What would a game with realistic markets look like?

Aug 12 JDN 2458343

From Pokemon to Dungeons & Dragons, Final Fantasy to Mass Effect, almost all role-playing games have some sort of market: Typically, you buy and sell equipment, and often can buy services such as sleeping at inns. Yet the way those markets work is extremely rigid and unrealistic.

(I’m of course excluding games like EVE Online that actually create real markets between players; those markets are so realistic I actually think they would provide a good opportunity for genuine controlled experiments in macroeconomics.)

The weirdest thing about in-game markets is the fact that items almost always come with a fixed price. Sometimes there is some opportunity for haggling, or some randomization between different merchants; but the notion always persists that the item has a “true price” that is being adjusted upward or downward. This is more or less the opposite of how prices actually work in real markets.

There is no “true price” of a car or a pizza. Prices are whatever buyers and sellers make them. There is a true value—the amount of real benefit that can be obtained from a good—but even this is something that varies between individuals and also changes based on the other goods being consumed. The value of a pizza is considerably higher for someone who hasn’t eaten in days than to someone who just finished eating another pizza.

There is also what is called “The Law of One Price”, but like all laws of economics, it’s like the Pirate Code, more what you’d call a “guideline”, and it only applies to a particular good in a particular market at a particular time. The Law of One Price doesn’t even say that a pizza should have the same price tomorrow as it does today, or that the same pizza can’t be sold to two different customers at two different prices; it only says that the same pizza shouldn’t have two different prices in the same place at the same time for the same customer. (It seems almost tautological, right? And yet it still fails empirically, and does so again and again. I have seen offers for the same book in the same condition posted on the same website that differed by as much as 50%.)

In well-developed capitalist markets in large First World countries, we can lull ourselves into the illusion that there is only one price for a good, because markets are highly liquid and either highly competitive or controlled by a strong and stable oligopoly that enforces a particular price across places and times. The McDonald’s Dollar Menu is a policy choice by a massive multinational corporation; it’s not what would occur naturally if those items were sold on a competitive market.

Even then, this illusion can be broken when we are faced with a large economic shock, such as the OPEC price shock in 1973 or a natural disaster like Hurricane Katrina. It also tends to be broken for illiquid goods such as real estate.

If we consider the environment in which most role-playing games take place, it’s usually a sort of quasi-medieval or quasi-Renaissance feudal society, where a given government controls only a small region and traveling between towns is difficult and dangerous. Not only should the prices of goods differ substantially between towns, the currency used should frequently differ as well. Yes, most places would accept gold and silver; but a kingdom with a stable government will generally have a currency of significant seignorage, with coins worth considerably more than the gold used to mint them—yet the value of that seignorage will drop off as you move further away from that kingdom and its sphere of influence.

Moreover, prices should be inconsistent even between traders in the same town, and extremely volatile. When a town is mostly self-sufficient and trade is only a small part of its economy, even a small shock such as a bad thunderstorm or a brief drought can yield massive shifts in prices. Shortages and gluts will be frequent, as both supply and demand are small and ever-changing.

This wouldn’t be that difficult to implement. The simplest way would just be to institute random shocks to prices that vary by place and time. A more sophisticated method would be to actually simulate supply and demand for different goods, and then have prices respond to realistic shocks (e.g. a drought makes wheat more expensive, and the price of swords suddenly skyrockets after news of an impending dragon attack). Experiments have shown that competitive market outcomes can be achieved by simulating even a dozen or so traders using very simple heuristics like “don’t pay more than you can afford” and “don’t charge less than it cost you”.

Why don’t game designers implement this? I think there are two reasons.

The first is simply that it would be more complicated. This is a legitimate concern in many cases; I particularly think Pokemon can justify using a simple economy, given its target audience. I particularly agree that having more than a handful of currencies would be too much for players to keep track of; though perhaps having two or three (one for each major faction?) is still more interesting than only having one.

Also, tabletop games are inherently more limited in the amount of computation they can use, compared to video games. But for a game as complicated as say Skyrim, this really isn’t much of a defense. Skyrim actually simulated the daily routines of over a hundred different non-player characters; it could have been simulating markets in the background as well—in fact, it could have simply had those same non-player characters buy and sell goods with each other in a double-auction market that would automatically generate the prices that players face.

The more important reason, I think, is that game designers have a paralyzing fear of arbitrage.

