Tuesday 10 September 2024

Tax and players' behavior in games

It's been a long time since I last (seriously) tried a MMORPG. Games like MapleStory, Fantasica, AventureQuest (does that even count as multiplayer?)...all sound like distant memories. But if there is a single thing that always trigger my curiosity that would be the economy inside a game. 

I want to talk about trading models.

Free trading is often too much to ask for, not only because game developers are greedy, but also in consideration of barring unfair advantages from unintended ways of gaming. Newbie perks for example, are usually untradable or otherwise players simply register loads of new account and trade all the perks into the main. Another common limitation is that accounts can't trade before a certain level/requirement is met. This is also to increase the cost of creating multis (multiple accounts). 

We always talk about the cost, because in the world of economics that decides whether a trade would happen or not. We know we can't stop all multis however the restrictions we imposed, but we can increase the cost of doing so. A real example is the embargo to Russia. While countries like Hungary and India still sneaks electronics through, the total cost of going that way is much higher than the usual route inside EU. It is not going to destroy Russia's economy overnight, but it's slowly wearing it down. 

Level requirements are temporary. In a longer term the cost is lifted by a simple way: tax. Tax is one of the three unavoidables in one's life, and you can't even avoid that in games. Some tax is indirect like equipments are fixed onto you once you first equipped it that costs either in-game currencies/items, or items requiring real money to clear the status before the equipments can be resold. A more universal approach is to tax every trade though.

Why tax though? Several reasons are clear:

To reduce arbitrage. The lower the trading tax is, the more profitable trading would be, defeating the purpose (supposedly) of the game. With the tax imposed people facilitate trades only if it is profitable enough, so they can focus on other more meaningful things in the game. Trading will be less frequent with a larger spread, but it won't go away because the price is limited to where arbitrage exists after the tax. 

To encourage players to try themselves. Market is put in secondary position and players can earn what's in the market by themselves, knowing that the market price is at least the tax amount higher than the market (agreed) value. If we are making a RPG there is no point having players stuck with a toxic market (but to be fair there will still be market makers even with tax).

To tighten money supply. There is a steady influx of currencies from battles, but demand for some items are likely one per players only hence constant over time. It is necessary to reduce money supply to keep items affordable and steady. Of course depending on the market it may not be the most effective way but certainly part of the plan.

The next part is how do we value so as to tax a trade? This is a fundamental reason why accounting exists and there is no way for us to answer that in full.

Luckily, game economics is much simpler not only because a failed system isn't likely to cause a collapse other than reduced trading activity (unless you creates a hyperinflation). 

Another reason is that in-game items are homogeneous. If a monster drops a certain item, your drop yesterday would be the same as my drop today. Every single item of the same type is equal regardless of ownership and time. Remember one of the important role of the government? It's standardization. It is costly to run a council regulating dentists but it is worth it if all citizens only visit chartered dentists that probably won't kill you in operations. Inside a game there is no need for standardization because it is automatic. The value of items does not depreciate over time and trade. All we need to consider is that finitely many item types and the corresponding market.

Very long time ago when I was playing Fantasica I wondered if it is possible to measure imbalances in trades so to catch trades involving real money. That was such a naive thought because (1) the devs probably like these trades although in theory they should not allow so (2) it is much harder to value items than one may have thought.

Below let us dive into a few models of trade taxing, and we will see how it works in each one. One very important note is that for each of the models I mentioned, there are existing games running in that way. 

(Apology for using $as dollar sign because the regular one would trigger the LaTeX script...)

1) Purely money based tax

If the game taxes monetary transaction only, players would go back to bartering. In a real society this might be complicated but in a game things are much simpler. The value of each item can explicitly be calculated with the only uncertainty being human effort input (or imperfect information for players who don't bother).

For example, a certain sword takes 200 pieces of copper to craft with 50% chance of success. The average cost would then be 400 pieces of copper, and we expect the price to be above 400. If the market price is at 500 pieces of copper it represents that the market agrees the effort is worth 100 pieces of copper.

Suppose now a piece of copper is worth $10 in-game (if recycled) and the tax is 10% on currencies. What is the expected market price of the sword? 

First the copper is likely to be sold at $12 or above because $11 yields zero profit. If the sword price is above $6666 players may as well buy copper directly from market, craft themselves and sell the sword because $6666 is $6000 post-tax equivalent to 500 pieces of copper. 

At the same time, there will be players who prefers to gather the copper by themselves. Assuming their valuation on copper to be $10-11 (post-tax revenue by selling copper), they are likely to sell their sword at $5500-6100. We expect the market price of the sword to hold within the range of $5500-6700 then. 

On the other side...you will see traders on the side, selling you the sword at the price of 500 copper. You can either gather them by yourselves, or buy that amount from the market at $5500 which is cheaper than any monetary deal out there. Furthermore you could even counteroffer maybe 480 pieces of copper because if he sells the sword on the market at say, $6000, then the copper-equivalent he receives post tax is 450-490, both less than the market value of 500. By trading with you at 480 pieces of copper, he is effectively buying copper from the market at $11.25 apiece, which is not bad of a deal. 

What I illustrated above is a typical example of understanding surpluses on both sides. The idea is that bartering is beneficial to both parties and there is no reason not to do that. For more complicated production chain or interactions between multiple items we could see chaotic oscillations, but in overall the general behavior is clear: bartering clearly avoids all tax. 

2) Items taxed at fixed valuation

The devs ("government") isn't happy because bartering avoids all taxes. They decide to tax on every items traded at the given valuation -- the vendor price.

