of 2013, trillions of dollars in various currencies

were traded across this market each day.

crediting any inferences that the jury might have drawn in its favor.” United States v.
Percoco, 13 F.4th 158, 164 n.3 (2d Cir. 2021) (quoting United States v. Rosemond, 841 F.3d 95,
99–100 (2d Cir. 2016)).
2 There are numerous ways in which FX market participants can trade. However, the
“basic trade” in the FX market is known as a “spot trade,” where one party simply agrees
to buy one currency from a counterparty in exchange for a different currency, with
settlement to follow in two business days. Gov’t Supp. App’x at 13.
                                              4
      Turning to the market participants themselves, typical customers in the FX

market include pension funds, hedge funds, insurance companies, and

international corporations. These customers transact with FX traders at “dealer”

banks, which are “mostly very large, well-capitalized banks” that “stand[] ready

to buy or sell foreign exchange upon demand.” Gov’t Supp. App’x at 15. If a

customer wants to make an FX trade, he or she can solicit prices from multiple

dealer banks for a given currency pair and then “pick the best price.” Gov’t Supp.

App’x at 36. In this context, potential customers are provided with a “two-way”

price quote (or “spread”)—the “bid,” i.e., the price at which the dealer bank would

be willing to buy a particular currency, and the “offer” or “ask,” i.e., the price at

which the dealer bank would be willing to sell a particular currency. Gov’t Supp.

App’x at 15, 29–30, 113; see also App’x at 34.

      In addition to facilitating transactions for customers, dealer banks trade

currencies with one another, through employee-FX traders, in part of the FX

market known as the “interbank” (or “interdealer”) market. Gov’t Supp. App’x at

24; App’x at 36. Whether they are competing for transactions with customers or

with each other in the interdealer market, dealer banks compete on the basis of

price across the FX market.

                                          5
      Notably, unlike markets such as the New York Stock Exchange, the FX

market is not centralized; instead, the FX market operates internationally and is

almost always open.       In the absence of a centralized exchange, trading is

conducted in a variety of ways, including directly between dealer banks and

customers (or between dealer banks), through brokers, or over an “electronic

broking system,” such as the “Reuters matching system” (the “Reuters

platform”). 3 Gov’t Supp. App’x at 29–30.

II.   The Alleged Conspiracy to Restrain Trade

      Aiyer, along with Christopher Cummins, Jason Katz, and Nicolas Williams

(together, the “co-conspirators”), worked as FX traders at different dealer banks

where they traded, in varying degrees, Central and Eastern European, Middle

Eastern, and African (“CEEMEA”) currencies, such as the Russian ruble (or

“RUB”), South African rand (or “ZAR”), and Turkish lira (or “TRY”).4 The banks

at which the co-conspirators worked all competed with each other to win FX

customers’ trades.

3  Using the Reuters platform, FX traders can input proposed bids and offers, execute
trades, observe market trends, and view “the best bid and the best offer in the market.”
Gov’t Supp. App’x at 147.

4 In the FX market, other currencies, such as the U.S. dollar (or “USD”) and the euro (or
“EUR”) are said to trade “against” these currencies. App’x at 33.
                                           6
      At various times spanning from as early as October 2010 to at least July 2013,

the co-conspirators agreed not to compete with one another in terms of pricing

and also to coordinate in order to affect pricing in the FX market. Katz, who pled

guilty pursuant to a cooperation agreement with the government, testified at trial

that “the point of not competing with each other, that was kind of an undercurrent

that would just be there on a constant basis.”        Gov’t Supp. App’x at 157.

Communicating through Bloomberg’s instant messaging platform (“Bloomberg

chat”), among other means, the co-conspirators dispensed with competing for

trades—in both the interbank and more general customer contexts—and, instead,

coordinated in relation to the timing and amounts of their bids and offers.

      As summarized by Cummins, who also pled guilty pursuant to a

cooperation agreement with the government, the co-conspirators engaged in,

among other things, the following activities in the FX market:

            There were times, for example, when a client would call
            up and ask a number of us in the chat room for the same
            thing all at the same time, so we would convey to the
            others what we were being asked, as far as what currency
            and what size, and then indicate what price we were
            showing to the client, and in that way we could kind of
            coordinate what we would show and whether or not we
            wanted to win the trade and kind of denote who might
            be the winner of the trade but still maintain the look of a
            competition in the eyes of the client.

                                         7
              ...

              There were [also] times in the course of trading where . . .
              myself and the other guys in the chat room might have
              the same interest, meaning I might have an interest to
              buy dollars as well as someone else in the chat room had
              an interest to buy dollars against a certain currency or we
              might have the same interest to sell dollars. So one of us
              would be the one to place the interest in the market so
              that it didn’t give the market the appearance that there
              were a lot of buyers entering the market at one time,
              because that might push the market against us and we
              might buy it at higher prices, meaning it would be
              unfavorable to us.

              ...

              [W]e would [also] spoof the market, meaning if someone
              in the chat needed to buy dollars against a certain
              currency, I might place offers in the market in order to
              try to drive the price lower into that person’s hands, . . .
              in order to help them out or vice versa. If my friend
              needed to sell dollars, I might go into the market and
              place buy orders in the hopes of driving the price higher.

Gov’t Supp. App’x at 50–51.

      During the relevant time period, the co-conspirators communicated with

each other almost every day, and, over time, various members of the conspiracy

participated in numerous FX trading episodes in furtherance of their agreement

not to compete. These trading episodes shed light upon several aspects of the

conspiracy.

                                           8
      First, the co-conspirators’ FX trading activity, as charged in the indictment,

revealed their coordinated efforts when competing for customers’ transactions.

For instance, on November 4, 2010, Aiyer and Katz coordinated in connection with

the prices they offered to a potential customer who was interested in selling

Russian rubles. More specifically, when communicating over Bloomberg chat that

day, Aiyer and Katz realized that the same customer was asking them for a “usd

rub” quote, App’x at 1132, 5 and they thereafter “agreed what bid we were going

to show them between the two of us,” Gov’t Supp. App’x at 168–69. Because the

customer wanted to sell currency, Aiyer and Katz knew that the customer was

seeking the highest offered price. For example, on one occasion, Aiyer informed

Katz that he offered the customer a price of “30.99,” so Katz responded that he

would “show 30.98” and indicated that “you can have” the transaction. App’x at

1132. Ultimately, the customer accepted Aiyer’s price. Immediately after this

trading episode, Katz wrote to Aiyer via Bloomberg chat that “conspiracies are

nice,” to which Aiyer replied, “hahaha . . . prolly shudnt puot this on perma chat.”

App’x at 1133.

5 Unless otherwise indicated, Bloomberg chat messages quoted herein appear as they do
in the record.
                                         9
       Second, other episodes of trading activity demonstrated the co-conspirators’

agreement to refrain from competing with each other on the Reuters platform. For

example, on September 23, 2011, Aiyer and Cummins both wanted to buy U.S.

dollars against Turkish lira. After noticing that Aiyer was “bidding [TRY] at [a

price of] 15,” Cummins noted on Bloomberg chat that he was bidding “at [a price

of] 10.” Gov’t Supp. App’x at 400. Cummins then wrote that he would “pull”—

or cancel—his bids so that he and Aiyer would not “get in front of each other.”

Gov’t Supp. App’x at 401.

       Third, the co-conspirators’ FX trading activity also demonstrated their

attempts to affect prices in the market. For example, on January 18, 2012, Aiyer

and Cummins both had identical U.S. dollar-South African rand stop-loss orders—

specifically, orders to “sell $25 million if the market goes lower to [a price of]

7.95.” 6 Gov’t Supp. App’x at 79–80. After this fact was disclosed on a Bloomberg

chat involving Aiyer, Cummins, and Katz, Katz wrote, “why dont we drive [the

price] down there and keep some,” Gov’t Supp. App’x at 500, which Cummins

6 A stop-loss order is an order a customer gives to a dealer bank to sell a specific currency
if the market price reaches a certain low price. The idea behind such orders is “risk
mitigation”—if the market price for the relevant currency continues to fall beyond the
stated price in the stop-loss order, the customer is “locking in a loss.” Gov’t Supp. App’x
at 127–28.
                                             10
testified meant “if you push it through now, it is likely that the market would

bounce back and . . . you could make a profit selling higher if the market bounces

higher.” Gov’t Supp. App’x at 81. Aiyer, Cummins, and Katz then “[w]ork[ed]

together on the stop-loss,” Gov’t Supp. App’x at 122, and were able to lower the

market price, with Aiyer writing on Bloomberg chat, “wow tht went,” Gov’t Supp.

App’x at 465. Around two hours later, Aiyer wrote to Cummins and Katz, “salute

to first coordinated . . . zar effort,” and Katz responded, “yep . . . many more to

come.” Gov’t Supp. App’x at 450.

III.    Procedural History

        A.     The Indictment

        On May 10, 2018, a grand jury returned an indictment charging Aiyer with

one count of conspiring to restrain trade in violation of Section 1 of the Sherman

Act, 15 U.S.C. § 1. The indictment alleged that, “[f]rom at least as early as October

2010 and continuing until at least July 2013,” Aiyer, along with Cummins, Katz,

and Williams, 7 “knowingly entered into and participated in a combination and

conspiracy to suppress and eliminate competition by fixing prices of, and rigging

bids and offers for, CEEMEA currencies traded in the United States and

7   Williams is identified in the indictment as CW1.
                                             11
elsewhere.” App’x at 38–39. The indictment further alleged, inter alia, that the co-

conspirators “engag[ed] in near-daily conversations through private electronic

chat rooms . . . and other means of communication, to reveal their currency

positions, trading strategies, bids and offers on Reuters, customer identities,

customer limit order price levels, upcoming customer orders, and planned pricing

for customer orders, among other information”; “agree[d] to suppress and

eliminate competition among themselves for the purchase and sale of CEEMEA

currencies by coordinating their bidding, offering and trading”; and “agree[d] on

pricing to quote to customers.” App’x at 39–40.

