————Edward Castronova，《Synthic Worlds：The Business and Culture of Online Games》
让我们在称之为“World of Flarks”的伪MMO（2013年秋）中进一步运用这个例子。所谓劳动力是指在工作的人数。根据怪的等级，我可以猜到劳动力资本（A和K）的一般等级。假设这些价值是固定的，那么我们可以任意改变其他变量以控制Vf，即像物品掉落率、怪的重刷率、怪的难度系数和怪的固定成本等这类东西。
《World of Flarks》：
虚弱的Flinkar（Flinkar the Weakling）：
位置：失败者森林（Forest of Losers）（世界刷出）
恶魔龙小小（Dinky the Diabolical Dinosaur）
Vf = ((击杀率) x (掉落率) x (宝剑价值)) – ((击杀率) x (固定成本))
0.5g = (3 x 掉落率 x 10g) – 3g
3.5g = 30g x 掉落率
0.117 = 掉落率
如果你认为本文的话题很有意思，不妨去读读我刚才引文出处的那本书《Synthetic Worlds: the business and culture of online games》。该书对游戏中的经济学解释得更加精辟清晰，确实值得所有人阅读。（本文为游戏邦/gamerboom.com编译，如需转载请联系：游戏邦）
Every System Designer Must Study Economics
by Mike Birkhead
How much experience should this monster give? What drop rate should we set on this item? How do we know two functionally distinct items are worth the same amount?
Economics is the study of choice under scarcity, and one of many ways to discuss player motivation is to view it through the lens of economics. This lens shows us that the player is constantly making choices: to play a game, to play YOUR game, to be a fighter instead of a wizard, or to take that +5 to slaying instead of that +4 to thinking. Her resources are limited, so how does she choose one over the other? Because one is more rewarding; because it makes her avatar stronger; because it enhances her status; because it makes her happy. All rewards can be expressed within economic terms, and by understanding the basics of economic theory you can answer important questions about your player’s reward system.
Players want to feel they have accomplished great things — i.e. her work product must be validated — and one way we do this is by rewarding her with Physical Capital (new gear, money, or potions), with Avatar Capital (new abilities and experience points), and with Human Goods (Fame, Story moments, or Achievements). When a system validates your work product (killing those hoplites) with rewards (red orbs) you feel good about your work; you feel your actions had purpose, and you want to keep going. You can even double the effect by adding a randomized element to the reward.
It is the system designer’s job to not only understand what drives accomplishment, but also to answer very important questions about their system: what are items worth, what drop rate should an item have, and what do the players spend their money on? The answers to all these questions comes from a good, strong understanding of the basics of Economics.
A Strong Foundation
You cannot build without a strong base, so before we analyze we must lay the foundation. One of the cornerstones of a sturdy foundation is a meaningful lexicon — something we struggle with in design, and is one of the benefits of borrowing from one that does (for now). The following is a short list of terms and their definitions.
Consumable Product — products that are destroyed after being used for the first time. Such as a health potion.
Dependable Product — products that persist after being used, but they depreciate in value over time. The quicker something depreciates in value the more it begins to act like a consumable.
Permeable Product — products that are never consumed, and also never depreciate in value over time. Hint: most items in a video game.
Physical Capital (K) — physical games objects of value to the player, which help the character overcome challenges in a more efficient manner. Deciding the importance of gear (and by extension it’s affect on the player’s production function) is going to drive the amount of enjoyment they get from receiving it.
Avatar Capital (A) — these are the abstract rewards we give the player. New skills and abilities. They have value, but they have no physical manifestation in the world. These are things that cannot be traded, but like Physical Capital, the impact on the player’s production function will drive their importance.
Human Capital (H) — the knowledge of our player is also a factor in the production function, and while we do not directly trade this to the player, we should always try and take into account the player’s growing knowledge and skills. A master player is going to produce at a much faster and more efficient rate than a novice. Take the example of God of War: you receive more orbs for destroying a stone’d monster (not something widely known), and you receive bonus orbs for maintaining long hit counts. These two bonuses could, if not handled well, drastically offset the production (number of orbs) of a master player.
