Ceasar's Mind

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Posts Tagged ‘economics

Games as Economies

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In a previous post, I wrote about how it’s impossible to price an object in a game according to a systematic formula, barring games of limited complexity, and objects that cover the same span (that is, there are just different multiples of the same vector). Instead I claimed at the time it was just arbitrary- that designers could set the prices to whatever they liked and that the game would always be fair so long as each player had equal opportunity. Thus, the designer’s job is really just to play with the prices until it produces the interplay he is looking for.

In another post, I wrote about how research in RTS games, and why spending resources in order to have the option to train new units can payoff. While upgrades obviously boost the strength of an army, research unlocks news units for a price, and that price is only worth paying if one can expect to use the unlocked units in such a way, that the utility of their use exceeds the initial cost of research. Thus, the price of research is also arbitrary.

Having since studied microeconomics, I’d like to revisit these topics.

An indifference curve is a line that shows combinations of goods among which a consumer is indifferent.

Economists call the phenomenon I just described the marginal rate of substitution or MRS for short. Formally, the MRS is defined as “the rate at which a person will give up good y for good x while remaining indifferent”. In other words, it’s the price at which you are willing to buy something using something else (ie, how much you are willing to shell out for a can of soda). What’s interesting about the MRS is that it changes- the more a person has of good x, the more one is willing to trade of good x for good y. Said another way, because billionaires have so much money, they don’t mind paying $5.00 for a hot dog.

This is a far more intuitive way of looking at things than trying to predict prices from the attributes of the game objects. In short, all one needs to understand now is that players will buy an object when the utility of a object exceeds its cost.

While the main point I wanted to convey has been made, I want to just put down some related ideas that don’t exactly deserve a post of their own but that I think are worth sharing.

-If you are familiar with Dominion, you may know MRS as “the Silver test”. (If you are not familiar with Dominion, all you need to know is that players regularly face the choice of buying cards with special effects or treasures, such as a Silver, which increase income.) That is, when making a non-trivial purchasing decision, one always has to consider if the object at hand is in fact better than a Silver. What I find most interesting about the Silver test is how many players completely fail to pick up this rule, instead being regularly mislead by the incorrect assumption that “things that cost more must be better”. Certainly changed a few paradigms of mine after noticing what was going on.

-Knowing when to buy what is the backbone of many games. In Dominion, playing cards is fairly trivial- but the decisions of which cards to buy each turn is often rather complex, and in the majority of cases, determines who wins. Likewise, in StarCraft, micro-ing units is fairly simple- but, again, the decisions of which units to buy and which tech to research is far more complex, and is far more important than any tactical feat. In short, your economics textbook may be more valuable than The Art of War.

Written by Ceasar Bautista

2011/08/27 at 19:39

Indifference Curves

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An indifference curve is a line that shows combinations of goods among which a consumer is indifferent. Since consumers always prefer more over less, a curve shifted to the top and right is preferable to a curve shifted left and down, but any point on any particular curve is equally preferable as any other point on that curve. (So, in this picture here, X is just as good as A which is just as good as B.)

The marginal rate of substitution (MRS) is the rate at which a person will give up good y (measured on the y axis) for good x (measured on the x axis) while remaining indifferent. The magnitude of the slope of an indifference curve measures the marginal rate of substitution. That is, if the indifference curve is steep, then the marginal rate of substitution is high and a person would be willing to give up a very large amount of y to obtain very little of x. If the curve is flat, the marginal rate of substitution is low. The person is willing to give up very little of y to obtain large quantities of x. Generally, there is a diminishing marginal rate of substitution, which means that people becomes more and more willing to give up large amounts of x for y when they have very little y.

For ordinary goods, we see curves that look like the one above. But sometimes the value of a good is influenced by another. For example, perfect substitutes will produce straight diagonal lines with slope -1: a pen from Walmart is equally preferable to the same pen from anywhere else. On the other hand, perfect complements on the other have L-shaped curves: a left shoe is worth nothing without the right, and two left shoes are worth nothing without two right shoes.

Predicting Consumer Choice

The best affordable choice is 1)on the budget line and 2) on the highest attainable indifference curve. This point is where marginal rate of substitution equals relative price. Changes in the price or utility of a good or a person’s income change the best affordable point.

Written by Ceasar Bautista

2010/11/14 at 17:28

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