       Aiyer moved to dismiss the indictment in part on March 22, 2019, arguing

that certain of the alleged offense conduct, such as the co-conspirators’

coordinated activities in the interdealer market: (1) was not subject to the per se

rule under Section 1 of the Sherman Act; (2) was, instead, subject to rule-of-reason

analysis; 8 and therefore (3) could not support a criminal indictment, given that the

8 As discussed in more detail below, under the Sherman Act, most alleged misconduct is
assessed under the rule of reason, where “the factfinder [must] decide whether under all
the circumstances of the case the restrictive practice imposes an unreasonable restraint
on competition,” but certain misconduct, such as price fixing, is considered illegal per se.
Arizona v. Maricopa Cnty. Med. Soc’y, 457 U.S. 332, 343, 346–47 (1982).

                                            12
government only prosecutes conduct that is subject to the per se rule. 9 In support

of his motion, Aiyer submitted two expert affidavits, in which the experts opined

that the co-conspirators’ activities in the FX market did not yield anticompetitive

effects and, in fact, had procompetitive benefits.

         On June 4, 2019, the district court entered an order denying Aiyer’s motion

to dismiss. As explained in its oral ruling at a conference the prior day, the district

court denied the motion on the grounds that “[t]he indictment properly alleges a

single overarching conspiracy” to fix prices and rig bids in the FX market and that

“[e]ach act committed by a coconspirator in furtherance of the conspiracy need not

be criminal in and of itself.” App’x at 191; see also App’x at 192 (“It is irrelevant

that certain activity set forth in the indictment may not alone constitute a per se

crime.     What is relevant is that those acts enable the defendant and his

coconspirators to carry out an unlawful conspiracy.”). In addition, the district

court concluded that Aiyer’s expert evidence was “improper at this stage of the

case and cannot be considered.” App’x at 191.

9 See U.S. Dep’t of Just., Just. Manual § 7-1.100 (2020)) (“When it comes to enforcement,
the Division’s policy, in general, is to proceed by criminal investigation and prosecution
in cases involving horizontal, ‘per se’ unlawful agreements such as price fixing, bid
rigging, and market allocation.”).
                                           13
      B.     The Motions in Limine

      Before trial, both Aiyer and the government filed motions in limine raising

numerous evidentiary issues. As is relevant on appeal, the government moved to

exclude evidence purporting both to demonstrate procompetitive justifications for

Aiyer’s trading activity in the FX market and to show that that conduct did not

have anticompetitive effects. In opposition, Aiyer argued, inter alia, that such

evidence was “critical to the Court’s determination of what behavior at issue, if

any, is per se illegal,” App’x at 291, as opposed to merely being subject to the rule

of reason.

      At a conference held on September 24, 2019, 10 the district court granted the

government’s motion to exclude evidence of competitive effects, reasoning that

“evidence of the lack of anticompetitive effects would be irrelevant [in the context

of this case] because price fixing and bid rigging are per se illegal,” and that, under

the law, Aiyer “should not be able to argue that the pro-competitive effects of

horizontal bid rigging or price fixing make such practices legal.” App’x at 311–15.

However, the court expressly left open the possibility that the parties could seek

10 The corresponding order regarding the parties’ motions in limine was entered on
September 25, 2019.

                                          14
to introduce evidence of procompetitive effects at trial, for example on the issue of

intent. Thus, the district court made clear that its decision on the government’s

motion to exclude was “without prejudice to the ability of the parties to raise the

issue with respect to specific evidence at trial.” 11 App’x at 315.

         C.     The Trial

         The district court held a jury trial from October 30 to November 20, 2019. At

trial, the jury heard testimony from numerous fact and expert witnesses, including

the government’s background expert, Dr. David DeRosa; cooperating witnesses

Cummins and Katz; 12 three asset managers who had been the co-conspirators’

customers in the FX market; the government’s FX-trading expert, Ross Waller; and

Aiyer’s expert, Professor Richard Lyons.

         After the government rested, Aiyer moved for a judgment of acquittal

pursuant to Federal Rule of Criminal Procedure 29. Among other things, he again

asserted that “none of the conduct at issue constitutes a per se violation of the

11 For his part, Aiyer moved to exclude evidence concerning interdealer trading and his
trading activity with Katz related to the Russian ruble because, in his view, that evidence
was irrelevant as it did not show that Aiyer participated in illegal price fixing or bid
rigging. The district court denied Aiyer’s motion, stating that Aiyer “acknowledges that
there is no basis at this time to exclude” such evidence. App’x at 330.

12   The government did not call Williams to testify.
                                             15
antitrust laws.” App’x at 964. The district court denied the motion without

prejudice to renewal, concluding that, based upon the evidence presented, a

reasonable jury could find that the government had proven the charge in the

indictment—that Aiyer entered into a conspiracy to fix prices and rig bids in the

FX market.

      During its charge to the jury, the district court gave the following

instruction:

      The goal of every price fixing conspiracy is the elimination of one
      form of competition—competition over price. Therefore, if you find
      that the charged price fixing conspiracy existed, it does not matter
      whether the prices agreed upon were high, low, reasonable, or
      unreasonable. What matters is that the prices were fixed. . . . Every
      conspiracy to fix prices unlawfully restrains trade regardless of the
      motives of the conspirators or any economic justification they may
      offer.

App’x at 1095–96; see also App’x at 1098–99 (same with respect to bid rigging).

Although Aiyer took issue with various aspects of the lengthy jury instructions,

he never objected to the substance of this particular instruction.

      On November 20, 2019, the jury found Aiyer guilty of the charged

conspiracy to restrain trade.

                                         16
      D.     The Allegations of Jury Misconduct

      On the day the jury reached its verdict, Juror No. 6 wrote a letter to the

district court in which he raised a number of allegations of juror misconduct and

expressed regret as to his participation in reaching the guilty verdict.

      In relevant part, Juror No. 6 alleged that he overheard Juror No. 3 state, “The

judge said we cannot talk about or look up information about the case, he never

said that my girlfriend can’t,” and “even my boss looked up the case.” Redacted

App’x at 3. Juror No. 6 also asserted that Juror No. 3 said he “had looked up

information on members of the counsel” and commented on one attorney’s

appearance. 13 Redacted App’x at 3.

      Following Juror No. 6’s revelation of potential jury misconduct, defense

counsel “searched through various public online social media platforms to assess

whether any additional improper communications by or among jurors occurred

during the trial.” Redacted App’x at 4. Counsel reported to the district court that,

13Although Aiyer does not raise Juror No. 6’s other allegations on appeal, we note that
he further alleged that he agreed to the verdict “based solely on the intimidation of five
members of the jury”; that Juror No. 3 also stated that, at one point, “he saw the facial
expression on the defendant and the defendant[’s] brother” and later said “they smile
now, but they [won’t] be smiling at the end of this”; and that, when certain jurors “were
puzzled with [the district court’s] instructions regarding the statute of limitation,
conspiracy, and agreement,” the jurors “piggybacked off” of Juror No. 10’s opinion that
“conspiracy equals agreement.” Redacted App’x at 3.
                                           17
on his weekly, publicly available podcast, Juror No. 4 made various comments

about his jury service while the trial was ongoing, including that he was “angry”

about being a juror, did not care about the case, and that he “started to not pay

attention at all in the court room,” but that he did not “identify[] the case by its

name and did not discuss any specific facts at issue.” Redacted App’x at 5.

      Less than a month after Juror No. 6 wrote his letter, the district court issued

an order directing Juror No. 3 to appear in court to be interviewed in the presence

of counsel for the government and Aiyer. At that interview, when the district court

asked whether he had conducted any outside “research about the case or any of

the parties or the lawyers” before the jury reached its verdict, Juror No. 3

unequivocally said that he had not. Redacted App’x at 18. In addition, Juror No.

3 informed the court that: when his girlfriend asked about the case, he told her he

was not permitted to discuss it; his father had become aware of the case’s name;

he had learned, post-trial, that his office manager had researched the case; and the

jurors had nicknames for some of the lawyers.

      On January 15, 2020, the district court issued an opinion and order

concerning all of the allegations of juror misconduct. See United States v. Aiyer, 433

F. Supp. 3d 468 (S.D.N.Y. 2020) (“Aiyer I”).       The district court held that no

                                         18
additional inquiry into Juror No. 3’s alleged misconduct was warranted because

his responses to the court were credible and there was “no reason to suggest that

there was any prejudicial information improperly brought to the attention of the

jury in this case.” Id. at 476. With respect to Juror No. 4’s comments on his podcast,

the district court concluded that those comments “[did] not raise any concerns that

necessitate a post-verdict inquiry” because the podcast “did not contain any

evidence of prejudice or evidence that the Juror did not deliberate fairly and

impartially.” Id. at 474. In sum, when considering all of the allegations of juror

misconduct, the district court determined that there was “no basis to vacate the

jury’s verdict.” Id. at 477.

      E.     The Post-Trial Proceedings

      After the jury returned its verdict, Aiyer renewed his motion for a judgment

of acquittal pursuant to Rule 29 and moved, in the alternative, for a new trial under

Rule 33, again arguing that the district court erroneously failed to determine

whether the charged offense conduct was subject to the per se rule or the rule of

reason. The district court denied these motions. See United States v. Aiyer, 470 F.

Supp. 3d 383, 391 (S.D.N.Y. 2020) (“Aiyer II”). In particular, in relation to Aiyer’s

contention that the district court was required to make a threshold determination

                                         19
as to whether the per se rule or the rule of reason applied to the conduct alleged in

the indictment, the district court stated:

      That question may be decided by the court in a civil case on a motion
      for summary judgment as a matter of law if there is no material
      dispute of fact that needs to be submitted to the jury. However, there
      are no motions for summary judgment in a criminal antitrust case,
      and it is a question for a properly instructed jury to determine
      whether the Government has proved beyond a reasonable doubt that
      the defendant knowingly participated in a conspiracy to fix prices and
      rig bids.

      The question on this Rule 29 motion is whether the evidence adduced
      at trial was sufficient for the jury to find, beyond a reasonable doubt,
      that the conspiracy to fix prices and rig bids alleged in the indictment
      actually existed and that the defendant knowingly joined that
      conspiracy.

Id. at 401–02 (footnotes omitted). The district court, after thoroughly analyzing the

trial evidence with respect to each of the elements of the offense, concluded that

“there was sufficient evidence from which a reasonable jury could conclude

beyond a reasonable doubt that the defendant knowingly joined a conspiracy to

fix prices and rig bids that affected interstate commerce and that existed within

the statute of limitations period,” and denied the Rule 29 motion. Id. at 409.

