The activity as described seems to have the following properties:
You always keep the cards you were originally dealt and don’t trade them for other ones (you just think about and discuss trades). And
The trades you think about and discuss are always ones involving the cards you were originally dealt. Therefore,
You get inconsistencies if and only if your exchange rates all have the same ratio across the cards you were originally dealt. In particular,
If you were originally dealt just one card, there’s no opportunity for inconsistency (other than meeting with the same person twice and picking different rates, I guess).
But what the text says about inconsistencies seems like it implies that something different is intended (laptop / plane ticket / bicycle / laptop), and it seems as if this sort of activity might be more interesting if participants sometimes actually swapped cards somehow.
So we could change the rules as follows:
Everyone’s cards have numbers on, indicating how much/many of the resource in question they own.
You can start with all the numbers being 1, or pick them all so that everyone has very handwavily on the order of $1000 worth of each thing, or whatever.
If people with cards A and B meet, and their A/B exchange rates differ, then they can pick an exchange rate in the middle (probably ideally the geometric mean, but this isn’t a competition and it’s fine to pick something near that but easier for calculation) and swap cards as follows: if player 1 has card A with quantity a, and player 2 has card B with quantity b, and the mutually-favourable exchange rate they agree on is that one unit of A is worth r units of B, then after the swap player 1 has card B with quantity ra and player 2 has card A with quantity b/r.
When everyone’s done with the activity, as well as hoping to have lots of exchange rates recorded and not to have been the victim of a Dutch-book-style cyclic ripoff, everyone looks at what they started with and what they have now and considers whether they do in fact consider themselves better off at the end than at the beginning, and whether they’ve learned anything interesting about their own priorities from what they ended up with.
[EDITED to add] I see that omark had essentially the same idea and had it first. Leaving this here because my version has more details :-).
The activity as described seems to have the following properties:
You always keep the cards you were originally dealt and don’t trade them for other ones (you just think about and discuss trades). And
The trades you think about and discuss are always ones involving the cards you were originally dealt. Therefore,
You get inconsistencies if and only if your exchange rates all have the same ratio across the cards you were originally dealt. In particular,
If you were originally dealt just one card, there’s no opportunity for inconsistency (other than meeting with the same person twice and picking different rates, I guess).
But what the text says about inconsistencies seems like it implies that something different is intended (laptop / plane ticket / bicycle / laptop), and it seems as if this sort of activity might be more interesting if participants sometimes actually swapped cards somehow.
So we could change the rules as follows:
Everyone’s cards have numbers on, indicating how much/many of the resource in question they own.
You can start with all the numbers being 1, or pick them all so that everyone has very handwavily on the order of $1000 worth of each thing, or whatever.
If people with cards A and B meet, and their A/B exchange rates differ, then they can pick an exchange rate in the middle (probably ideally the geometric mean, but this isn’t a competition and it’s fine to pick something near that but easier for calculation) and swap cards as follows: if player 1 has card A with quantity a, and player 2 has card B with quantity b, and the mutually-favourable exchange rate they agree on is that one unit of A is worth r units of B, then after the swap player 1 has card B with quantity ra and player 2 has card A with quantity b/r.
When everyone’s done with the activity, as well as hoping to have lots of exchange rates recorded and not to have been the victim of a Dutch-book-style cyclic ripoff, everyone looks at what they started with and what they have now and considers whether they do in fact consider themselves better off at the end than at the beginning, and whether they’ve learned anything interesting about their own priorities from what they ended up with.
[EDITED to add] I see that omark had essentially the same idea and had it first. Leaving this here because my version has more details :-).