Production Function (q) — in short, this is a function that expresses how much someone can produce given their current assets, skills, and resources with a certain amount of labor. For a game, this means how quickly they kill monsters, how quickly they solve puzzles, how easily they access new areas of the game, or how quickly they finish quests — all actions that grant them rewards.
Small Open Economy (SOE) — this is the market defined by trade among players of the game, if your game is multiplayer. This is in contrast to trade between players and NPC merchants, or even players and the “outside world” (ebay).
Global Market (GM) — the market defined by NPC Merchants. In most games NPC Merchants provide an infinite supply, they consume an infinite demand for any given item, and they are self contained so that trading within that market has no impact on either the player market or the NPC merchants.
A lot of the following discussion will use MMO’s as the example. Though they make perfect test cases for dissection, they are by no means the sole domain where this can be applied. God of War has an economy; Uncharted has an economy; Mortal Kombat has an economy. As long as the player is making choices with their time, and as long as you are giving them rewards, then you are dealing in the market of their time. You are trading with them. So I will attempt, while mindful of verbosity, to relate with as many examples as possible.
Production And Wages
Everything we now discuss derives from the basic premise that you can assign value to a commodity in the game. A sword has a value much like a skill has a value, and you can have meaningful discussions about the merits of choosing one over the other. For this to occur, however, you must overcome two major hurdles: what mechanics in the game assign value to something, and what do those values mean.
The former is simple, and if you have been paying attention we have already defined the answer: the Production Function.
The Production Function
To put it simply (though, in practice it is not) the production function is the interaction of three factors (resources, capital, and labor). But don’t take my word for it, what does a real economist have to say?
In synthetic worlds, output (q) is going to be some object—pieces of loot from a hunted monster, items that have been crafted, rewards from quests. This good is produced by the player, who expends her own time (L) to get it. Her ability to get the good depends on four other factors: her skills as a player, or human capital, H; her avatar’s skill levels or experience levels, or avatar capital, A; her avatar’s gear, or physical capital, K; and the number of monsters, crafting inputs, or quests provided by the world, or resources, R
-Edward Castronova, Synthic Worlds: The Business and Culture of Online Games
This definition gives us a function.
Product (q) = (Labor)(PhysicalCapital)(AvatarCapital)(HumanCapital)(Resources)
q = f(L,K,A,H,R)
Now, items that are produced have some value and can be sold for a price (p). The player’s wages (w) are now expressed in a new function.
w = p x f(L,K,A,H,R)
As any factor increases, so does the player’s ability to produce, and by extension her earned wages. If my gear (K) improves , my ability to kill monsters increases. If I know the secret weakness to every enemy (H), then I kill them quicker and easier. All things being equal between two players (same labor, L; same knowledge, H; same resources, R), if two players are able to earn the same wages, then it is safe to say that their K and A are equivalent, and it is this basic premise that allows us to compare value of items in a meaningful way.
The value of something –especially in the real world– is complicated. Something can have sentimental value or confer status, which overrides any kind of rational analysis. In a game, however, items and skills have limited value, besides serving the ultimate goal of increasing someone’s fun. We play games because they are fun. Progression to the secondary goal of beating a game is accomplished by working, and the speed of that is controlled by the production function.
So one could say that to maximize your production function is to maximize your fun.
But it is more than that. Production matters, because it lets us compare and contrast choice in a meaningful way — quite the opposite of saying, “gee, I just like this weapon more.” That’s not good enough. To a user, maybe, but not to a System Designer. You must know, because if you can’t judge the opportunity cost of two weapons, than neither can the player; moreover, if the player cannot judge, then you will leave them dissatisfied.