      In also denying the Rule 33 motion for a new trial, the district court

separately addressed the six arguments raised by Aiyer in support of that motion.

In particular, as relevant to this appeal, the district court rejected the argument

                                             20
that “procompetitive justifications for conduct at issue and evidence of the lack of

anticompetitive effects of conduct at issue was improperly excluded at trial.” Id.

at 413. In doing so, the district court reiterated the basis for its prior rulings on

this issue:

       As the Court previously ruled prior to and during the trial, in per se
       Sherman Act cases in which the question for the jury is whether the
       conduct at issue amounted to a conspiracy to fix prices and rig bids,
       evidence of the lack of anticompetitive effects or the presence of
       procompetitive justifications is inadmissible for the purpose of
       proving that the price fixing or bid rigging conspiracy was reasonable
       or beneficial. The Court’s prior rulings were properly decided.

Id. at 413–14 (internal citation omitted). The district court further emphasized that,

notwithstanding that ruling, it did allow the defendant the opportunity to

introduce such evidence “for the limited and permissible purpose of showing that

the defendant or one of his alleged coconspirators lacked the specific intent to

engage in the conduct that comprised the object of the conspiracy, namely fixing

prices and rigging bids.” Id. at 414. Thus, the district court concluded that Aiyer

had failed to explain how that ruling, which was consistent with Supreme Court

precedent, provided any basis for a new trial.

       On September 17, 2020, the district court sentenced Aiyer to eight months’

imprisonment, to be followed by a two-year term of supervised release, and

                                         21
imposed a $150,000 fine. The judgment reflecting this sentence was entered on

October 2, 2020. 14

                                     DISCUSSION

       Aiyer raises three arguments on appeal. Specifically, he contends that the

district court: (1) legally erred by failing to review his proffered evidence of

competitive effects and refusing to make a threshold determination as to whether,

under the Sherman Act, the per se rule or rule of reason applied to his trading

activity in the FX market; (2) abused its discretion in precluding the admission of

his evidence concerning competitive effects; and (3) abused its discretion

conducting only a limited investigation into allegations of juror misconduct that

came to light post-trial. As set forth below, we discern no error in the district

court’s refusal to make a threshold determination as to which analytical

framework under the Sherman Act governed this case, and we further conclude

that the district court did not abuse its discretion in connection with either its

evidentiary rulings or its post-trial investigation into alleged juror misconduct.

14Although the district court denied Aiyer bail, see United States v. Aiyer, 500 F. Supp. 3d
21 (S.D.N.Y. 2020), this Court granted Aiyer’s motion for bail pending appeal on
December 2, 2020.
                                            22
   I.      The Applicable Antitrust Framework

        Aiyer’s primary argument on appeal is that the district court erred by

consistently failing to evaluate purported evidence that his conduct in the FX

market lacked anticompetitive effects, and, in fact, had procompetitive benefits, in

order to decide whether the per se rule or rule of reason applies to that conduct.

        Notably, in relation to this issue, Aiyer does not challenge the district court’s

rulings on his motion to dismiss the indictment or his later motion for a judgment

of acquittal or a new trial under Rules 29 and 33, nor does he contend that the

district court erred in its legal instructions to the jury. Instead, he makes the more

amorphous argument that, at some point during the lengthy proceedings below,

the district court should have made a threshold determination as to which

analytical framework under the Sherman Act—the per se rule or the rule of

reason—should be applied in assessing the alleged offense conduct. We construe

this aspect of Aiyer’s appeal as raising a question of law, which we review de novo.

See United States v. Skelos, 988 F.3d 645, 658 (2d Cir. 2021); see also United States v.

Apple, Inc., 791 F.3d 290, 313, 321–30 (2d Cir. 2015) (reviewing de novo the question

whether the per se rule or rule of reason applied to alleged conduct in a civil

antitrust case); California ex rel. Harris v. Safeway, Inc., 651 F.3d 1118, 1124 (9th Cir.

                                           23
2011) (“The selection of the proper mode of antitrust analysis is a question of law,

which we review de novo.”). As set forth below, we find no error in the district

court’s conclusion that it was not required to review Aiyer’s proffered evidence of

competitive effects of his trading activity in the FX market or to make a threshold

determination as to whether, under the Sherman Act, the per se rule or rule of

reason applied at his criminal trial.

      A.     Legal Context

      Under Section 1 of the Sherman Act, Congress declared “[e]very contract,

combination . . . , or conspiracy, in restraint of trade or commerce . . . to be illegal.”

15 U.S.C. § 1. Although the plain language of this provision broadly covers any

agreement to restrain trade, it is axiomatic that “Congress intended to outlaw only

unreasonable restraints.” Texaco Inc. v. Dagher, 547 U.S. 1, 5 (2006) (quoting State Oil

Co. v. Khan, 522 U.S. 3, 10 (1997)); see also Ohio v. Am. Express Co., 138 S. Ct. 2274,

2283 (2018) (“[The Supreme] Court has long recognized that, ‘[i]n view of the

common law and the law in this country’ when the Sherman Act was passed, the

phrase ‘restraint of trade’ is best read to mean ‘undue restraint.’” (alteration in

original) (quoting Standard Oil Co. of N.J. v. United States, 221 U.S. 1, 59–60 (1911))).

                                           24
      Typically, alleged restraints on trade challenged under the Sherman Act are

analyzed under the rule of reason. See Dagher, 547 U.S. at 5 (stating that “[the

Supreme] Court presumptively applies rule of reason analysis” in Sherman Act

cases); Khan, 522 U.S. at 10 (noting that “most antitrust claims are analyzed under

a ‘rule of reason[]’”). As its name suggests, the rule of reason requires that “the

finder of fact . . . decide whether the questioned practice imposes an unreasonable

restraint on competition, taking into account a variety of factors, including specific

information about the relevant business, its condition before and after the restraint

was imposed, and the restraint’s history, nature, and effect.” Khan, 522 U.S. at 10;

see also Am. Express, 138 S. Ct. at 2284 (“The rule of reason requires courts to

conduct a fact-specific assessment of market power and market structure . . . to

assess the [restraint]’s actual effect on competition. The goal is to distinguis[h]

between restraints with anticompetitive effect that are harmful to the consumer

and restraints stimulating competition that are in the consumer’s best interest.”

(alterations in original) (internal quotation marks and citation omitted)); Gatt

Commc’ns, Inc. v. PMC Assocs., L.L.C., 711 F.3d 68, 75 n.8 (2d Cir. 2013) (“When

applying the rule of reason, courts weigh all of the circumstances surrounding the

challenged acts to determine whether the alleged restraint is unreasonable . . . .”).

                                         25
      However, certain restraints are subject to the per se rule—that is, they are

categorically   unreasonable     restraints    on   trade,   given   their   inherently

anticompetitive nature. See Khan, 522 U.S. at 10 (“Some types of restraints . . . have

such predictable and pernicious anticompetitive effect, and such limited potential

for procompetitive benefit, that they are deemed unlawful per se.”). As we have

stated, the per se rule “‘reflect[s] a longstanding judgment’ that case-by-case

analysis is unnecessary for certain practices that, ‘by their nature[,] have a

substantial potential’ to unreasonably restrain competition.” Apple, 791 F.3d at 321

(alterations in original) (quoting FTC v. Superior Ct. Trial Laws. Ass’n, 493 U.S. 411,

433 (1990)). “To justify a per se prohibition a restraint must have manifestly

anticompetitive effects, and lack . . . any redeeming virtue.” Leegin Creative Leather

Prods., Inc. v. PSKS, Inc., 551 U.S. 877, 886 (2007) (alteration in original) (internal

quotation marks and citation omitted). Under this rule, there is no “need to study

the reasonableness of an individual restraint in light of the real market forces at

work.” Id. Thus, in a criminal antitrust case alleging conduct falling within the

per se rule, the government “need prove only that [the offense conduct] occurred

in order to win [its] case, there being no other elements to the offense and no

                                          26
allowable defense.” United States v. Koppers Co., 652 F.2d 290, 294 (2d Cir. 1981)

(internal quotation marks omitted).

       The paradigmatic example of a per se illegal restraint on trade under the

Sherman Act is a horizontal conspiracy to fix prices with competitors. See United

States v. Socony-Vacuum Oil Co., 310 U.S. 150, 223 (1940) (“Under the Sherman Act

a combination formed for the purpose and with the effect of raising, depressing,

fixing, pegging, or stabilizing the price of a commodity in interstate or foreign

commerce is illegal per se.”); Catalano, Inc. v. Target Sales, Inc., 446 U.S. 643, 647

(1980) ( “A horizontal agreement to fix prices is the archetypal example” of a per

se unreasonable practice). 15 In addition, the Supreme Court has held that the

practice of allocating markets is subject to the per se rule. See Palmer v. BRG of Ga.,

Inc., 498 U.S. 46, 49–50 (1990). Moreover, we have ruled that bid rigging—which

is simply another “form of horizontal price fixing”—is a per se violation of the

Sherman Act. See Koppers, 652 F.2d at 294 (“In cases involving behavior such as

bid rigging, . . . the Sherman Act will be read as simply saying: An agreement

among competitors to rig bids is illegal.” (internal quotation marks omitted)); see

15 “[C]oncerted action [between competitors at the same level of the market] is usually
termed a ‘horizontal’ restraint, in contradistinction to combinations of persons at
different levels of the market structure, e.g., manufacturers and distributors, which are
termed ‘vertical’ restraints.” United States v. Topco Assocs., Inc., 405 U.S. 596, 608 (1972).

                                             27
also United States v. Joyce, 895 F.3d 673, 677 (9th Cir. 2018); United States v. Fenzl, 670

F.3d 778, 780 (7th Cir. 2012) (defining “bid rigging” as “a form of price fixing in

which bidders agree to eliminate competition among them, as by taking turns

being the low bidder”); accord 15 U.S.C. § 7a note (Findings; Purpose of 2020

Amendment) (“Congress finds [that] . . . [c]onspiracies among competitors to fix

prices, rig bids, and allocate markets are categorically and irredeemably

anticompetitive and contravene the competition policy of the United States.”).