Players are of course free to sell items to NPC. Guaranteed, this is the lowest price they can find elsewhere. If an item is sold lower than the vendor price, they will be bought and sold to vendor for arbitrage. Therefore we know the market price is always above the vendor price (+tax in fact).

Trash items with no further added value, the market price is likely to be pinned merely above the vendor price. However valuable items that are traded high already, wouldn't be affected by this taxation much. For example a ruby may worth $100 upon recycling, but it is also a key material to craft a highly sought necklace with magical effects so it is sold at $1000 in the market. Upon trading a tax if $100 * 10% = $10 per ruby occurs which gives an effective rate of 1%. Sounds bad to be positive but not really significant most of the time.

In fact, the existence of such item helped us to avoid taxes in general. Now that we know trading ruby as above gives an effective tax rate of 1% we might as well just use ruby as a trading medium. Suppose I am selling you the sword worth $6000 pre-tax. I may as well pay using 6 rubies. What about the $60 tax? Just like the example in (1), it's even better to ask the sword seller to return $200 pre-tax and it's still beneficial to both parties.

Do you still remember the definition of money? Can I take ruby a type of money in-game? Let's check the the list one by one. Fungible, durable and portable? Check. Acceptable? In a liquid market yes. Divisible? Partially, but the small increase in transaction cost won't harm. But the last one...scarcity failed. Ruby is an item that can be generated in-game over and over again and limited supply is not guaranteed.

Yes, we know ruby will be consumed in the form of turning into necklace, but the supply is unknown. It is possible that more players go and grind rubies at higher price, but other reasons are well possible like associated supply or simply because more players joined the game. The unpredictability of price makes it hard to become an alternate currency.

Like rubies, there are so many candidates as money but players only need one or two of them. They look for the best substitution where supply is really limited. One possible approach is real money associated items -- remember Fantasica? Time Elixir and Potions are the de facto money in game (forget about coins that are useless), but it can be bought at the rate of 1:1 USD. Points, memberships,...these are the ideal currencies. One problem though: players are often not allowed to trade these because devs don't want to get into trouble of money laundering. 

So, another approach is to choose items that are hard to craft, meaning there is no arbitrage by crafting the item. Like, if you can craft a ceremonial sword that is useless in battle but can be shown on your character's back using 1000 pieces of copper ($10 each from our above example). We estimate the market price of the ceremonial sword to be something like $12000-14000, but no. The observed price of the sword is pinned at around $10000-10500. The lack of incentive to craft and recycle makes sure that the price is rather stable. In case the price goes out of the range, market makers will swiftly produce or recycle them to restore the balance.

Does it sound like stable cryptocurrencies? It's because they works in an almost identical principle as well.

3) Item taxed at average market price

Can you imagine your local tax authorities knocking your door asking you why are you undervaluing your item sold? Yes, the devs are now upset and wants to make sure everyone gets taxed fairly. 

Now other than the vendor price there is also a market average price, possibly a VWAP over the past n days. Now ruby with a market price of $1000 is taxed at $100, possibly more because upward spike is usually much higher. But the players are ready to strike back.

Remember, players observe the market but they trade personally. That means, trades are not necessarily following the highest bid and lowest ask. They did so because that's the most market efficient way, but since the devs are making them unhappy they are going to do the same thing to the devs too.

We pick a rarely traded item and create enormous amount of cheap trades, by such we can fake the market price and the taxing system. To be honest, at this stage most players would choose to go with the tax anyway. The game must be pretty generous to keep players around despite the harsh tax, no?


How about setting a clearing center out of the game? Instead of using risky in-game currencies, we just put the money into one central bank. Any monetary transaction is accounted in the clearing system but not in-game until they withdraw from the bank. In that way the money is only taxed in depositing and withdrawing but not in transactions. Items are still taxed -- this is unavoidable because the item must from one side to the other.

It surely works, but for what motivation would you do that? If it charges real money then instead of game devs the tax authorities is coming for you now...

4) Shut down personal trades, market with ask-bid pairing

Sounds harsh but look at steam, many games are already doing that.

Is there any loophole left? In theory not because the market is efficient, but in practice, it depends on how competitive (or in gamer's perspective, toxic) the market is. 

In the world of option trading, you may find an option with bid/ask of $3 and $7 when the fair price is $5. What if you sell at $4? Your order will be filled immediately and market makers won't even thank you.

There must be many independent markets in the game where no one ever visited. For example a sword can be upgraded 20 times, each of the 21 tiers are treated as different goods. The most popular ones must be the 0/20 one and the 20/20 one, followed by 1/20 then 2/20 etc. But what about 14/20? It is likely that no one ever crafted a 14/20 one for sell, and no one is going to buy a 14/20 one. 

In an efficient market, there will be bots watching at every single item at any time. If you makes a silly offer it will immediately be filled. But in reality, games are likely not that competitive and that 14/20 sword market will be up to you to transform. 

Large scale trading may not be possible because (1) that may attract others to look into that market (2) items corresponding to these market must be very scarce that the supply does not support that, but it can be utilized to reduce tax involved.

If I want to get a 20/20 sword, it'd be nice if someone is selling a 14/20 one at low enough price where it's beneficial for you to upgrade the sword by yourself...and then the devs starts to appreciate the system where upgrading weapon comes with a risk of destroying the whole weapon.

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And that's it!

Although we have discussed player behaviors against different models, I shall emphasize that just like our discussion in (4) what happens actually largely depends on whether players act collectively competitive. And, this is NOT the case in reality really.

What that means is, instead of reading above to learn about player behaviors, this is actually a guide to earn from those less sharp in trading! I hope you will enjoy that. :)

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