What determines the price of games?
This article will be my first of many attempts to explain the behavior of Steam's markets and community. The problem tackled today is one of game pricing. Have you ever wondered how the prices of games form? Surely, each game has its own set of characteristics and its own set of consumers forming demand, however more general trends can be identified. If you have heard some of Gabe Newell's speeches you will know he frequently mentions interesting statistics that Steam has established through research. For example, if a game is made freetoplay, on average its active player count increases tenfold and income from related products/services triples, when compared to a similar game with a normal price arrangement. This is then a nice deal, as the marginal cost of distributing each next copy of a game is bubcus these days.
The goal of this article is to find a characteristic that determines the prices of games, specifically multiplayer games. Now, you yourself can form some ideas of what quantifiable characteristics are worth considering and feel free to share them in the comments. I will give one good example here.
Main bit
One of the key features of a multiplayer game is in fact the players playing it. A larger amount of active players and more diverse community greatly increases the perceived value of a multiplayer game. In addition, it reassures the consumer that the game is well received and frequently enjoyed by others. A greater variety of servers, more mods and community content is also an added bonus.
My hypothesis is therefore, that the amount of active players (and implied community size) of a given game positively affects the current price of the game.
To investigate this relation, I will use a sample of 15 popular Steam games and look at their prices, as well as amount of active players at the time of observation (September 15th round 19:00 Amsterdam time). The initial part of the analysis will be simple enough  firstly, I calculate the price per each thousand of active players. This gives a quick estimate for how much each game "charges" for the benefit of having more playmates. An average of 2,1 Eur/1k active players is estimated. This lets us form the last column, which just compares each games ratio to the average. Here we can form a rough conclusion of whether a game is "overpriced" or "underpriced" in terms of how much you pay for joining a community.
So what can we learn from this? Well. The price/active players ratio varies quite a bit over these games. Ark costs 28 Eur and has a whopping 38k active players, so the resulting ratio is only 70 cents per each 1000 active players. One must consider, however that Ark is a beta, which explains a lower price to enter the community.
Age of Empires, on the other hand has a modest player count of 3,6 thousand, but costs a fortune  20 Eur for a game that is pretty much from the 90's... The explanation here is that AoE2 has a loyal consumer base that is willing to pay high premiums.
So there is a little bit we can gather here. But now let's do something more fancy. Lets plot the "active player count" on the X axis and retail price on the Y axis. Given the hypothesis, I am hoping to see a nice neat line of dots. What I am expecting however, is nothing like that, as the amount of active players is certainly not the only variable contributing to the price. Not to mention, each game has its own unique features that certainly overstep any ceteris paribus assumptions that are necessary for seeing the exact isolated effect on the price.
Well. Not a very neat line, if you dont count the black trendline that I drew. So what do we see here..?
Well, first of all, the R^2 value suggests that, in this sample, 68% of the variation in price does fit the trendline. This is not a very reliable statistic for deciding the models legitimacy, but for simplicity, we will take what we can.
Assuming there is some truth to this trendline, we have estimated that a multiplayer game with no active players is expected to cost 13 Eur. However, with each next 1000 of active players, the price consumers are willing to pay increases by around 0,8 Eur.
Here is a neat table with the results.
Interesting right? Well, lets go another step. Intuition surely tells us that the size of the community only matters to a certain point. In other words, if there are 2 other players, you will probably not want to play that much. If there were 1000, you would be more interested. At 2000 you would be pretty happy and get some community benefits, but at some point you would already have enough potential friends, foes, servers, mods and forums to go around, so the size of the community would not matter that much anymore.
So how do we test his? Well, here is what I propose. Lets quickly make another model, only now lets use the 10 least popular games from the list. The "critical community size" estimate will then be 25k active players. After 25k, we assume that the critical size is reached and adding more players does not significantly affect the games price. We will estimate the same model for games that have a smaller active player count.
Here is the picture for the small multiplayer games.
The line seems to look good, however, one must notice that less popular games are priced quite similarly, as well as run discounts, with 19,99 Eur being a popular number.
But what do the numbers say?
Well, first of all, the R^2 isnt excellent  50% of deviation fits the model. However, we can see that less popular games have a lower expected price with no players playing it  only 10,5 Eur, compared to 13, when 5 more popular games were included. This tells us that the "constant premium" gamers are willing to pay is lower for untested and unpopular games. Makes sense right?
The marginal price increase per active player count, however is much higher. People are willing to pay 1,1 Eur for each next 1000 players, compared to 0,8 when all games were considered. So the marginal benefit of extra players is higher for games that are less popular. Also corresponds with our intuition.
Now. Here is a little thing I have to admit. Ten games is far too little data and two Excel regressions are far too little analysis to prove these relations, however we can certainly form some understanding from this.
What have we learned?
The analysis suggests that there is reason to consider active player count as one of the variables forming the price of multiplayer games. Moreover, the marginal effect is strictly positive for games with very small communities and decreases as the community grows larger. Crucially, however this analysis is far from robust and considers a narrow set of games. The differences in contribution of each active player to the communities value should also be considered, as additional players are crucial for some games and complementary for others. A cost of congestion, if active player count is too high or poorly managed should also be considered. In addition, further analysis should be done on a greater sample and with more explanatory variables, to form a more precise model.
Hope you enjoyed the article and learned a little bit about economic reasoning and the video game industry. Leave a comment with your thoughts!

Good games attract more players and players are willing to pay more for them; thus they attain higher popularity and are able to charge more.

Its a valid point. That is certainly a factor assuming consumers tend to have a shared perception of "a good game".
I would say, however that it does not explain why developers would "be able to charge" more for the first 25k players and then increasingly less for the following amounts. If its "a supreme game", demand should increase at the same rate as popularity.
What's more, if you actually do the same model for copies sold, you will find that, as the developers sell a great amount of copies (in 100's of thousands), the price tends to decrease (presumably as they start running out of "high interest consumers" and look to sell to those who know about the game purely due to popularity). Frictional Games recent free Amnesia download stunt is an interesting example, I guess.
So its not always the case that popularity of the product itself lets you charge more. It seems to me that having a valuable and inviting community is worth much more.