      Despite the categorical nature of the per se rule, there are certain exceptions

to its application. For example, the “ancillary restraints doctrine,” which “governs

the validity of restrictions imposed by a legitimate business collaboration, such as

a business association or joint venture, on nonventure activities,” Dagher, 547 U.S.

at 7, “exempt[s]” such agreements “from the per se rule,” such that the rule of

reason applies, Aya Healthcare Servs. Inc. v. AMN Healthcare, Inc., 9 F.4th 1102, 1109

(9th Cir. 2021) (quoting Rothery Storage & Van Co. v. Atlas Van Lines, Inc., 792 F.2d

210, 224 (D.C. Cir. 1986)). When this doctrine applies, “courts must determine

whether the nonventure restriction is a naked restraint on trade, and thus invalid,

or one that is ancillary to the legitimate and competitive purposes of the business

association, and thus valid.” Dagher, 547 U.S. at 7.

                                            28
      Apart from the ancillary restraints doctrine, courts have also relieved

alleged misconduct from per se treatment in “[limited] situations where the

‘restraints on competition are essential if the product is to be available at all.’”

Apple, 791 F.3d at 326 (quoting Am. Needle, Inc. v. Nat’l Football League, 560 U.S. 183,

203 (2010)). As we have explained when discussing this second exception to the

per se rule, courts “apply the rule of reason [under these circumstances] only when

the restraint at issue was imposed in connection with some kind of potentially

efficient [formal or informal] joint venture.” Id. (“Put differently, a participant in

a price-fixing agreement may invoke only certain, limited kinds of ‘enterprise and

productivity’ to receive the rule of reason’s advantages.” (emphasis omitted)).

      B.     Application

      Aiyer argues that the district court erred in declining to assess his

competitive effects evidence and refusing to make a threshold determination as to

whether the per se rule or the rule of reason applied to the conspiracy to restrain

trade alleged in the indictment.        We disagree.      Aiyer’s argument is both

procedurally and substantively flawed.

      As a procedural matter, contrary to Aiyer’s contention, the district court did

not “abdicate[] its gate-keeping responsibilities” by “refus[ing] to analyze the

                                          29
charged conduct in light of the proffered economic evidence and decide whether

it should be evaluated under the per se rule or the rule of reason,” Aiyer Br. at 36,

because it has no such responsibilities in this criminal case.          Before trial, a

defendant “may raise by . . . motion any defense, objection, or request that the

court can determine without a trial on the merits,” including a motion alleging “a

defect in the indictment.” Fed. R. Crim. P. 12(b)(1)(B). On such a motion, “[a]n

indictment is sufficient as long as it (1) ‘contains the elements of the offense

charged and fairly informs a defendant of the charge against which he must

defend,’ and (2) ‘enables the defendant to plead an acquittal or conviction in bar

of future prosecutions for the same offense.’” United States v. Dawkins, 999 F.3d

767, 779 (2d Cir. 2021) (quoting United States v. Wedd, 993 F.3d 104, 120 (2d Cir.

2021)). Additionally, although a district court can “make factual determinations

in matters that do not implicate the general issue of a defendant’s guilt” when

assessing a Rule 12 motion, it cannot resolve “a factual dispute that is inextricably

intertwined with a defendant’s potential culpability,” as that is a role reserved for

the jury. United States v. Sampson, 898 F.3d 270, 281 (2d Cir. 2018).

      Beyond a Rule 12 motion, “[a] defendant has no right to judicial review of a

grand jury’s determination of probable cause to think a defendant committed a

                                         30
crime.” Kaley v. United States, 571 U.S. 320, 333 (2014). Thus, “[a]n indictment

returned by a legally constituted and unbiased grand jury, . . . if valid on its face,

is enough to call for trial of the charge on the merits.” Costello v. United States, 350

U.S. 359, 409 (1956) (footnote omitted); accord United States v. Ciambrone, 601 F.2d

616, 623 (2d Cir. 1979).

      Here, in its denial of Aiyer’s motion to dismiss the indictment—which is not

challenged on appeal—the district court properly concluded that the indictment

adequately alleged a conspiracy to fix prices and rig bids in the FX market. As a

result, the government was entitled to present its per se case against Aiyer to the

jury without any pre-trial determination by the district court as to the sufficiency

of the government’s proof of the alleged per se charges. See Costello, 350 U.S. at 409.

      In reaching this decision, we emphasize that this is a criminal case, and

“summary judgment does not exist in federal criminal procedure.” Wedd, 993 F.3d

at 121 (quoting Sampson, 898 F.3d at 282). In other words, “although a judge may

dismiss a civil complaint pretrial for insufficient evidence [on a motion for

summary judgment], a judge generally cannot do the same for a federal criminal

indictment.” Sampson, 898 F.3d at 280. Moreover, unlike a civil antitrust case,

where the government may proceed in the alternative under a rule of reason

                                          31
theory and the availability of the rule of reason impacts the scope of evidence at

trial, see Apple, 791 F.3d at 297, the government’s criminal case here was going to

rise or fall solely on its ability to prove the per se categories of restraint alleged in

the indictment. In other words, there was no possibility that the government could

argue to the jury in the alternative that, if the government’s proof fell short of a per

se violation, Aiyer could still be found guilty under the rule of reason. As noted

supra, the government does not pursue criminal charges under the rule of reason

as a matter of policy and, in any event, the indictment here—charging only a per

se case—would have foreclosed any such attempt to switch theories during trial.

Simply put, in a criminal antitrust case, a district court has no pretrial obligation

to consider a defendant’s evidence of competitive effects in order to determine

whether or not the indictment properly charges an actual per se offense. Thus,

there was no procedural error in the district court’s failure to assess Aiyer’s

proffered evidence and decide which rule under the Sherman Act applied here. 16

16 We are unpersuaded by Aiyer’s suggestion that we have previously required courts to
conduct a preliminary, “sophisticated economic inquiry” to determine whether a
challenged restraint is properly characterized as per se unlawful. Aiyer Br. at 35 (quoting
Volvo N. Am. Corp. v. Men’s Int’l Pro. Tennis Council, 857 F.2d 55, 71–72 (2d Cir. 1988)). As
a threshold matter, we note that Volvo was a civil case, and thus, as discussed supra, is
subject to different procedures for pre-trial determinations regarding sufficiency of the
evidence. In any event, the substance of our decision in Volvo does not conflict with our
analysis here. In that case, plaintiffs alleged, among other things, that a professional
                                             32
       Aiyer’s argument is equally without merit from a substantive standpoint

based upon well-settled antitrust jurisprudence. Having correctly determined that

the indictment charged price fixing and bid rigging as per se violations of criminal

antitrust laws, the district court properly concluded that precedent from both the

Supreme Court and this Court has long foreclosed consideration by the district

court (whether pre-trial or at some later procedural posture) of the competitive

effects—i.e., reasonableness—of that alleged conduct in an attempt by Aiyer to

avoid the per se rule. See, e.g., Maricopa Cnty., 457 U.S. at 351 (“The anticompetitive

potential inherent in all price-fixing agreements justifies their facial invalidation

even if procompetitive justifications are offered for some.”); Socony-Vacuum, 310

U.S. at 218 (“[The Supreme] Court has consistently and without deviation adhered

tennis council conspired to fix compensation for certain professional tennis matches. 857
F.2d at 71. The district court granted defendants’ motion to dismiss as to this claim. See
id. at 62. We reversed, but noted in dicta that “[a]ssuming . . . appellants succeed in
proving the foregoing allegations, . . . we express no opinion at this time as to whether
[defendants’] conduct should be condemned as per se unlawful or, instead, should be
analyzed under the Rule of Reason.” Id. at 71. We further explained that it was not
immediately clear that the per se rule should apply in the context of that case because
“professional sporting events cannot exist unless the producers of such events agree to
cooperate with one another to a certain extent, and that the antitrust laws do not condemn
such agreements when coordination is essential if the activity is to be carried out at all.”
Id. at 71–72. As discussed below, Aiyer does not—and cannot—argue that his conduct
was essential to the functioning of the FX market. In any event, we did not suggest in
Volvo that a defendant is entitled to a pre-trial determination on these issues in a criminal
case.
                                             33
to the principle that price-fixing agreements are unlawful per se under the

Sherman Act and that no showing of so-called competitive abuses or evils which

those agreements were designed to eliminate or alleviate may be interposed as a

defense.”); Apple, 791 F.3d at 321 (explaining that “case-by-case analysis [of

competitive effects] is unnecessary” in per se cases); Koppers, 652 F.2d at 295 n.6

(stating that “the per se rule makes certain conspiracies illegal without regard to

their actual effects on trade”).

      As the Supreme Court explained in 1940, “[w]hatever economic justification

particular price-fixing agreements may be thought to have, the law does not permit

an inquiry into their reasonableness. They are all banned because of their actual or

potential threat to the central nervous system of the economy.” Socony-Vacuum,

310 U.S. at 224 n.59 (emphasis added). Therefore, even assuming arguendo that

Aiyer is correct that the charged “conspiracy to ‘fix prices’ or ‘rig bids’ did not

actually have a material effect on supply, demand, or consumer price,” Aiyer Br.

at 36, that fact has no legal consequence because actual effects on the market are,

subject to only a few, narrow exceptions, irrelevant in a case alleging a per se

violation of the Sherman Act. 17 Therefore, any inquiry into Aiyer’s proffered

17 Relatedly, this long-standing principle also renders Aiyer’s argument that the
government “showed no increased prices or reduced supply,” Aiyer Br. at 45, unavailing.
                                          34
economic evidence below would not only have been unnecessary on the issue of

reasonableness with respect to a per se violation, cf. Taylor v. Illinois, 484 U.S. 400,

410 (1988) (noting that “[t]he accused does not have an unfettered right to offer

testimony that is . . . inadmissible under standard rules of evidence”), but indeed,

would have been legal error absent a properly asserted exception to the per se rule,

none of which are at issue here.

