Free to play business model versus traditional retail purchase; how it is more profitable to have item shops

There has been a large and growing movement in the video game industry towards the free to play business model. World of Warcraft, Team Fortress 2, World of Tanks, and League of Legends are a few prime examples. To compensate for being free to play, firms run in-game item shops that charge for additional gameplay content or provide services such as making the grind easier. The question for the economist is then, why are firms acting in such a manner?

Like many things, the answer is not so straight forward. There are multiple reasons all acting in conjunction, but let’s first examine this with some microeconomics. Below is your traditional monopoly and profit maximization. I use a monopoly model because a lot of games are monopolies. You may have substitutes in the form of other games in a genre, but realistically speaking, Halo is Halo. Marginal cost is constant for simplicity, but also because software (video games included) really don’t have a marginal cost. The cost of letting someone download a copy of your game is virtually negligible. Profits below ignore fixed costs.

As we can see, there is a fair amount of dead weight loss. Monopolies restrict output in order to raise price which means not everyone is able to play the game. By comparison, the free to play model has no dead weight loss although quality may suffer which is something that will be discussed later.

Price in this model is set at marginal cost. In the case of games, the marginal cost is basically zero, hence, free to play. Profits for the firm is then determined by the giant orange triangle. Here it gets a little more complicated. Profits made by the firm is determined by how well they can extract consumer surplus through price discrimination via item shops. In terms of item shops, this is the revenue of producing item shop content minus the cost of producing it and the marginal cost of production (because the firm did not cover that cost by selling on quantity).

The reason for why there is such a large range in the pricing for item shops is not because making premium content such as Pulsefire Ezreal is very expensive (it probably does cost a bit more than the usual stuff), but because it’s targeted at people who have high consumer surplus. For all the software developers out there, do be careful about what you market to your consumers. Eve Online’s monocles are still a laughing stock among gamers.

As we can see, if the firm can minimize the cost of item shops, there is much potential profits to have. Furthermore, the lower the marginal cost, the more effective free to play is in terms of producing profits.

There are other factors outside of the graphical models above. For instance, firms have a definite incentive to cheat on item shops by simply restricting content already in-game. Similarly, the restriction of content can reduce the quality of the product (i.e. Runescape). Information-wise, a free to play model lets consumers sample the product. If we think of information as an additional cost for the consumer, the free to play model basically removes it altogether. Demos exist for this purpose, but they’re not as effective having the full game.

Sim City Music

Long before I even knew the definition of economics, I was an avid gamer. While I don’t play Sim City regularly anymore, I still have nostalgia over its music. Here are two of my favorites, and I listen to them on the occasion.

Equilibrium in Video Games

Most competitive games reach an equilibrium stage that’s often called the metagame. An important distinct to note is that while gamers can reach an equilibrium, it is not necessary the solution to the game, rather, the metagame is the solution to what everyone currently understands and know in the game’s player base.

There are also games that do not have an equilibrium. For instance, there is no equilibrium strategy to play in Rock, Paper, Scissors. By comparison, marines and medics is often considered an equilibrium strategy for playing Terran in Starcraft. The player can choose to build purely medics, purely marines, or a mixture of both. Their best decision tends to be to build a mixture. In game theory, this is called the dominant strategy because compared to the alternative strategies, the dominant strategy is always better.

Practically speaking, it is very difficult to design a game that has no equilibria. It is also very difficult to build complex games with an equilibrium in mind. Most games have evolved outside of their creator’s predictions; it’s why games tend to be imbalanced until substantial play testing has occurred. A game designer can try to influence the equilibrium, but it’s unlikely that he’ll predict what ultimately will be done in a competitive environment. The collective gaming community has proven to be far superior in finding the best strategies. Afterall, I doubt that the original designers of Starcraft even considered building supply depots in front of their bunkers.

From a game theory perspective, games that have no equilibrium have no solutions. To an extent, games, in particular, RTS, that do not have very strong equilibrium strategies tend to be casual. The lack of equilibrium strategies make it difficult to win, at least in terms of strategic thinking because there are no “solutions” that can be played by higher skilled players. In other words, there is no hierarchy; no ladder or ranking system because you cannot be better than another player. When strategic play becomes less important, the next most important factor is the player’s performance which is reflexes, mental state, micro, and other factors that can be improved by practice. It may not matter what you play in Rock, Paper, Scissors, but you can at least intimidate him with mind games which I suppose could give you the winning edge.

There is another form of competitive gaming that should be noted. There are games that are won by strategies which we can discuss using the tools of game theory, however, there are also games that rely on performance. Games like Soccer and Counter-Strike have some degrees of metagame, but compared to a RTS, they tend to be more dependent on player performance (ie. how fast you can headshot someone with the AK as opposed to choosing between building more troops versus expanding). Competitive gaming exists outside of game theory solutions, but those tend to be games of performance rather than strategy.

Would a rational actor ever build a weapon that would destroy both himself and his opponent?

If we take it at face value, it would seem that it’s never a good idea to make something that would harm you and your opponent. Afterall, despite man’s impeccable’s record for finding new ways of killing, he still values self preservation fairly highly. Even in scenarios such as suicide bombing, the bomber is usually convinced that he’s dying for a good cause or that there is an afterlife which is worth blowing himself up for.

So here’s a basic sequential game. The actor, row, goes first and the actor, column, goes second. Row’s nuclear weapon does not harm himself while column’s nuclear weapon is self destructive. A utility of 1 means survival. A utility of 0 means destruction.

The Nash Equilibrium for this game is 1, 1. If row decides to Nuke, column can punish row by nuking as well. To column, it makes no difference. Once row has launched his missiles, he is as good as dead. Because row knows that if he nukes, column will punish, his best strategy is to not nuke. Column’s best decision is then to not nuke.

