Clearly Pierce is trying to lure us into a labyrinth of emotional manipulation and strategic instigation. And I think we're all smart enough to know we should quit while we are not ahead.
The study group arrives in Group Study Room F having just attended Pierce's Reformed Neo Buddhist funeral. In their possession is an Energon pod supposedly containing Pierce's "life vapor". Ben Chang shows up and mocks the everyone's somber attitude pointing out how much they disliked Pierce. A man identifying himself as "Mr. Stone" then appears claiming to be carrying out a private inquest at the behest of Pierce's will. As two technicians set up a polygraph device Stone tells the study group and Chang that they will have to submit to a lie detector test. It’s to determine if any of them were responsible for Pierce's death.
"Aw shnizzle! You guys are in trouble!
Everyone agrees but Stone's questions bring some secrets to light: Shirley is a platinum level donor to a Pro-Life organization which angers Britta, Jeff's Netflix account is being used without his permission by Troy and Abed, Chang leaves after admitting he masturbated in the study room, and Annie confesses she is overcharging Troy and Abed on their share of the rent. As the argue Stone tells them that the first round of questions was just for equipment calibration. Jeff suggests to the group they should quit the test before the questions gets worse. Stone tells then if they quit they won't receive bequeathments from Pierce's estate which is valued at over 20 million dollars.
Everyone agrees to continue resulting in more revelations: Shirley served Britta (who is a vegan) a meat-like tofu substitute, Britta was high on marijuana during the baptism of Shirley's child, Jeff kept souvenirs of his sexual conquests including Britta's panties, Abed learns Troy did not create their signature handshake, Abed planted geo-trafficking devices in all of them, Annie once dosed the group with amphetamines to keep them studying and Abed is revealed to have been "cat fishing" Annie. The group starts arguing again when Jeff pleads with the group to stop letting Pierce manipulate them. Stone points out that he stopped asking questions a while ago and that most of those revelations were volunteered.
Abed literally keeps track of the group -even a buried Pierce.
Jeff then realizes the "lesson" this activity was meant to teach them: They are all as flawed as Pierce was, he was just more honest about it. Jeff suggests they embrace their imperfections and admits he is such a narcissist he would rather look at himself naked rather than the women he sleeps with, Annie admits to hitting Jeff's Lexus in the parking lot, Britta only gives to the homeless if she is with someone, Troy has never been to Lego Land, Shirley admits to being passive aggressive, and Abed hates when anyone chews gum in his presence. With all their secrets now out in the open, Jeff defiantly tells Mr. Stone to continue his inquest.
The polygraph technicians monitor the groups vitals.
Stone starts the final round of questions with Britta and tells her Pierce believed that she should stop hating herself and her passion inspired him. Britta is bequeathed a used iPod Nano along with a cylinder of Pierce's sperm. Shirley is next and Stone tells her that Pierce always had great respect for both her strength of character and business acumen. She is bequeathed Pierce's timeshare in Florida and a cylinder of his sperm. Annie is told by Stone she was always Pierce's favorite. She is given a tiara he tried bequeathing her several years ago and along with sperm. Stone then questions Jeff's sexuality again before bequeathing him a bottle of fine scotch and his own canister of Pierce's sperm.
The gift that keeps on giving.
Stone tells Abed Pierce believed he was crazy before handing him a canister of sperm. Troy is then told that Pierce believed he had untapped potential. Along with the obligatory share of sperm, Troy is also bequeathed Pierce's shares to Hawthorne Wipes valued at 14.3 million dollars. The only condition is that Troy sail Pierce's boat, "The Childish Tycoon", around the world. It was a task his father, Cornelius Hawthorne, gave him to earn his fortune which he failed to complete. It was something he always regretted and wants to give Troy the same chance in order to become his own man. Jeff steps in and argues that the condition can be contested but Troy states that he will do it. The study group is shocked but Abed pretends to be okay with his decision. However, one of the polygraph technicians monitoring his vitals confirms that he is lying.
Mr. Stone and the study group are at a restaurant having a drink. Stone is inebriated and has dropped the dour façade he was using at the inquest. He reveals to the group that the cause of Pierce's death was dehydration from filling up all the sperm cylinders he bequeathed to the group.