       At oral argument, Aiyer relied heavily on the Supreme Court’s decision in

Leegin for the proposition that “a ‘departure from the rule-of-reason standard must

be based upon demonstrable economic effect rather than . . . upon formalistic line

drawing.’” 551 U.S. at 887 (alteration in original) (quoting Cont’l T. V., Inc. v. GTE

Sylvania Inc., 433 U.S. 36, 58–59 (1977)). Therefore, he argued, the district court

was required to consider economic effects before determining whether the per se

rule applied here. However, Aiyer misunderstands the import of that case. In

Leegin, the Court considered whether a specific category of restraints on trade—

“vertical minimum resale price maintenance agreements”—“should continue to

be treated as per se unlawful.” Id. at 885. Thus, upon reviewing the relevant

We reiterate that, in a per se case, resulting anticompetitive effects need not be proved.
See, e.g., Copperweld Corp. v. Indep. Tube Corp., 467 U.S. 752, 768 (1984) (explaining that
agreements subject to the per se rule “are thought so inherently anticompetitive that each
is illegal per se without inquiry into the harm [they have] actually caused”).
                                            35
economic evidence, the Court concluded that the rule of reason, rather than the per

se rule, was “the appropriate standard to judge vertical price restraints,” and

overruled prior caselaw holding otherwise. Id. at 889–99, 907. Similarly, in GTE

Sylvania, the Court was asked to determine whether certain vertical franchise

agreements that “limited the number of franchises granted for any given area”

were subject to the per se rule or the rule of reason. 433 U.S. at 38, 41–42. There

too, the Supreme Court overruled a prior case and determined that the rule of

reason applied to the challenged restraints. Id. at 58–59.

      Here, by contrast, the Supreme Court and this Court have long held that the

categories of restraints alleged in the indictment—price fixing and bid rigging—

are subject to the per se rule, see, e.g., Catalano, 446 U.S. at 647; Socony-Vacuum, 310

U.S. at 223; Koppers, 652 F.2d at 293–94, “because of their pernicious effect on

competition and lack of any redeeming virtue,” Nw. Wholesale Stationers, Inc. v. Pac.

Stationery & Printing Co., 472 U.S. 284, 289 (1985). Indeed, in Leegin itself, the

Supreme Court reiterated that “[r]estraints that are per se unlawful include

horizontal agreements among competitors to fix prices.” 551 U.S. at 886. Thus,

there was no need for the district court to consider “demonstrable economic

effect[s],” id. at 887 (internal quotation marks omitted), given the well-established

                                          36
principle that the “anticompetitive potential inherent in all price-fixing

agreements justifies their facial invalidation,” Maricopa Cnty., 457 U.S. at 351.

      On appeal, Aiyer also asserts that “[e]ven when no formal cooperative

venture exists, conduct that technically would fall within the per se category may

still warrant rule of reason analysis when it promotes productivity,” Aiyer Br. at

33, but that assertion is overstated and, in any event, has no application to the facts

here. As we explained in Apple, a joint venture-related exception to the per se rule

arises “only when the restraint at issue was imposed in connection with some kind

of potentially efficient joint venture.” 791 F.3d at 326. A court may then consider

the alleged misconduct under the rule of reason. Id. Cases applying this exception,

however, tend to be “limited to situations where the ‘restraints on competition [at

issue] are essential if the product is to be available at all.’” Id. (emphasis added)

(quoting Am. Needle, 560 U.S. at 203). In addition, in Apple itself we rejected

application of this exception where “there was no joint venture or other similar

productive relationship between any of the participants in the conspiracy.” Id. 18

Aiyer does not, nor could he, claim that, even if he and the other co-conspirators

18 Although Aiyer complains that the government’s interpretation of this exception
incorrectly requires the existence of a formal joint venture, we made clear in Apple that a
“similar productive relationship” suffices as well. Id.

                                            37
had the requisite “productive relationship,” their trading activity in the FX market

was “essential” for CEEMEA currencies “to be available at all.” Id. (internal

quotation marks omitted). 19 In short, the district court did not err in refusing to

assess Aiyer’s competitive effects evidence to decide whether that evidence

counseled in favor of applying the rule of reason to this facially valid indictment

charging a per se case. To hold otherwise would be to unconstitutionally infringe

upon the factfinding function of the jury in a criminal trial, and likewise cause “the

per se rule [to] lose all the benefits of being ‘per se.’” Id.

       Aiyer suggests that “without the trial court’s meaningful, on-the-record

analysis of proffered economic evidence to determine whether the per se rule

19 Aiyer’s substantial reliance on civil cases applying the ancillary restraints doctrine or
joint venture-related exception to the per se rule is therefore misplaced. For example, in
In re Sulfuric Acid Antitrust Litigation, the Seventh Circuit determined that the rule of
reason should apply to alleged misconduct where the defendants—which were affiliate
firms—entered a joint venture with another company to supply sulfuric acid in the
United States because “the[ir] coordination [was] ancillary to (that is, supportive of) the
legitimate business purpose of the venture.” 703 F.3d 1004, 1013 (7th Cir. 2012); see also
Med. Ctr. at Elizabeth Place, LLC v. Atrium Health Sys., 922 F.3d 713, 719, 725–31 (6th Cir.)
(assessing whether the ancillary restraints doctrine applied to alleged coordinated
conduct among various hospitals where those hospitals’ functions were governed by a
joint operating agreement), cert. denied, 140 S. Ct. 380 (2019); Polk Bros., Inc. v. Forest City
Enters., Inc., 776 F.2d 185, 188–90 (7th Cir. 1985) (concluding that, under Illinois law
(which “refers courts to federal antitrust law as a guide to questions of interpretation”),
the rule of reason applied to an “ancillary” restraint stemming from “a new venture—the
building of a joint facility—that would expand output”). Simply put, such cases, which
we assume arguendo were correctly decided and which do not bind this Court in any
event, are distinguishable on their facts and inapplicable here.
                                              38
applies, the [Sherman Act] would be unconstitutional” and “violate basic

principles of due process.”      Aiyer Br. at 43.     This perfunctory assertion is

unsupported by the law or the record in this case. In Koppers, we explicitly

“decline[d] the invitation” to find that the per se rule could not be applied

constitutionally absent a finding that the challenged agreement was factually

unreasonable and noted that “[t]his argument asks us in effect to overrule the

Supreme Court’s decisions.” 652 F.2d at 293; see also id. at 294 (“Since the Sherman

Act does not make ‘unreasonableness’ part of the offense, it cannot be said that the

judicially-created per se mechanism relieves the government of its duty of proving

each element of a criminal offense under the Act.”). To be sure, the absence of a

“reasonableness” element in a per se violation does not alter the government’s

burden to prove each of the existing elements of a per se violation to the jury

beyond a reasonable doubt. However, as set forth below, Aiyer was not precluded

from legally and factually challenging each of the elements of the alleged per se

charge in full accord with due process.

      First, if a defendant seeks to challenge the application of the per se rule to his

offense conduct by arguing to the jury that such conduct fell within one of the

exceptions to the per se rule, he would have had every right to make those

                                          39
arguments and present evidence on such exceptions at trial. Aiyer was given a

full opportunity to do so. He could have introduced evidence (or argued) that his

coordinated activities in the FX market either fell within the ancillary restraints

doctrine, see Dagher, 547 U.S. at 7, or otherwise were in furtherance of some joint

venture-like enterprise that yielded significant efficiencies, see Apple, 791 F.3d at

326. Indeed, the district court denied the government’s motion in limine to exclude

evidence that Aiyer’s challenged conduct was subject to any joint venture-related

exception to the per se rule. Importantly, although Aiyer suggested prior to trial

that the ancillary restraints doctrine or other joint venture-related exception could

apply to his conduct, he did not make specific arguments regarding, or offer any

evidence related to, those exceptions at trial. In fact, Aiyer did not even ask that

the jury be instructed regarding any of these potential exceptions to the per se rule.

Thus, Aiyer chose not to pursue these exceptions at trial.

      Second, as discussed further infra, Aiyer was permitted to present some

competitive effects evidence on the intent element by cross-examining witnesses

regarding the actual effects of the co-conspirators’ trading activity. The district

court reasoned, “having gone through all of the evidence that the purpose of [the

conspiracy] was not only . . . to agree to set a price to a customer, but, rather, to

                                         40
move the prices up or down in order to be able to make more money and to effect

supply and demand, it would . . . be remarkable not to admit evidence [of] whether

what they intended to do, in fact, had any effect.” App’x at 821–22. Thus, on

several occasions, Aiyer was able to elicit testimony supporting his argument that

the co-conspirators’ trading activity did not yield significant price effects. Insofar

as Aiyer argues that he should have been permitted to introduce more evidence of

competitive effects in relation to intent, as discussed below, we reject that

argument because, as we have held—and reemphasize today—under these

particular circumstances “nothing more is required than a showing that the

defendant intentionally engaged in conduct that is a per se violation of the

Sherman Act, which was proven here.” Koppers, 652 F.2d at 298. In addition to

arguing to the jury that he lacked the requisite intent, Aiyer argued that there was

no agreement among the alleged co-conspirators, and that any agreement that may

have existed was not an agreement among competitors or an agreement to not

compete on pricing. Therefore, Aiyer was fully able to attack the government’s

proof as to each element of a per se case.

      Third, Aiyer had the opportunity to ensure that the government’s proof met

the correct legal standard for a per se violation by challenging the district court’s

                                             41
jury instructions with respect to the elements. Although he asserts that he objected

to the court’s instructions on price fixing and bid rigging, Aiyer’s counsel, in fact,

objected more narrowly to the district court’s decision not to use certain of his

proposed instructions—namely, instructions that interdealer trading and trading

in the Russian ruble do not constitute price fixing or bid rigging. 20 Thus, there was

no objection to the district court’s specific language in the ultimate instruction that

stated that price fixing and bid rigging “unlawfully restrain[] trade regardless of

the motives of the conspirators or any economic justification they may . . . offer.”

App’x at 1096 (price fixing); see also App’x at 1098–99 (same with respect to bid

rigging).   Further, had Aiyer presented any evidence going to the ancillary

restraints doctrine or joint venture-related exception to the per se rule, he could

have requested that the district court instruct the jury on those issues. Tellingly,

on appeal, Aiyer does not make any specific challenges to the substance of any of

the language in the district court’s jury instructions. 21

20Aiyer’s counsel also contended that “any instruction on bid rigging was not necessary
because there was no bid rigging proved.” App’x at 1059.
21  Although Aiyer generally argues on appeal that the district court “could have
instructed the jury to consider the reasonableness of [his] conduct,” Aiyer Br. at 42, he is
incorrect. As discussed supra, absent an applicable exception, the per se rule “eliminates
the need to study the reasonableness” of a challenged restraint on trade. Leegin, 551 U.S.
at 886 (emphasis added); accord Socony-Vacuum, 310 U.S. at 224 n.59.

