It is not particularly difficult to identify the entities and the resources that comprise an economy, but it is harder to get a good perspective on the system as a whole. If you were to make graphs of the elements in your economy, what shapes would the graphs reveal? Is the amount of a given resource increasing over time? How does the distribution of resources change? Do resources tend to accumulate in the hands of a particular player, or does the system tend to spread them out? Understanding the structure of your economy will help you find the answers.
In the real world, people represent features of an economy with charts and figures (Figure 4.1). These graphs have a few interesting properties. At the small scale, their lines move chaotically, but at larger scales, patterns become visible. It is easy to see whether a line is going up or down in the long run and to identify good and bad periods. In other words, we can recognize and identify distinctive shapes and patterns from these types of charts.
Figure 4.1. Graph of the stock market crash leading to the Great Depression. Most movement is chaotic, but the crash is clearly visible.
We can draw similar charts displaying the fortunes of players in a game. As you will see, distinctive shapes and patterns emerge from the internal economy of a game. However, there is no one shape that identifies quality gameplay. What constitutes good gameplay depends on the goals you set for your game and the context that surrounds it. For example, in one game you might want the player to struggle for a long time before managing to come out on top (Figure 4.2). In another, you might aim for quick reversals in fortune and a much shorter play-through (Figure 4.3).
Figure 4.2. A long game in which the player triumphs after an extended struggle against a powerful opponent
Figure 4.3. A short game with quick reversals of fortune
The Shape of a Game of Chess
We can take the development of players’ fortunes in a game of chess as a basis for studying shapes in game economies. In chess, the important resources are the players’ pieces. Chess players (and computer chess programs) assign a point value to each piece depending on what kind it is. For example, in one system, pawns are worth one point, rooks five, and the queen nine. Adding up the value of all the pieces one player has on the board produces a number called material. Players use their pieces to maneuver on the board to gain strategic positions. Strategic advantage can be measured as an abstract resource in the game. Figure 4.4 depicts what might be the course of play between two players in a game of chess.
Figure 4.4. The course of a particular game of chess. The color of a line indicates the color of the player it refers to.
You can discover a few important patterns in this chart. To start with, the long-term trend of both players’ main resource (material) is downward. As play progresses, players will lose and sacrifice pieces. Gaining material is very difficult. In chess, the only way to gain a piece is to bring a pawn to the other side of the board to be promoted to another, stronger piece, which would lead to an increase of material. This is a rare event that usually initiates a dramatic change of fortune for the players. If we consider only the material, chess appears to be a battle of attrition: Players who can make their material last longest will probably come out on top.
Strategic advantage is more dynamic in the game; it is gained and lost over the course of play. Players use their material to gain strategic advantage or reduce the strategic advantage of their opponents. There is an indirect relationship between the different amounts of material the players have and their ability to gain strategic advantage: If a player has more material, then gaining strategic advantage becomes easier. In turn, strategic advantage might be leveraged to take more pieces of an opponent and reduce that player’s material. Sometimes it is possible to sacrifice one of your pieces to gain strategic advantage or to lure your opponent into losing strategic advantage.
A game of chess generally progresses through three different stages: the opening, the middle game, and the endgame. Each stage plays a particular role in the game and is analyzed differently. The opening usually consists of a sequence of prepared and well-studied moves. During the opening, players try to maneuver themselves into a position of advantage. The endgame starts when there are relatively few pieces left, and it becomes safer to involve the king in the game. The middle game falls somewhere between the opening and the endgame, but the boundaries between the stages are not clear. These three stages can also be identified from the economic analysis in Figure 4.4. During the opening, the number of pieces decreases only slowly, while both players build up strategic advantage. The middle game starts when players are exploiting their strategic advantage to take their opponents’ pieces; it is characterized by a sharper decline of material. During the endgame, the material stabilizes again as the players focus on their final attempts to push the strategic advantage to a win.
From Mechanics to Shapes
To produce a particular economic shape, you need to know what type of mechanical structures create what shapes. Fortunately, there is a direct relationship between shapes in a game’s economy and the structure of its mechanics. In the next sections, we discuss and illustrate the most important building blocks of economic shapes.
Negative Feedback Creates an Equilibrium
Negative feedback (as discussed in Chapter 3, “Complex Systems and the Structure of Emergence”) is used to create stability in dynamic systems. Negative feedback makes a system resistant to changes: The temperature of your refrigerator is kept constant even if the temperature outside the refrigerator changes. The point at which the system stabilizes is called the equilibrium. Figure 4.5 displays the effects of negative feedback.
Figure 4.5. The effect of negative feedback
The simplest shape of the equilibrium is a straight horizontal line, but some systems might have different equilibriums. An equilibrium might change steadily over time or be periodical (Figure 4.6). Changing equilibriums requires a dynamic factor that changes more or less independently of the negative feedback mechanism. The outside temperature throughout the year is an example of a periodical equilibrium that is caused by the periodic waxing and waning of the available hours of daylight and the relative strength of the sun.