So the above scenario is still fairly abstract. There are a few things to note. The game does not predict what will happen in the future. It may well be that both parties will decide to develop even more destructive and effective weapons, or it could be that both parties will try to negotiate disarmament. I cannot forecast how the game will change, but I can say that under the circumstances in the above game, it is entirely rational to have a weapon that’s self destructive.

The key is that column does not build the self destructive weapon because he wants everybody to die. In fact, everybody dying is equally as bad as having row nuke for column. He builds the weapon because row will react differently if he knows that he cannot nuke with impunity. Having the weapon is better than having no weapon. Having no weapon is effectively declaring to row that you will always play a no nuke strategy in which case column’s fate depends on whether or not row feels like destroying column. If we modify row’s utility value from deciding to nuke to be 1.1 so that it’s higher than 1, row still does not have an incentive deviate if it knows that column will nuke if it does so. We can interpret the 1.1 utility as row’s increased utility from not having an opponent. Now if column is forced to play a not nuke strategy because it does not have the weapon available, then row’s best decision would be to nuke. Column has a clear incentive to have the weapon.

Economist at Valve: a blog to follow

A friend linked this to me.

I’ve written a small bit about Valve and their digital distribution system, Steam, but it’s from an outside perspective and admittedly, an amateurish one at that. A blog on one of my favorite video game developers combined with a professional economist’s analysis with what would seem to be unfettered access to all the data has got my attention.

The effects of theft or destruction of goods on a monopoly

Firms are always complaining about theft and how there are enormous economic impacts associated with it. From the recent Stop Online Piracy Act (SOPA) and the Protect IP Act (PIPA), it is clear that the politicians have been paying a lot of attention to the issue. For an economist, there’s a lot of questions to be had here. Below is a basic profit maximization model modified to accommodate destruction or theft of goods.

Before I begin my analysis, I must make clear that the model assumes that α, the percentage of goods received by the firm, is a completely independent variable, meaning it is not affected by other variables. One could account for the obvious notion that price and the willingness of people to steal (and conversely the amount of goods paid for) by having α be a function of price. However, that adds a fair amount of math, and so we’ll leave that out. Furthermore, the demand function is linear.

If we look at where MC is low, the effects of destruction and theft on quantity produced is minimal. It makes intuitive sense. If it’s cheap to produce a good, then who cares if half of what you make gets destroyed; just make more! So at a MC of 2, even when the firm only receives half of what it makes, the quantity produced is barely affected with a change of only 1.

Now when MC gets high, the firm produces a fair amount less. But when the firm receives only half of what it makes along with a high MC, there is another massive reduction in quantity produced. From this relationship, it seems that if government desires to benefit society, they should focus on removing theft, piracy, or destruction of goods on firms with high MC than firms with low MC.

Another interesting note we should examine is how profits have changed for the firm. Remember how the firm with low MC produced nearly the same amount despite receiving payment for only half of its goods? Its profits have fallen by about 50%. As we can see, firms have a huge incentive to complain about theft. In the case of firms with low MCs, theft hurts them more than it hurts society.

Software firms fit the model very well. For the most part, software tends to be monopolistic and in many cases, full blown monopoly. Their MC is also very low. If we take the above model to be true, then it’s no wonder that a lot of the lobbying has been about online piracy. Software firms have a lot to lose in profits.

Why massed marines beat massed zerglings

There is a very common phenomenon in RTS games that’s often forgotten: massed ranged units tend to beat massed melee units. Even more so, good massed ranged units will beat inferior massed ranged units. The benefit from massing ranged units is their ability to lower the firepower of opposing units before they can inflict harm. For instance, a pair of zerglings will beat a marine, but 24 zerglings will lose to 12 marines.

During my time as a volunteer balance developer for a mod, I had to understand and apply core game mechanics. Below is an instrument with a very basic model that I call the Effective Range Firepower (ERF). It measures how well a cluster of units perform. We can interpret X as simply the number of units. Alpha would be a measure of well the unit performs when massed. In Starcraft, this is the unit’s attack range. In a more complex game such as Company of Heroes, this is the unit’s attack range, accuracy, cooldown/reload modifiers, etc.

There are two assumptions that the model makes. 1) There is no limit to the number of units aggregated. This is generally true until your units start physically blocking one another from attacking. If that’s the case, their ERF simply comes to a plateau. 2) There are no stacking penalties. In certain games, units actually debuff each other.

In Company of Heroes Opposing Fronts, there is actually an upgrade for the Panzer Elite faction that makes aggregating units even better. Although it’s only speculations, the fact that the design team behind that title was inexperienced leads me to believe that whoever designed that ability didn’t have a good understanding of how massed ranged units function. Subsequently, there was a huge host of problems associated with the blobbing of Panzer Grenadiers who inherently already had pretty good ERF.

When balancing these effects, we have to take many other variables into account. Generally speaking, we ask ourselves how easy is it for players to pull off unit aggregations. We don’t want to make the unit so expensive that only the best players can make use of the unit. At the same time, if we price the unit so low so that even the weakest players can use the unit, we risk having skilled players maximizing the unit’s ERF. In the worst case scenarios, we employ hard caps which effectively stops the unit’s ERF at a certain value. My favorite solutions tend to be the introduction of abilities or other units that punish unit aggregations. These things can range from the ensnare ability on the queen from Starcraft, or something like the machine gun unit in Company of Heroes that gets more accurate as the enemy gets more units together. These creative solutions have their own dangers of introducing even more variables to a game, but the risk is often worth the freedom that it will ultimately grant players.