                                            42
      Finally, with respect to judicial review of the adequacy of the government’s

proof in the per se case against him, Aiyer was permitted to—and did—challenge

the sufficiency of the government’s evidence in a Rule 29 motion for a judgment

of acquittal. See Fed. R. Crim. P. 29. Of course, Aiyer carried a heavy burden

because, on a Rule 29 motion, “a reviewing court must sustain the jury’s guilty

verdict if viewing the evidence in the light most favorable to the prosecution, any

rational trier of fact could have found the essential elements of the crime beyond

a reasonable doubt.” United States v. Ho, 984 F.3d 191, 199 (2d Cir. 2020) (quoting

United States v. Heras, 609 F.3d 101, 105 (2d Cir. 2010)). Under that standard, in its

thorough and well-reasoned decision, the district court denied Aiyer’s motion and

concluded that there was sufficient evidence from which a reasonable juror could

find beyond a reasonable doubt that Aiyer “knowingly joined a conspiracy to fix

prices and rig bids that affected interstate commerce and that existed within the

                                         43
statute of limitations period.” 22 Aiyer II, 470 F. Supp. 3d at 409. Aiyer does not

challenge that ruling, regarding the sufficiency of the evidence, on appeal. 23

22  As described in detail in the district court’s decision, see Aiyer II, 470 F. Supp. 3d at
392–400, the government’s proof included compelling, direct evidence of a per se
violation. Taking just one example, as described above, on January 8, 2012, Aiyer and
Cummins realized that they had the same U.S. dollar–South African rand stop-loss
order—to sell $25 million if the market price reached a certain low point. Once this
situation was made known to Katz on a Bloomberg chat involving him, Aiyer, and
Cummins, Katz wrote, “why dont we drive [the price] down there and keep some,” Gov’t
Supp. App’x at 464, which Cummins understood to mean, “if you push it through now,
it is likely that the market would bounce back and . . . you could make a profit selling
higher if the market bounces higher,” Gov’t Supp. App’x at 81. Then, as Cummins
testified at trial, the three co-conspirators “[w]ork[ed] together on the stop-loss.” Gov’t
Supp. App’x at 122. There was evidence introduced at trial that, through this coordinated
effort, Aiyer, Cummins, and Katz lowered the market price for the South African rand,
after which Aiyer wrote in the chatroom, “wow tht went.” Gov’t Supp. App’x at 465.
Later that day, Aiyer wrote on Bloomberg chat, “salute to first coordinated . . . zar effort,”
to which Katz replied, “yep . . . many more to come.” Gov’t Supp. App’x at 450. The
evidence of criminal intent was further bolstered by Aiyer’s prior comments on
Bloomberg chat, such as telling Katz, “u shud introduce me to the zar mafia,” Gov’t Supp.
App’x at 395; writing that he “want[ed] in to the zar mafia,” Gov’t Supp. App’x at 396;
and that, “between [him and Katz] . . . we can ryun zar,” Gov’t Supp. App’x at 395; see
also App’x at 1133 (Bloomberg chat where, in response to Katz’s comment that
“conspiracies are nice,” Aiyer writes, “hahaha . . . prolly shudnt puot this on perma
chat”).

23 Aiyer does attempt to relitigate that, in connection with Russian ruble trading, his role
was more akin to that of a supplier in a vertical relationship, such that his conduct should
be assessed under the rule of reason. See Apple, 791 F.3d at 321 (explaining that “the
Supreme Court in recent years has clarified that vertical restraints—including those that
restrict prices—should generally be subject to the rule of reason” (citing Leegin, 551 U.S.
at 882 and Khan, 522 U.S. at 7)). However, the jury heard arguments that this was not a
horizontal price agreement among competitors and implicitly rejected those arguments
as a factual matter with its verdict, and, again, Aiyer does not challenge the sufficiency
of the evidence supporting the verdict on appeal.

                                             44
         In sum, the district court did not commit legal error in declining to review

Aiyer’s proffered competitive effects evidence and refusing to determine, as a

threshold matter, whether the per se rule or the rule of reason applied in this case.

Having had the ability to test the facial validity of the indictment in a motion to

dismiss under Rule 12, to present arguments and evidence to the jury on

exceptions to the per se rule (which he choose not to do), to question some

witnesses regarding competitive effects of the trading activity on the issue of

intent, to challenge the district court’s jury instructions, and to move for a

judgment of acquittal under Rule 29, Aiyer was given a full opportunity to legally

and factually challenge the per se case against him throughout the proceedings

below.

   II.      The Evidentiary Challenges

         Next, Aiyer relatedly challenges the district court’s decision to exclude at

trial his proffered evidence—including expert testimony—that his conduct in the

FX market lacked anticompetitive effects and, in fact, yielded procompetitive

benefits. More specifically, he asserts that this competitive effects evidence should

have been admitted to help the jury assess: (1) the “unreasonableness” of his

                                          45
conduct; and (2) “whether [he] had the necessary criminal intent to form the

alleged conspiracy.” Aiyer Br. at 52.

      “We review the district court’s evidentiary rulings for abuse of discretion.”

United States v. Willis, 14 F.4th 170, 185 (2d Cir. 2021). However, “we will disturb

an evidentiary ruling only where the decision to admit or exclude evidence was

manifestly erroneous.” United States v. Litvak, 889 F.3d 56, 67 (2d Cir. 2018)

(internal quotation marks omitted). “Even if a decision was manifestly erroneous,

we will affirm if the error was harmless.” Id. (internal quotation marks omitted).

“These principles apply equally whether a [proffered] witness is testifying based

on personal knowledge or special expertise.” United States v. Felder, 993 F.3d 57,

71 (2d Cir. 2021) (citing United States v. Romano, 794 F.3d 317, 330 (2d Cir. 2015)).

      Aiyer’s first evidentiary challenge—that his competitive effects evidence

was relevant to whether his conduct was reasonable—is without merit. Under the

Federal Rules of Evidence, “[e]vidence is relevant if: (a) it has any tendency to

make a fact more or less probable than it would be without the evidence; and (b)

the fact is of consequence in determining the action.” Fed. R. Evid. 401. Although

relevant evidence is generally admissible, “[i]rrelevant evidence is not

admissible.” Fed. R. Evid. 402 (emphasis added).

                                          46
      As we discussed above, restraints on trade that are subject to the per se rule,

such as price fixing and bid rigging, are categorically unreasonable, such that proof

of reasonableness—which is to say, a lack of anticompetitive effects and/or the

presence of procompetitive benefits—is not required. See, e.g., Leegin, 551 U.S. at

886 (explaining that, under the per se rule, there is no “need to study the

reasonableness of an individual restraint [including price fixing] in light of the real

market forces at work”); Socony-Vacuum, 310 U.S. at 224 n.59 (“Whatever economic

justification particular price-fixing agreements may be thought to have, the law

does not permit an inquiry into their reasonableness.”); Koppers, 652 F.2d at 293

(explaining the Supreme Court’s holding in Socony-Vacuum that “certain types of

conduct, including price-fixing, are so patently anticompetitive that they violate

the [Sherman] Act without proof of unreasonableness in each case”). Here, the

indictment alleged that Aiyer entered into a conspiracy to fix prices and rig bids.

These restraints, if proven, “must automatically be treated as unreasonable.”

Koppers, 652 F.2d at 294 (emphasis added). Thus, reasonableness was not a “fact .

. . of consequence in determining” Aiyer’s guilt, Fed. R. Evid. 401, and the district

court therefore properly concluded that “[e]vidence of pro-competitive effects, or

the lack of harm, is not relevant” on that issue, Gov’t Supp. App’x at 228; accord

                                          47
App’x at 313 (concluding, in connection with the motions in limine, that “if the

price fixing charges are substantiated, evidence of anticompetitive [or

procompetitive] effects is irrelevant”); see also United States v. Guillory, 740 F. App’x

554, 556 (9th Cir. 2018) (determining that “[t]he district court did not preclude any

relevant evidence by granting the government’s motion in limine to prohibit

[defendant] from introducing evidence or argument that the bid-rigging

agreements were reasonable” because “the rule of reason inquiry . . . is

inapplicable if the restraint falls into the category of agreements which have been

determined to be per se illegal” (internal quotation marks and alteration omitted)).

      Aiyer separately asserts that “the district court’s exclusion of effects

evidence was error because it significantly impaired the defense’s ability to prove

that [he] lacked the requisite criminal intent.” Aiyer Br. at 53. To be sure, “intent

is a necessary element of a criminal antitrust violation.” United States v. U.S.

Gypsum Co., 438 U.S. 422, 443 (1978). Further, with respect to the element of intent

this Court has clarified that, when the per se rule governs the restraint of trade at

issue, “nothing more is required than a showing that the defendant intentionally

engaged in conduct that is a per se violation of the Sherman Act.” Koppers, 652

F.2d at 298.

                                           48
      Although Aiyer contends that the government must also “prove that the

defendant knew that anticompetitive effects would ‘most likely follow’ from his

conduct,” Aiyer Br. at 54 (quoting U.S. Gypsum, 438 U.S. at 444), our decision in

Koppers forecloses that approach in per se cases. In Koppers, the defendant road tar

producer was convicted of conspiring to rig bids and allocate territories in

violation of Section 1 of the Sherman Act. 652 F.2d at 291–93. More specifically, a

jury found that the defendant and its sole competitor coordinated their bids for

the sale of road tar to the State of Connecticut and that, as a result, the defendant

was awarded all of the road tar sales contracts in eastern Connecticut, while its

competitor was awarded all such contracts in western Connecticut. See id. On

appeal, the defendant asserted, among other things, that the district court’s jury

instructions on intent were legally erroneous because they “permitted the jury to

convict if it found that the defendant had known the objective of the conspiracy to

rig bids and had intentionally become a member of it,” without considering

whether the defendant “also intended that the conspiracy result in anticompetitive

effects.” Id. at 295 n.6. We rejected the defendant’s assertion, reasoning that:

      By allowing the jury to find criminal intent without addressing the
      issue of intent to unreasonably restrain trade, the district court was
      merely being consistent in its application of the per se rule to this case.
      Since the per se rule makes certain conspiracies illegal without regard

                                          49
       to their actual effects on trade, it would be illogical to refuse to allow
       a jury to consider whether the defendant’s acts had resulted in an
       unreasonable restraint, on the one hand, and then require it to find
       the specific intent to produce those effects, on the other. Where per
       se conduct is found, a finding of intent to conspire to commit the
       offense is sufficient; a requirement that intent go further and envision
       actual anti-competitive results would reopen the very questions of
       reasonableness which the per se rule is designed to avoid.