Figure 4.6. Negative feedback on changing equilibriums. On the left, a rising equilibrium; on the right, a periodically changing equilibrium.
Positive Feedback Creates an Arms Race
Positive feedback creates an exponential curve (Figure 4.7). Collecting interest on your savings account is a classic example of such a curve. If the interest is the only source of money going into your savings account, the money will spiral upward, gaining speed as the accumulated sum creates more and more interest over time. In games, this type of positive feedback is often used to create an arms race between multiple players. A good example is the harvesting of raw materials in StarCraft (or similar constructions in many other RTS games). In StarCraft, you can spend 50 minerals to build a mining unit (called an SCV, for Space Construction Vehicle) that can be used to collect new minerals. If StarCraft players set aside a certain portion of their mineral income to build new SCVs, they get the same curve as money in a savings account.
Figure 4.7. Positive feedback creates exponential curves.
Obviously, StarCraft players do not spend their resources only on SCV units. They also need to spend resources to build military units, to expand their bases, and to develop new technology. However, the economic growth potential of a base in StarCraft is vital in the long run. Many players build up their defenses first and harvest many resources before pushing to destroy their enemy with a superior capacity to produce military units.
One of the most useful applications of positive feedback in games is that it can be used to make players win quickly once a critical difference is created. As should become clear from Figure 4.7, positive feedback works to amplify small differences: The difference between the balances of two bank accounts with equal interest rates but different initial deposits will only grow over time. This effect of positive feedback can be used to drive a game toward a conclusion after the critical difference has been made. After all, nobody likes to keep playing for long once it has become clear who will win the game.
Long-Term Investments vs. Short-Term Gains
If StarCraft were a race to collect as many minerals as possible without any other considerations, would the best strategy be to build a new SCV unit every time you’ve collected enough minerals? No, not exactly. If you keep spending all your income on new SCVs, you would never save any minerals, which is what you need to win the game. To collect minerals, at some point you need to stop producing SCVs and start stockpiling. The best moment to do this depends on the goals and the constraints of the game—and what the other players do. If the goal is to accumulate the biggest pile of minerals in a limited amount of time or to accumulate a specific number of minerals as quickly as possible, there is an ideal number of SCV units you should produce.
To understand this effect, look at Figure 4.8. It shows that as long as you’re investing in new SCVs, your minerals do not accumulate. However, as soon as you stop investing, the minerals increase at a steady pace. This pace depends on the number of SCV units you have. The more you have, the faster your minerals will increase. The longer you keep investing, the later you will start accumulating minerals, but you will eventually catch up and overtake anybody who started accumulating before you did. Depending on the target goal, one of those lines is the most effective.
Figure 4.8. A race of accumulation
It is a good thing StarCraft is about more than just collecting minerals. Spending all your minerals on SCV units is a poor strategy because eventually you will be attacked. You have to balance your long-term goals with short-term requirements such as the protection of your base. In addition, some players favor a tactic in which they build up an offensive force quickly in a gambit to overwhelm their opponent before they can build up their defenses—the “tank rush,” which was first made famous in Command & Conquer: Red Alert. On some maps, initial access to resources is limited, and you must move around the map quickly to consolidate your access to future resources. Investing in SCV units is a good strategy in the long run, but it requires you take some risk in the beginning, possibly giving up on quick military gains via the tank rush.
Feedback Based on Relative Scores
During Marc LeBlanc’s talk on feedback mechanisms in games at the Game Developers Conference in 1999, he described two alternate versions of basketball. In “negative feedback basketball,” for every five points that the leading team is ahead, the trailing team is allowed to field one extra player. In “positive feedback basketball,” this effect is reversed: The leading team is allowed to field one extra player for every five points they are ahead. The effects of using the difference between two players to create a feedback mechanism are slightly different from using absolute values to feed this mechanism: The effects of the feedback mechanisms affect the difference between the players, not their absolute resources. This can produce some counterintuitive effects. The economic chart of negative feedback basketball, for example, shows the lead of the better team settling on a stable distance at which the lack of the skill of the trailing team is offset by the extra players they can field (Figure 4.9).
Figure 4.9. Score graph of negative feedback basketball
When two teams are playing positive feedback basketball, the differences in skills are aggravated. When one side is better than the other, this will result in a very one-sided match. However, when both sides are closely matched, a different pattern emerges: The game will probably remain close, until one side manages to take a decisive lead after which the match becomes very one-sided again. In this latter case, a small difference in skill, an extra effort, or sheer luck can become the decisive factor.
In Chapter 6, we explore the gameplay effects of positive and negative feedback on basketball in more detail.