Recurring or debuting plot points in this episode:
As a gift from Pierce, Britta receives an iPod nano. The captions at the end of the Season One episode "The Art of Discourse" predict that Britta will be become the proud owner of a used iPod nano in the year 2014.
Annie is also given a tiara as a gift once and was said to be Pierce's favorite once again, which was seen first in the Season Two episode "Intermediate Documentary Filmmaking."
Pierce's will challenges Troy to embark on a solo voyage around the world in a sailing vessel. Troy and Pierce took a sailing course in "Beginner Pottery".
School uniform: In keeping with Pierce's beliefs, the study group wears teal ceremonial Laser Lotus outfits. A similar outfit was last seen being worn by Pierce himself in the Season Two "The Psychology of Letting Go".
IRL: Chang walking into the study room with the line "What up, N-bombs, how was the funeral?" is a reference to the alleged use of the N-word by actor Chevy Chase while shooting an episode. 
Résumé: In his bequeathal to Troy, Pierce encourages Troy to become his own man. As a condition to receive his bequeathment, Troy must sail Pierce's boat "The Childish Tycoon" around the world. Donald Glover, who plays Troy, is leaving the show in order to be in control of his own career. He is set to "write, executive produce and play the lead in a half-hour comedy, which has landed at FX for development."("[Deadline.com]") In addition, Glover records and performs as a rap artist under the name Childish Gambino and begins an international tour in the spring of 2014.
Up against the wall: The episode is another "bottle episode" in the series. The title "Cooperative Polygraphy" is a reference to the first bottle episode, Season Two's Cooperative Calligraphy.
In a November 25 interview with Entertainment Weekly online, actor Walton Goggins discussed his role as "Mr. Stone" on Community. He mentioned he is a fan of the show and was eager to guest star:
“I’m always looking to not only challenge myself, but to put myself in situations where I’m not just intimidated but outright insecure.”
In the episode everyone but Abed is shown to receive a personal bequeathal from Pierce along with their complimentary canisters of his sperm. In one of the original drafts of the episode's script, Abed is actually about to be bequeathed something but refuses before he could be told what it is. He instead decides to forego his bequeathment in exchange for the phone number of the female polygraph technician named "Mara". This is done on his part as a homage to the 1992 film "Sneakers" which a flattered Mara immediately picks up on. After she accepts his proposal, Abed is told by Mr. Stone (originally "Kobayashi") that his bequeathment was a limited edition caricature of Muhammad (any images of the Muslim prophet are strictly forbidden by most followers of the religion). Writer Alex Ruebens posted a picture of the script page for this unfilmed scene HERE on his twitter account.
A deleted scene from the original script.
According Mr Stone, the total inheritance from Pierce Hawthorne is over 20 million dollars. The shares in the Hawthorne Wipes Company given to Troy is worth 14.3 million dollars leaving 5.7 million dollars unaccounted for. It is highly unlikely the remaining fortune was used entirely on the rest of the study group's bequethals plus the 6 canisters of sperm. It could be speculated that it was possibly used for any alimony payments Pierce owed to his seven ex-wives.
“Mrs. Bennett, is true you are a Platinum level donor for the Pro-Life organization prenatal patriots.org?”— Mr. Stone
“Keep it cool, girls.”— Jeff
“It's my money and my choice.”— Shirley
“Yeah, well, if I wanted the government in my uterus I would fill it with oil and Hispanic voters!”— Britta
“Mr. Winger, your name please.”— Mr. Stone
“Jeffrey Winger.”— Jeff
“Are you gay?”— Mr. Stone
“Are you sure?”— Mr. Stone
“Gay murderer says what?”— Mr. Stone
“I have been instructed to inform you that that means you're gay.”— Mr. Stone
“SILENCE WENCH!”— Troy
“I didn't just masturbate in the study room... I masturbated everywhere. EVERYWHERE!!!”— Ben Chang
“Do you care about people at all, Abed? Answer on the polygraph!”— Annie
“(after a pause) Jeff made me apply for handicapped parking so he can get a better spot.”— Abed
“Britta's the one that invited Garrett to Annie's birthday party!”— Jeff
“Troy won't sit on a toilet seat after Jeff!”— Britta
“When we're alone Shirley refers to you guys as 'those people'!”— Troy
“Oh! When Annie's with other females she calls Jeff her uncle!”— Shirley