Id. (emphasis added). It follows that, because conspiring to fix prices and rig bids

is “illegal without regard to [its] actual effects on trade,” id., there is likewise no

need for the government to prove that a defendant in a criminal antitrust case was

consciously aware that anticompetitive effects would most likely result from his

alleged misconduct.

       To the extent Aiyer argues that this conclusion is inconsistent with United

States Gypsum, we disagree. There, the Supreme Court was considering the

parameters of intent under criminal antitrust law, but the restraint of trade at

issue—“the exchange of price information among competitors” 24—was subject to

the rule of reason. U.S. Gypsum, 438 U.S. at 441 & n.16. Thus, the Court had

occasion to analyze intent in a context where the presence or absence of

anticompetitive effects was highly relevant. See id. at 444 n.21 (“We hold only that

24 To be clear, the exchange of price information is different from the primary restraint of
trade at issue here—price fixing—which, as noted, has consistently been held to be the
quintessential per se violation under the Sherman Act.
                                            50
[an] elevated standard of intent [requiring proof that the defendant intended to

cause anticompetitive effects] need not be established in cases where [such] effects

have been demonstrated; instead, proof that the defendant’s conduct was

undertaken with knowledge of its probable consequences will satisfy the

Government’s burden.”).      Here, by contrast, the existence of anticompetitive

effects was immaterial in this per se case and, thus, as to intent, the government

was required to prove nothing more than that Aiyer intentionally engaged in a

conspiracy to fix prices and/or rig bids. See Koppers, 652 F.2d at 298.

      In connection with his alleged intent, Aiyer argues that the district court

should have permitted him to present evidence that his conduct did not yield

anticompetitive effects in the FX market—namely, that there was no effect on

prices—because such evidence raises the inference that the co-conspirators lacked

the intent to fix prices or rig bids. Cf. U.S. Gypsum, 438 U.S. at 446 (“[A]n effect on

prices may well support an inference that the defendant had knowledge of the

probability of such a consequence at the time he acted.”). Aiyer’s logic essentially

is that he and his co-conspirators—as sophisticated and knowledgeable

participants in the FX market—would never have intentionally conspired to fix

                                          51
prices or rig bids if it would not have had an effect on the market. 25 Although

evidence of the lack of an effect on price during a conspiracy could be relevant on

the issue of intent, as noted above, the district court did allow some cross-

examination concerning the extent of the price effects Aiyer’s trading activity

caused. For example, during the cross-examination of cooperating witness Katz,

defense counsel utilized exhibits to point out to Katz that he and Aiyer were

unable to affect the price on a number of transactions notwithstanding their

alleged illegal coordination. App’x at 823–29. Based upon that cross-examination,

Aiyer’s counsel argued in summation that Aiyer lacked the requisite intent to fix

prices:

       And Mr. Katz’s testimony is: What I was trying to do was show
       buying interest that would move the price higher. That was my
       purpose. I wanted to move the price higher. And then you see what
       actually happens a couple of minutes later is Mr. Aiyer does in fact
       sell, but he sells at a lower price, not a higher price. . . . You have to
       ask yourself, on this episode and the next one, is what Mr. Aiyer is

25 Aiyer selectively quotes Matsushita Electric Industrial Co. v. Zenith Radio Corp., 475 U.S.
574, 592 (1986), to argue that the failure of the alleged scheme to affect prices in three
years is “strong evidence” of a lack of intent to do so. Aiyer’s Br. at 55. However, in his
opening brief, he elides the key fact that the Supreme Court made this comment in light
of evidence that the alleged conspiracy at issue had been ineffectual for around twenty
years. See 475 U.S. at 592 (explaining that an “alleged conspiracy’s failure to achieve its
ends in the two decades of its asserted operation is strong evidence that the conspiracy
does not in fact exist”). Thus, the strength of the inference here regarding the lack of a
price effect (to the extent that could be proven) is not analogous to the factual
circumstances in Matsushita.
                                             52
      trying to do here move the price lower—which doesn’t happen—or is
      he trying to stimulate interest in the market so that he can find a
      counterparty, for get [sic] about the price, just to get out of his
      position?

Gov’t Supp. App’x at 338; see also id. at 339 (“And what you see happens next, five

minutes later, is Mr. Aiyer, who is a buyer, he wants the lowest possible price, is

successful in buying 5 million Euros against the Hungarian forint. But if you look

at the price, it’s a higher price, not a lower price. So, again, can you conclude

beyond a reasonable doubt that his intention was to move the price higher or lower

as opposed to just stimulating market activity?”).

      Although Aiyer contends he was entitled to introduce additional evidence

that his trading activity did not produce anticompetitive effects, including expert

testimony, he cannot use the element of intent as a backdoor to bring an undue

amount of competitive effects evidence before the jury. See Koppers, 652 F.2d at

295 n.6; see also Apple, 791 F.3d at 326 (“[T]he per se rule would lose all the benefits

of being ‘per se’ if conspirators could seek to justify their conduct on the basis of its

purported competitive benefits in every case.”). Federal Rule of Evidence 403

provides that a district court “may exclude relevant evidence if its probative value

is substantially outweighed by a danger of . . . unfair prejudice, confusing the

issues, [or] misleading the jury.” See Skelos, 988 F.3d at 662–63 (“In the context of

                                           53
Rule 403, we conduct [our] review recognizing that [a] district court is, of course,

in the best position to do the balancing required.” (second alteration in original)

(internal quotation marks omitted)).

         Given that the government did not need to prove that the conspiracy to fix

prices and rig bids alleged in the indictment was unreasonable, allowing unlimited

evidence of a lack of anticompetitive effects or the existence of procompetitive

benefits in connection with the alleged conduct would have risked “cloud[ing] the

issue” of whether Aiyer was guilty of a per se violation of the Sherman Act and

would have potentially confused or misled the jury, otherwise resulting in unfair

prejudice to the government. United States v. Gatto, 986 F.3d 104, 117–18 (2d Cir.

2021).

         Because of this concern, the district court carefully parsed through Aiyer’s

evidence regarding a lack of anticompetitive effect and weighed its probative

value on the issue of intent against its potential prejudicial effect. For example,

with respect to the opinions of Aiyer’s expert witness, although the district court

allowed some of that testimony, it noted, “to the extent that [the expert opinion]

attempts to suggest why the alleged conspirators in this case acted as they did, it

would be an impermissible attempt for an expert to testify as to the state of mind

                                          54
of the alleged conspirators.” Gov’t Supp. App’x at 227; see also Gov’t Supp. App’x

at 228 (“[T]o the extent that the analysis of [defense expert] Professor Lyons is

based on an analysis of market conditions to negate the intent of the conspirators,

the evidence should be excluded for the additional reason that there is no proffer

that the alleged conspirators were aware of the conditions relied upon by Professor

Lyons[.]”); Gov’t Supp. App’x at 236 (“It is one thing to cross-examine a witness

on what the witness’s intent was based upon what the witness knew, and in

particular, the point I made at the sidebar, the chart with respect to moving the

price up or down. . . . But it’s another thing to say then independently we’re going

to present evidence that the ultimate transaction benefitted the client or had no

effect on the client. It didn’t affect prices. That is a different question, and it is

removed from the cross-examination of the witness about what the witness knew

or thought and whether the witness’s testimony was, in fact, credible

testimony.”). 26

26 The district court noted, in ruling on the admissibility of certain defense exhibits, that
“witnesses could be re-called” if the defense wanted to establish the necessary foundation
for additional evidence on the intent issue by showing that the conspirators were “aware
of what was going on in the market.” Gov’t Supp. App’x at 249. Aiyer did not recall any
witnesses or otherwise establish such a foundation.
                                             55
      Ultimately, the district court determined that any probative value of this

additional evidence on intent was substantially outweighed by its potential

prejudice.   Having reviewed the district court’s careful consideration of this

complex evidentiary issue, we conclude that the district court properly balanced

the need to allow Aiyer to rebut the government’s intent evidence with the

importance of preventing irrelevant competitive effects evidence from coming

before the jury in this per se case and confusing the jury on the requisite elements

of the crime. Accordingly, the district court did not abuse its discretion in limiting

Aiyer’s evidence purporting to show that the FX trading activity he engaged in

lacked anticompetitive effects and had procompetitive benefits.

   III.   The Alleged Juror Misconduct

      Finally, Aiyer contends that the district court abused its discretion in

handling allegations of juror misconduct. In particular, he argues that the district

court erroneously accepted Juror No. 3’s “self-serving denials” of the allegations

during his post-trial interview in court, Aiyer’s Br. at 56, and that, instead, the

district court should have also interviewed Juror No. 6, who made the post-trial

allegations in a letter to the court. Aiyer additionally asserts that another juror’s

                                         56
mid-trial podcasts, discovered after trial, suggested that further investigation was

required. 27

       We review a district court’s investigation into alleged juror misconduct for

abuse of discretion. United States v. Baker, 899 F.3d 123, 130 (2d Cir. 2018). When

“[f]aced with a credible allegation of juror misconduct during trial, a court has an

obligation to investigate and, if necessary, correct the problem.” United States v.

Haynes, 729 F.3d 178, 191 (2d Cir. 2013). We have warned, however, “that district

judges should be particularly cautious in conducting investigations into possible

jury misconduct after a verdict.” United States v. Sabhnani, 599 F.3d 215, 250 (2d

Cir. 2010); see also United States v. Stewart, 433 F.3d 273, 302 (2d Cir. 2006) (“Post-

trial jury scrutiny is disfavored because of its potential to undermine full and frank

discussion in the jury room, jurors’ willingness to return an unpopular verdict,

and the community’s trust in a system that relies on the decisions of laypeople.”)