I find it particularly aggravating how frequently games will set it up so that the price at which you buy and the price at which you sell are constrained so that the buying price is always higher, often as much as twice as high. This is not at all how markets work in the real world; frankly it’s only even close to true for goods like cars that rapidly depreciate. It make senses that a given merchant will not sell you a good for less than what they would pay to buy it from you; but that only requires each individual merchant to have a well-defined willingness-to-pay and willingness-to-accept. It certainly does not require the arbitrary constraint that you can never sell something for more than what you bought it for.

In fact, I would probably even allow players who specialize in social skills to short-change and bamboozle merchants for profit, as this is absolutely something that happens in the real world, and was likely especially common under the very low levels of literacy and numeracy that prevailed in the Middle Ages.

To many game designers (and gamers), the ability to buy a good in one place, travel to another place, and sell that good for a higher price seems like cheating. But this practice is call being a merchant. That is literally what the entire retail industry does. The rules of your game should allow you to profit from activities that are in fact genuinely profitable real economic services in the real world.

I remember a similar complaint being raised against Skyrim shortly after its release, that one could acquire a pickaxe, collect iron ore, smelt it into steel, forge weapons out of it, and then sell the weapons for a sizeable profit. To some people, this sounded like cheating. To me, it sounds like being a blacksmith. This is especially true because Skyrim’s skill system allowed you to improve the quality of your smithed items over time, just like learning a trade through practice (though it ramped up too fast, as it didn’t take long to make yourself clearly the best blacksmith in all of Skyrim). Frankly, this makes far more sense than being able to acquire gold by adventuring through the countryside and slaughtering monsters or collecting lost items from caves. Blacksmiths were a large part of the medieval economy; spelunking adventurers were not. Indeed, it bothers me that there weren’t more opportunities like this; you couldn’t make your wealth by being a farmer, a vintner, or a carpenter, for instance.

Even if you managed to pull off pure arbitrage, providing no real services, such as by buying and selling between two merchants in the same town, or the same merchant on two consecutive days, that is also a highly profitable industry. Most of our financial system is built around it, frankly. If you manage to make your wealth selling wheat futures instead of slaying dragons, I say more power to you. After all, there were an awful lot of wheat-future traders in the Middle Ages, and to my knowledge no actually successful dragon-slayers.

Of course, if your game is about slaying dragons, it should include some slaying of dragons. And if you really don’t care about making a realistic market in your game, so be it. But I think that more realistic markets could actually offer a great deal of richness and immersion into a world without greatly increasing the difficulty or complexity of the game. A world where prices change in response to the events of the story just feels more real, more alive.

The ability to profit without violence might actually draw whole new modes of play to the game (as has indeed occurred with Skyrim, where a small but significant proportion of players have chosen to live out peaceful lives as traders or blacksmiths). I would also enrich the experience of more conventional players and helping them recover from setbacks (if the only way to make money is to fight monsters and you keep getting killed by monsters, there isn’t much you can do; but if you have the option of working as a trader or a carpenter for awhile, you could save up for better equipment and try the fighting later).

And hey, game designers: If any of you are having trouble figuring out how to implement such a thing, my consulting fees are quite affordable.

Reasonableness and public goods games

Apr 1 JDN 2458210

There’s a very common economics experiment called a public goods game, often used to study cooperation and altruistic behavior. I’m actually planning on running a variant of such an experiment for my second-year paper.

The game is quite simple, which is part of why it is used so frequently: You are placed into a group of people (usually about four), and given a little bit of money (say $10). Then you are offered a choice: You can keep the money, or you can donate some of it to a group fund. Money in the group fund will be multiplied by some factor (usually about two) and then redistributed evenly to everyone in the group. So for example if you donate $5, that will become $10, split four ways, so you’ll get back $2.50.

Donating more to the group will benefit everyone else, but at a cost to yourself. The game is usually set up so that the best outcome for everyone is if everyone donates the maximum amount, but the best outcome for you, holding everyone else’s choices constant, is to donate nothing and keep it all.

Yet it is a very robust finding that most people do neither of those things. There’s still a good deal of uncertainty surrounding what motivates people to donate what they do, but certain patterns that have emerged:

  1. Most people donate something, but hardly anyone donates everything.
  2. Increasing the multiplier tends to smoothly increase how much people donate.
  3. The number of people in the group isn’t very important, though very small groups (e.g. 2) behave differently from very large groups (e.g. 50).
  4. Letting people talk to each other tends to increase the rate of donations.
  5. Repetition of the game, or experience from previous games, tends to result in decreasing donation over time.
  6. Economists donate less than other people.

Number 6 is unfortunate, but easy to explain: Indoctrination into game theory and neoclassical economics has taught economists that selfish behavior is efficient and optimal, so they behave selfishly.