How To Use Production
Once we have the function we can begin to ask real questions about the game. A good question, and one that you should constantly be asking yourself: “What happens if the player cheats?”. Simple, think of cheating as unfairly maximizing any of the factors of production. When studying your system try and consider what happens when someone has infinite capital (insane gear), infinite resources (duplicating items), or infinite labor (automated scripts). If any of these situations throws the entire system out of balance, then you should probably restructure the system. That particular input steam might have too much influence on resources and production.
Another question you can ask, “what would players want more: Item A, Item B, or 400 experience points.” The short answer is the item that has the greatest impact on the player’s fun. The long answer returns us back to the Production Function. If we assume that maximizing the Production Function maximizes our fun, then the answer depends on the player’s current context. Item A, on paper, is superior to Item B, but it is the value to the player that matters. Contextually Item A is only a marginal upgrade, while item B is a major upgrade, so the player, judging his opportunity costs effectively, chooses item B, as it will have the greater impact on the player’s overall production capabilities. He might not see it those terms, but that is how it is expressed in the lexicon of economics.
Without the ability to break it down this way, you might miss the crucial point: He can only make that choice accurately–some might argue happily–if he is given the knowledge to compare and contrast his choices, and he can only gain this knowledge if the system teaches him, and lastly, but most importantly, the system cannot teach him if it is not expressly designed into the game by you — by the designer.
We can compare, but we have no value. So where do we start? The next step is to find your Ryu, your grunt. In Street Fighter everything was designed around Ryu fighting Guile. In God of War 2 everything was designed around the Skeletons. In Chains of Olympus it was the Hoplites. Every game has its Ryu – its base. Do not go randomly assigning values to everything. You see, when everything’s value is derived from the base character, then they are scalable factors of the base, so when the base changes you already know how to adjust everything else. It is a system adjusting in concert, as opposed to wild stabbing.
Understanding your production function and its control over value is good, but what’s more, once you have a strong understanding of the production level of your player(s), you can begin to calculate not only the value of objects, but also the rate they should enter (or exit) the system.
Calculating Drop Rates
Dropped items, experience points, and even gold pieces are Value (think “money”) entering the system. Your goal is to keep the money entering the system equal to the money leaving a system. Otherwise known as preventing inflation. This Value entering the market is like someone quickly turning on a faucet in a sink. Let’s call the rate of money coming into the system: Vf. This Value spirals around inside the market (sink) to various people (or just stays with the player), and eventually drains out of the market removing Value from the economy. Let’s call the total rate of Value coming out of the market as: Vd. Thus, you want the following equation to hold true:
Vf = Vd
In God of War, when I kill a monster it gives me Red Orbs (Vf). These orbs are Value entering the system. I accumulate Orbs over time, and then I open the menu and I spend these orbs to upgrade something (Vd). I have essentially traded on the Global Market, and in return I get to upgrade my Avatar Capital. This upgrade (my magic is more powerful) increases Kratos’s ability to kill, and in turn increases the rate of Vf. See how it’s all connected?
Let’s take this example further with a fake MMO we are going to call: “World of Flarks” (COMING FALL 2013). The labor force is the number of people on a server, and due to the level of the mob I can guess the general level of Capital (A and K) of the labor force. Assuming those values are fixed, then we are free to play with other variables in an effect to control our Vf. Things like the drop rate of the item, the spawn rate of the mob, the difficulty of the mob, and the Fixed Cost of the mob.
Let’s define some values, and a sample mob.