(internal quotation marks omitted). Thus, in the post-verdict context, a hearing

into allegations of juror misconduct is required only “when reasonable grounds

for investigation exist” and “[r]easonable grounds are present when there is clear,

27  Aiyer raises no arguments concerning that juror’s post-trial podcast wherein he
discussed his jury service. Accordingly, we consider any such arguments abandoned.
See Cohen v. Rosicki, Rosicki & Assocs., P.C., 897 F.3d 75, 87 n.9 (2d Cir. 2018).

                                          57
strong, substantial and incontrovertible evidence that a specific, nonspeculative

impropriety has occurred which could have prejudiced the trial of a defendant.”28

United States v. Moon, 718 F.2d 1210, 1234 (2d Cir. 1983) (internal citation omitted).

Moreover, “in the course of a post-verdict inquiry on this subject, when and if it

becomes apparent that . . . reasonable grounds to suspect prejudicial jury

impropriety do not exist, the inquiry should end.” Id. As set forth below, we find

no abuse of discretion in the district court’s handling of these post-trial allegations

of juror misconduct.

       After the district court received the letter from Juror No. 6 regarding Juror

No. 3’s alleged misconduct, it directed Juror No. 3 to return to court for an

interview with lawyers for both sides present. The district court first asked Juror

No. 3 whether he had done “any research about the case or any of the parties or

the lawyers.” Redacted App’x at 18. Juror No. 3 indicated that he had conducted

no such research during the trial and volunteered that, after the trial, he learned

28  We have clarified that “[t]he requirements of ‘strong, substantial and incontrovertible
evidence’ do not demand that the allegations be irrebuttable; if the allegations were
conclusive, there would be no need for a hearing.” United States v. Ianniello, 866 F.2d 540,
543; accord Baker, 899 F.3d at 130–31. For example, in Ianniello, we found that a post-trial
hearing was warranted based upon three affidavits from jurors that “contain[ed] concrete
allegations of inappropriate conduct [by the trial judge and a federal marshal] that
constitute[d] competent and relevant evidence.” 866 F.2d at 543.
                                            58
that his office manager—who had seen a notice related to Juror No. 3’s jury

service—had researched this case. Juror No. 3 also denied seeing any pictures of

any attorneys involved in the trial and reported only that the jurors had

“nicknames for some of the lawyers.” Redacted App’x at 19. With respect to the

suggestion that his girlfriend or boss may have given him outside information

before the jury reached its verdict, Juror No. 3 explained that they did not provide

him with any such information and that they “respected that the United States

Code is to leave the juror alone.” Redacted App’x at 20. He also stated, “[i]n one

instance, my girlfriend did ask [about the case], but I told her I was not allowed to

speak about it.” Redacted App’x at 20. Before Juror No. 3 was dismissed, counsel

for both the government and Aiyer informed the district court that they had no

additional questions for Juror No. 3.

      The district court did not abuse its discretion in concluding that, in light of

Juror No. 3’s interview, “there [was] no reason to suggest that there was any

prejudicial information improperly brought to the attention of the jury.” Aiyer I,

433 F. Supp. 3d at 476. After interviewing Juror No. 3, the district court found that

he “was forthcoming in his answers and explained [them] in matter-of-fact and

credible terms.” Id. Moreover, the district court explained:

                                         59
      To the extent that there is any conflict between Juror No. 3’s testimony
      and the allegations contained in Juror No. 6’s letter, Juror No. 3’s
      direct statements are more credible than the alleged comments that
      Juror No. 6 claims to have overheard, particularly when the Court
      instructed the jurors to bring to the Court’s attention during the trial
      if any juror violated the Court’s instructions not to look at or listen to
      anything about the case outside the courtroom. Further, Juror No. 6
      brought his concerns to the Court only after he became dissatisfied
      with the unanimous verdict.

Id. at 476–77. Given that “the district court is best situated to evaluate jurors’

credibility” in these circumstances, United States v. Cox, 324 F.3d 77, 87 (2d Cir.

2003), we decline to second-guess the district court’s finding that Juror No. 3 was

more credible than Juror No. 6.

      Moreover, the district court did not abuse its discretion in concluding that,

even assuming that Juror No. 6’s allegations were true, those allegations failed to

demonstrate that Juror No. 3 had, in fact, been exposed to any prejudicial

information. In other words, even if Juror No. 3’s girlfriend and boss had looked

up this case, and even if he had looked up a member of the defense team and

commented on that attorney’s appearance, Juror No. 6 made no allegation that

Juror No. 3 received or otherwise heard anything that could have prejudiced

Aiyer’s trial. In addition, given the level of detail in Juror No. 6’s letter, as well as

the district court’s instruction that jurors immediately bring misconduct concerns

                                           60
to its attention, the court was well within its discretion to doubt that Juror No. 6

had any more details to provide and to conclude that the investigation could end

because “reasonable grounds to suspect prejudicial jury impropriety” did not

exist. Moon, 718 F.2d at 1234.

      To the extent Aiyer relies on United States v. Resko, 3 F.3d 684 (3d Cir. 1993)

in support of his position, we are unpersuaded. There, the district court was

informed mid-trial that “members of the jury had been discussing the case during

their recesses and while waiting in the jury room.” Id. at 687. After “summon[ing]

the jurors en masse” and informing them of the issue, the court gave them a two-

question questionnaire with the following yes-or-no questions: (1) “Have you

participated in discussing the facts of this case with one or more other jurors

during the trial?”; and (2) “If your answer to Question No. 1 is ‘Yes,’ have you

formed an opinion about the guilt or non-guilt of either defendant as a result of

your discussions with other jurors?” Id. at 688. Although “[a]ll twelve jurors

answered ‘yes’ to the first question and ‘no’ to the second question,” the district

court denied the defendants motion for a mistrial and resumed the trial. Id.

      On appeal, the Third Circuit vacated the defendants’ convictions,

concluding that “the questionnaire raised more questions than it answered”

                                         61
because, among other things, the jurors’ answers indicated that they all “engaged

in premature discussions,” but “ there [was] no way [of] know[ing] the nature of

those discussions—whether they involved merely brief and inconsequential

conversations about minor matters or whether they involved full-blown

discussions of the defendants’ guilt or innocence.” Id. at 690–91. Thus, the Third

Circuit concluded that the district court abused its discretion by “declining to

engage in further inquiry—such as individualized voir dire—upon which it could

have determined whether the jurors had maintained open minds.” Id. at 691.

      Here, by contrast, after it received the specific allegations of misconduct by

Juror No. 3, the district court promptly recalled Juror No. 3 for an interview, asked

him focused questions related to the specific allegations, and received answers

denying any impropriety, which the district court found credible. Thus, in light

of its knowledge of the specifics of the allegations from Juror No. 6’s letter and its

credibility determination as to Juror No. 3 after interviewing him, the district court

was able to conclude confidently that it was “apparent that . . . reasonable grounds

to suspect prejudicial jury impropriety do not exist,” and thus, “the inquiry should

end.” Moon, 718 F.2d at 1234. Additionally, it is significant that the allegations in

this case, unlike in Resko, arose after the jury reached its verdict, a time when

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district courts “should be[] hesitant to haul jurors in [to court] . . . in order to probe

for potential instances of bias, misconduct or extraneous influences.” Id.

      In essence, Aiyer asks us to decide that, where a juror informs a district

court—post-trial—about potential juror misconduct in detail in writing, and an

accused juror’s subsequent denial of those allegations is deemed credible, the

district court is still obligated in every instance to interview, at a minimum, the

accusing juror. We decline to adopt such a categorical rule, which would be

inconsistent with our precedent. Indeed, we are mindful that “[a] district court’s

investigation of juror misconduct or bias is a delicate and complex task.” Cox, 324

F.3d at 86 (internal quotation marks omitted). In performing that task, there are a

series of discretionary (and often countervailing) factors that could impact a

district court’s determination on whether one or more jurors should be

interviewed when an allegation of misconduct arises, including, among others, the

nature of the allegations, the level of detail in the allegations, the strength of the

allegations on their face and in the context of other information and observations

already possessed by the court before conducting any investigation, as well as an

ongoing assessment of the merits of the allegations based on the results of any

investigation that the court decides to conduct (including, here, any credibility

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determination it makes as to an accused juror if that juror is interviewed first). In

short, this type of delicate inquiry should not be subject to any bright-line rule on

how a district judge must proceed, but rather should be a fact-specific,

discretionary determination that must be carefully assessed on a case-by-case

basis. See also United States v. Aiello, 771 F.2d 621, 629 (2d Cir. 1985) (“The extent

of that investigation and the method of conducting it will, of course, depend on

the surrounding circumstances, including the content of the communication and

the apparent sensitivity of the juror. The trial judge must be given wide discretion

to decide upon the appropriate course to take, in view of his personal observations

of the jurors and parties.”), abrogated on other grounds, 116 S. Ct. 1241 (1996). Under

the particular facts here, the district court did not abuse its discretion in

concluding, after interviewing Juror No. 3 and finding the juror’s responses to the

allegations credible, that the inquiry could end without interviewing the accusing

juror to further assess the credibility of that juror’s allegations or to determine if

there were any additional unreported allegations.

      As to Juror No. 4’s mid-trial podcasts, we similarly conclude that the district

court did not abuse its discretion in finding that, when considered in their entirety,

the podcasts “[did] not raise any concerns that necessitate a post-verdict inquiry.”

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Aiyer I, 433 F. Supp. 3d at 474. Of course, Juror No. 4’s mid-trial, public comments

on the podcast that he did not care about the case, was “angry” that he was a juror,

and that he “started to not pay attention at all” were cause for concern. Redacted

App’x at 5. However, the district court did not rely on snippets of the podcasts

provided by Aiyer after the trial; instead, it reviewed all of Juror No. 4’s mid-trial

podcasts and found that, notwithstanding his many complaints, he also explained

that “he would refrain from discussing the case during the trial”; “he would be

unbiased in deliberations[] at the end of the day”; and “he understood the gravity

of his role and . . . would render a fair and just decision.” Aiyer I, 433 F. Supp. 3d

at 474–75. Based on this record, the district court was well within its discretion in

determining that “reasonable grounds to suspect prejudicial jury impropriety [no

longer] exist[ed],” and that no further investigation was warranted. Moon, 718

F.2d at 1234.

         Accordingly, we conclude that there was no abuse of discretion in relation

to the district court’s post-trial investigation into potential juror misconduct.

                                  CONCLUSION

         For the reasons set forth above, we AFFIRM the judgment of the district

court.

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