Not sure I totally follow, but does this help? Suppose it’s true that 10 of 50 people who got mugs prefer the pen, so 20% of them prefer the pen. Since assignments were randomized, we should also expect 10 of 50 (20% of) people who got pens to prefer the pens. That means that the other 40 pen-receivers prefer mugs, so those 40 will trade too. Then we have 10 mugs-to-pens trades + 40 pens-to-mugs trades, for a total of 50 of 100 trades.
Not sure I totally follow, but does this help? Suppose it’s true that 10 of 50 people who got mugs prefer the pen, so 20% of them prefer the pen. Since assignments were randomized, we should also expect 10 of 50 (20% of) people who got pens to prefer the pens. That means that the other 40 pen-receivers prefer mugs, so those 40 will trade too. Then we have 10 mugs-to-pens trades + 40 pens-to-mugs trades, for a total of 50 of 100 trades.
...are they trading with, like, a vending machine, rather than with each other?
Ah, sorry! Yes, they’re exchanging with the experimenters, who have a excesses of both mugs and pens. That’s important, sorry to be unclear!