World of Flarks
Server Population: 2,000
Max Level: 20
Population at or above level 10: 500
Population between levels 9-12: 100
Sword of the Flarkmaster
Flinkar the Weakling
Location: Forest of Losers (World Spawn)
Quantity in Zone: 1
Spawn Rate: 5 Minutes
Mob Level: 10
Sword Drop Rate: 50%
Here we have Flinkar the Weakling, who has managed to acquire the Flarkmaster’s Sword. Oh Flinkar, you crafty little scamp you. He spawns in the world, so there are no fixed costs associated with killing him. He’s the only one of his kind in the game, and he spawns 12 times an hour. Since he is a low difficulty mob, player skill (H) is less of an issue. Therefore, I will assume that all players at (or above) level 10 can use this resource. Since there are 500 potential users that match this criteria I can assume that this resource is being Perfectly Consumed (he is killed and looted as soon as he spawns). Given this simple set up, I can determine the rate of value (Vf) entering the economy every hour.
Vf = (Kills Per Hours) x (Drop Rate) x (Sword Value)
60g = 12 x 0.5 x 10g
60g an hour is pretty high. Even given no information about our desired Vd, I think it’s safe to say that my economic goals are not being met. I have several options here. Since the value of the item and level of the mob are constant, I am left with changing the drop rate, adding fixed costs, or altering the mob spawn rate. Let’s try a different mob:
Dinky the Diabolical Dinosaur
Location: Flarkmaster’s Grove (Instanced, 5 Man Dungeon)
Quantity in Zone: Optional Boss (1)
Summoning Materials Cost: 1g
Average Dungeon Length: 1 hour
Mob Level: 10
Sword Drop Rate: X
0.5g / hour
This is a more complicated scenario. The mob is now located in a dungeon, he has a cost for summoning him that must be paid, and he’s a difficult mob to boot. Also, this time we are going to start with a desired Vf (0.5g / hour), and solve for our drop rate.
The first new wrinkle is that I need to determine how quickly people are going to be killing this mob. From looking at the world statistics I see that the there are 100 players between the levels of 9 and 12, which feels like a good range for people that would be running this dungeon. However, Dinky is a pretty tough –it does say diabolical– Dino who requires more skill and better gear. Only 60 of those 100 players have the required Capital (H, K, and A) to effectively take down Dinky.
This is a 5 man dungeon, so those 60 players are grouped into 12 groups; additionally, it is an Instanced dungeon, which means that those 12 groups can all be running this dungeon at the same time. This assumes, however, that all 60 of those people are playing all the time, and they are always perfectly grouped with each other. From the article “Alone Together” (http://is.gd/gcqWT) it was shown that players only spend about 30-40% of their time in groups, so for the sake of this we can assume that only 3 to 4 groups are running concurrently at any given moment. Given that this is an optional boss we can reduce it to 3.
The last consideration is the Fixed Cost. Regardless of whether Dinky drops that sweet sword, every group must pay a fee of 1g in order to summon him. With this final bit I can finally draw up the new equation:
Vf = ((Kill Rate) x (Drop Rate) x (Sword Value)) – ((Kill Rate) x (Fixed Cost))
0.5g = (3 x DropRate x 10g) – 3g
3.5g = 30g x DropRate
0.117 = Drop Rate
Given this current mob, this current labor force, and this desired faucet value, the desired drop rate for this item is around 12%. A simple case, but you can see the power of thinking like an economist. So far we have focused on money coming INTO a system, but what about money LEAVING a system?
Inflation Versus Deflation
Almost every action the player makes is some kind of inflationary act. They are constantly bringing money into the market, such as red orbs from killing monsters in God of War, or sweet loots dropping off Nefarion in WoW. Monsters do not work to create these items and resources, therefore it is some Value that is being created solely for the player, which is fine. Your job, now, is to find ways for money to exit the system. Though you may not think of it in these terms, things like “upgrade trees” are essentially designed to be deflationary actions for the player to take.
There are three effective means of removing money from an economy, and each of these has various degrees with which it can be applied to increase or decrease its effectiveness. The first method is by pushing trade onto the Global Market, the second is by using Taxes and the last is by creating social mobility through market Risk.