Number 3 is also fairly easy to explain: Very small groups allow opportunities for punishment and coordination that don’t exist in large groups. Think about how you would respond when faced with 2 defectors in a group of 4 as opposed to 10 defectors in a group of 50. You could punish the 2 by giving less next round; but punishing the 10 would end up punishing 40 others who had contributed like they were supposed to.

Number 4 is a very interesting finding. Game theory says that communication shouldn’t matter, because there is a unique Nash equilibrium: Donate nothing. All the promises in the world can’t change what is the optimal response in the game. But in fact, human beings don’t like to break their promises, and so when you get a bunch of people together and they all agree to donate, most of them will carry through on that agreement most of the time.

Number 5 is on the frontier of research right now. There are various theoretical accounts for why it might occur, but none of the models proposed so far have much predictive power.

But my focus today will be on findings 1 and 2.

If you’re not familiar with the underlying game theory, finding 2 may seem obvious to you: Well, of course if you increase the payoff for donating, people will donate more! It’s precisely that sense of obviousness which I am going to appeal to in a moment.

In fact, the game theory makes a very sharp prediction: For N players, if the multiplier is less than N, you should always contribute nothing. Only if the multiplier becomes larger than N should you donate—and at that point you should donate everything. The game theory prediction is not a smooth increase; it’s all-or-nothing. The only time game theory predicts intermediate amounts is on the knife-edge at exactly equal to N, where each player would be indifferent between donating and not donating.

But it feels reasonable that increasing the multiplier should increase donation, doesn’t it? It’s a “safer bet” in some sense to donate $1 if the payoff to everyone is $3 and the payoff to yourself is $0.75 than if the payoff to everyone is $1.04 and the payoff to yourself is $0.26. The cost-benefit analysis comes out better: In the former case, you can gain up to $2 if everyone donates, but would only lose $0.25 if you donate alone; but in the latter case, you would only gain $0.04 if everyone donates, and would lose $0.74 if you donate alone.

I think this notion of “reasonableness” is a deep principle that underlies a great deal of human thought. This is something that is sorely lacking from artificial intelligence: The same AI that tells you the precise width of the English Channel to the nearest foot may also tell you that the Earth is 14 feet in diameter, because the former was in its database and the latter wasn’t. Yes, WATSON may have won on Jeopardy, but it (he?) also made a nonsensical response to the Final Jeopardy question.

Human beings like to “sanity-check” our results against prior knowledge, making sure that everything fits together. And, of particular note for public goods games, human beings like to “hedge our bets”; we don’t like to over-commit to a single belief in the face of uncertainty.

I think this is what best explains findings 1 and 2. We don’t donate everything, because that requires committing totally to the belief that contributing is always better. We also don’t donate nothing, because that requires committing totally to the belief that contributing is always worse.

And of course we donate more as the payoffs to donating more increase; that also just seems reasonable. If something is better, you do more of it!

These choices could be modeled formally by assigning some sort of probability distribution over other’s choices, but in a rather unconventional way. We can’t simply assume that other people will randomly choose some decision and then optimize accordingly—that just gives you back the game theory prediction. We have to assume that our behavior and the behavior of others is in some sense correlated; if we decide to donate, we reason that others are more likely to donate as well.

Stated like that, this sounds irrational; some economists have taken to calling it “magical thinking”. Yet, as I always like to point out to such economists: On average, people who do that make more money in the games. Economists playing other economists always make very little money in these games, because they turn on each other immediately. So who is “irrational” now?

Indeed, if you ask people to predict how others will behave in these games, they generally do better than the game theory prediction: They say, correctly, that some people will give nothing, most will give something, and hardly any will give everything. The same “reasonableness” that they use to motivate their own decisions, they also accurately apply to forecasting the decisions of others.

Of course, to say that something is “reasonable” may be ultimately to say that it conforms to our heuristics well. To really have a theory, I need to specify exactly what those heuristics are.

“Don’t put all your eggs in one basket” seems to be one, but it’s probably not the only one that matters; my guess is that there are circumstances in which people would actually choose all-or-nothing, like if we said that the multiplier was 0.5 (so everyone giving to the group would make everyone worse off) or 10 (so that giving to the group makes you and everyone else way better off).

“Higher payoffs are better” is probably one as well, but precisely formulating that is actually surprisingly difficult. Higher payoffs for you? For the group? Conditional on what? Do you hold others’ behavior constant, or assume it is somehow affected by your own choices?

And of course, the theory wouldn’t be much good if it only worked on public goods games (though even that would be a substantial advance at this point). We want a theory that explains a broad class of human behavior; we can start with simple economics experiments, but ultimately we want to extend it to real-world choices.