This is a silly little brain teaser I first invented quite some time ago. Read through the story and the statements first, then follow the instructions underneath them when you're ready to try and solve the puzzle. Good luck!

The Story

The Gym Leaders and Elites of the Pokémon world didn't get their jobs just by looking pretty. They're all expert Pokémon Masters with a detailed understanding of all sorts of Pokémon, well-versed in dealing with hundreds of moves, species, abilities and tricks. A great deal of this knowledge comes from Pokémon that the league officials actually own or have owned at one time—they may only use Pokémon of a specific type during battles for badges or titles, but that doesn't mean that they don't experiment with other Pokémon at all. And they are always on the lookout for more. In fact, in recent years the Pokémon League has held "swap meets" for its officials, giving them an opportunity to gather and trade rare Pokémon with one another. The swap meets are always big successes, and everyone goes home with a slew of new Pokémon to try out.

Brendan has recently triumphed over the Hoenn League and, as an official Pokémon League Champion, has been invited to one of these swap meets. He looks around for a while and sees that Cynthia is offering her Milotic up for trade. Endless fishing in the river on Route 119 has turned up absolutely no Feebas, and Brendan would give just about anything for a chance to add the elusive Milotic to his collection. He offers Cynthia a mighty Gyarados for it, certain that the two Pokémon are of approximately equal power. To his surprise, Cynthia turns him down, insisting that the trade is not fair at all. He tries adding a Heracross to sweeten the deal, but she still won't accept. As Brendan sits back and tries to figure out what else he could possibly offer Cynthia without cheating himself, Candice approaches her and offers a tiny Bonsly and a rather weak Mothim. To Brendan's surprise, Cynthia readily agrees to the trade.

"How did you get her to trade you that Milotic?" Brendan asks Candice.

Candice shrugs. "I just gave her some Pokémon of equal value," she says. "What else do you do when you trade?" Before Brendan can ask her how on earth a Bonsly and a Mothim are a fair trade for a rare, powerful Milotic, Candice walks off to strike a deal with someone else.

Now thoroughly baffled, Brendan continues to walk around and observe the other trainers as they work out their trades. It soon becomes clear that they have a very unusual understanding of what constitutes a good deal; what's more, different trainers seem to disagree about the value of the same Pokémon, and they will not trade directly with a trainer who doesn't subscribe to their system. Brendan overhears the following in listening to their conversations:

-Bugsy offers Whitney a Gloom and an Aipom for her Feraligatr and Teddiursa, and she accepts.

-Brock is offering a shiny Heracross, and Lt. Surge trades him a normally-colored Heracross for it.

-Ethan, who has also recently been crowned Champion and is also very confused, sees the lieutenant's new shiny Heracross and offers him a shiny Pinsir for it. Lt. Surge tells him that the trade is unfair and flatly refuses.

-Juan wants Drake's Magmar and offers him a Ralts and a Slowpoke for it, but while Drake agrees that that's a fair deal he isn't interested in either one. After some negotiation Juan offers Grumpig and Spheal for Magmar instead, and Drake accepts the trade.

-Sabrina, Will, Lucian, Tate and Liza are discussing the value of certain Pokémon over lunch. Sabrina thinks that three Gastly are worth one Taillow, Will thinks that three Gastly are worth one Remoraid and Lucian thinks that three Gastly are worth one Glalie. Tate and Liza, however, insist that there is no single Pokémon equal to three Gastly in value.

-Dawn, yet another terribly confused new Champion, tries to offer Erika a Staravia for her Pidgeotto. Erika politely declines, stating that she'd feel terrible about herself if she ripped Dawn off like that. "If only I had a Latias," says Erika, "then I'd happily trade that and Pidgeotto for your Staravia."

-Champion Lyra is also perplexed by the bizarre trades, even moreso when she finds herself dragged into one as a middleman. Jasmine wants a Sandslash and she knows that Brawly is offering one, but rather than talk to Brawly directly she approaches Lyra, asks for a favor and then gives Lyra an Abra and a Machoke in exchange for an Ivysaur. Following Jasmine's directions, Lyra trades the Abra and the Machoke for Brawly's Sandslash, then trades the Sandslash to Jasmine for a Caterpie and a Metapod. Jasmine and Brawly seem satisfied, while Lyra sits and stares, dumbfounded, at the Caterpie and Metapod she ended up with.

It takes Brendan a while to decipher this strange bartering system, but at long last he finally figures out how to negotiate deals with the league officials. He approaches Volkner, who has another Pokémon that he wants. He offers a Vulpix and a Pichu for this Pokémon, but Volkner insists that that isn't a good deal and that Brendan doesn't have anything that he would consider fair. Undeterred, Brendan offers the Vulpix and Pichu to Flannery for a Bayleef. Flannery happily accepts. The Bayleef catches Morty's eye, and he trades Brendan two Chikorita for it; Lorelei, in turn, trades Brendan an Aron for the two Chikorita. Now confident that he's almost ready to talk to Volkner again, Brendan trades the Aron to Norman and receives an Azumarill and a Wurmple in return. When Brendan heads back over to Volkner, the gym leader is impressed. "Now that's a fair trade," he says, and he accepts Azumarill and Wurmple for the Pokémon Brendan originally wanted from him.

What is the Pokémon that Brendan got from Volkner?