The most effective means of removing money from a game is to provide unique, high-use, consumable products on the global market, which will have minimal impact on the player’s production function — sounds a mouthful, but it’s simple to understand. Any time a player purchases something from the GM it is an opportunity to remove money from the SOE. The more often they do this (or the more expensive the product) the more money will be drained from the player economy. Since the GM has infinite supply, infinite demand, and the price is controlled by the designers, the price will not change regardless of how much the players consume, and the players can sell or buy as much as they want. Let’s return to our requirements. Why is it unique, why make it consumable, and what’s this about the production function?
Unique – By making the product unique it means that it is a product that is unavailable in the SOE. This drives trade onto the GM, and the price of the object can be adjusted as the GM (the game designer) sees fit.
Consumable — By making it a consumable product the players will have to keep returning to this market to drain money out. If the product provided is a dependable (or even worse a permeable), then no matter how deflationary the cost of the item, the gradual inflationary acts of the player will overcome the buying of this one item. Very expensive dependables are a great means to dump LARGE amounts of money out of the market very quickly (think mounts in WoW), but they are not effective means of keeping the market from inflating over the long term.
Production – The product provided on the GM must be something that does not impact the production function of the player in a major way. As we have discussed, the more effective I am at killing the more I produce. Therefore if the deflationary product provided on the GM makes me a more effective producer, then I am essentially increasing the inflation rate (and undoing the work of trying to deflate it!)
Well, this all sounds great, but not every item can be a consumable. What about dependables? What about permeables? Are we totally fucked? Thankfully, no. Our savoir comes from a pretty dirty word in modern society. The second half of all that is certain in life: taxes.
The second most effective (though sometimes unpopular) means of removing money from the market is to provide a desired service that charges the rich more than the poor. This is also known as “progressive taxation.” The classic example of this is repairing your armor in WoW. Whenever a monster hits you, your armor’s durability is reduced. If you die you also lose a large chunk of your armor durability. If the durability is reduced to zero you may no longer use this item. The only way to repair this gear is to go to an NPC merchant and pay them to repair it. The better quality the armor that you wear, the more expensive it is to repair. An interesting point is that at first glance this may have the appearance that these items are “dependable” and simply depreciating in value. This is incorrect. Since they are 100% effective up until the moment they break and when they are repaired they return to 100% effectiveness, these products have actually not depreciated. They are just as good as the day you bought them (or made them). These are actually permeable, but have a periodic usage tax (and you didn’t even realize it!)
Another method of removing money from the system is by providing Risk based ventures for people to spend their money on. A common problem in games, particularly in MMOs, is that once the rich acquire massive wealth they stay wealthy. They have nothing to spend their large amounts of money on, so their wealth gets dumped onto mules, or they buy out the entire auction house to corner the market. Imagine a system where I could buy stock in various commodities in a medieval world. I believe in the worth of the Kalimdor wheat, a risky bet, but I think it’s a growth market. The following day, however, a horde of dragons swoop in from the north and raze the countryside. Three things have happened here. One, money (possibly lots of money) has been taken from the market, as the trade in Kalimdor wheat plummets. Two, the killers have been brought into the market trade. I can gather some friends together, and we can try to kill the dragons before they do too much damage – possibly salvaging the price. Three, users are encouraged to pay attention to the state of the game on both the inside and the outside. Say the game provided a web-based means for me to check the current prices on the in-game commodities market. Even better, what if these dragons make it a regular thing to come swooping down and screwing with my wheat? This turns the Kalimdor wheat into a high risk, but high yield commodity.
I can keep going.
But I won’t, even though there is so much to say. Once you understand the importance of economic discussions, you can move onto new questions. How about adding a crafting system to your game. What purpose does it serve? Should the items be as good as drops? Economics got you back! These are posts in their own right, and maybe once I give my wrists a break I can tackle them.
If you have found this at all interesting, you owe it to yourself to read the following book: Synthetic Worlds: the business and culture of online games. It explains this better and clearer than I ever could, and it should be read by everyone.（source:flarkminator）