Can letting players take resources from others prevent inflation despite the lack of money sinks?

For a long time I've been idly thinking about a competitive game with strong collection elements with such a rule that players will win or lose resources at the expense of each other during each match.

Sorry if this seems unclear; let me provide a concrete example: Chess with an ecosystem.

Each player starts with a standard set of a king, a queen, two bishops, two knights, two rooks, eight pawns. Each time, during a match, a figure or pawn is captured, it permanently goes to the player who captured it (promoted pawns count as pawns for this purpose, not as whatever they were promoted to). This is the only way players can earn pieces¹.

The game is divided into several leagues: each league restricts the total value of pieces both players may start with. As long as each player only uses pieces they own and their value doesn't exceed their league's maximum, they can start with any pieces they desire. Thus each player who's just founded their account will start at a mediocore league that enforces the total value of pieces of up to 43 (8 pawns * 1 + 2 bishops * 3 + 2 knights * 3 + 2 rooks * 5 + 1 queen * 9 + one king * 4 = 8 + 6 + 6 + 10 + 9 + 4 = 43); if they lose pieces they will lose access to the starting league and be demoted to lower leagues, down to the lowest league that only accepts the total value of pieces of 5 (meaning that, aside from the mandatory king, it only allows one pawn); if they earn pieces they are promoted to higher leagues that allow them to start with more total material. (Players may also play lower leagues than their league if they wish, but not higer). If they lose so much pieces they cannot even play at the lowest league, they lose permanently and have to start with a fresh account.

Now from this follows that since there are no sinks and the total material of the game will only be increasing with people founding more and more accounts. From this we can expect that as more and more players lose permanently, we will have more and more players having hundreds and thousands of pieces, so inflation happens.

But if, regardless of their league, players are always matchmade according to their elo and if there are so many players that the matchmaking works and is unpredictable (granted, big 'if's...), their winrates should sit at 50%! Thus their earn/lose balance should be around zero. Pieces have a fixed cost: Getting them requires winning against an opponent of equal skill.

Ugh... Looking at the problem from these two different perspectives yields conflicting results. What am I missing? Would inflation happen in such a game?

Note this chess example is really only an example: I only provided it because it is the only concrete example I could muster. However, we can easily think about a collectible card game with a system similar to this, and I suppose such a TCG example would be even better here.

¹ Well, almost. If a player loses a king and have no more kings they must buy another king. To this end they must sell other pieces: pawns for one gold piece each, knights and bishops: three pieces each, rooks for 5 gold pieces each, queens for 9 gold pieces each; this in-game currency goes to the 'king fund' that will be used to buy kings from the in-game shop, 4 gold pieces for each king. No other pieces can be purchased for gold gained in such a way.

• If you can make a new account at any time in order to get back up to the basic collection, why not make a new account as soon as you've lost more than you've won, instead of waiting until you've lost everything? Commented Oct 9, 2019 at 16:36

The average winrate between a player who loses all their pieces and one who gains all those pieces is 50%, but the player who loses all their pieces then goes on to make a new account, so now amongst those two people there are three complete sets of pieces, and you have inflation.

As for the middle and high-rank players accumulating more pieces over time despite not getting any better in rank: Imagine a ladder of people who are each just a tiny bit better than the one before them, close enough that they get matched against the adjacent players: on average, each player will collect pieces from the slightly worse player, and give pieces to the slightly better player, so over (a probably pretty long) time pieces will go up the chain, from the bottom where new pieces are generated, to the top where the greatest players are.

This will cause inflation.

Having the total material increase with people creating more and more accounts is a sound argument.

The argument that win rates should be around 50% and thus the pieces will remain constant is flawed:

For the average win rate: Initially, how many pieces a player has corresponds to their win rate. Players who lost all their pieces would have a win rate of less than 50%. When you give a player pieces to "reset" them, you're increasing how many pieces they have, but you're not increasing their win rate, so the number of pieces no longer corresponds to the win rate. Thus the win rate can remain 50% while the total number of pieces increases.

Alternatively, if you consider these to be new accounts, you're removing accounts with a sub-50% win rate and replacing them with new accounts. This would increase the average win rate and thus also the total number of pieces.

For the individual win rate: every player will not have a win rate of 50%, even in a perfectly balanced skill-based game. The best players can consistently win, since there's no-one who can beat them. The worst players can consistently lose. If these players are put back in the middle, they will likely drop again and other players at the same ranking will win more often. The ranking of those players will increase, which will pit them against stronger players, who will beat them, which will decrease the ranking of the weaker player back to where it was and increase the ranking of the stronger player. This effect will keep going (albeit slowly) until it gets to the top players, who have no stronger players to play against, thus their win rate and ranking will simply increase.

Players quitting can also cause inflation

The above only exactly applies to a closed system (one where no players are added or removed) or when players are added and removed randomly.

If players at the top no longer feel challenged or like there isn't anything more to achieve, they may stop playing. This could cause negative inflation to counteract the inflation discussed above, but frequently having your best players quit is usually a pretty bad sign.

Players at any level may simply get bored with the mechanics of the game. For arguments sake, one might assume this happens at every level with equal likelihood (although this may happen more frequently at lower ranking, since these players may miss some of the nuances and complexity making the game more fun for higher ranking players).

Other players may quit out of frustration. This would almost certainly happen much more frequently with players losing too often, especially ones who has mostly been losing since they started. These players would likely have a sub-50% win rate and thus them quitting would increase the average number of pieces per player, which is inflation.

Having ranking tied so directly to strength (through number of pieces) will always be a problem.

If you want to do something like this, you could:

Limit the number of pieces per player

There are two ways this could be done:

• Limit on the number of pieces each player can have.

This may cause a whole lot of players eventually reaching the maximum instead of fewer players having more and more pieces, which is still not great, but may be preferable.

• Have players pick a subset of pieces to play with (and there's a limit on how many they can pick).

Having players constantly gain unusable pieces may not be that much fun for them, but this may also be better than the alternative.

You could have players upgrade pieces to improve them by combining pieces together. This is assuming you can define an upgrade system which makes sense in the context of your game.

If pieces are taken, the other player gets a piece with no upgrades.

This would be a sink for pieces, which could counteract inflation.

Alternatively, you can let players take the upgrades too. In that case, the upgrades should probably be very minor, so a better player can still beat a weaker player with much better upgrades. There would still be inflation, but this could slow it down an extreme amount.

A minimum number of pieces

I'm assuming that playing with very few pieces wouldn't be all that much fun.

So I'd suggest, instead of having players go down to zero pieces, you can have them go down to a minimum. When at the minimum, any taken pieces will not be removed from the losing player, but instead just give the winning player a duplicate.

Then remove the idea of "resetting" a player's pieces, since this is no longer necessary.

This doesn't really address inflation, but should make the game more fun for the players with lower ranking.

This also has the added benefit of not constantly resetting weak players, where they'll then play against stronger players.

Take only one piece per game

When winning, you only get one of the opponents pieces (either one which was taken or any which was played with, which can either be picked or random).

This wouldn't stop inflation, but it would be slower than having all taken pieces go to the other player.

Tournament format

Have constant tournaments, each with a fixed start and end date. Pieces only last for the duration of the tournament and gets reset when another tournament starts.

There would be inflation, but this might even be a good thing when you're just resetting everything at some point.