Play Time

Play Time: Principles of MMORPG Asymmetric Trade

• Jeremy Kelly1
• www.anthemion.org
• support@anthemion.org

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Abstract

The popularity of eBaying — the real-world sale of game goods — raises many questions about the nature of MMORPG play. This work translates the conclusions of an earlier work into simple microeconomic models that reveal possible effects of such trade. It shows how wages and game preferences determine the player’s role in the market for game goods, and it argues that — in a strictly economic sense — these exchanges benefit players, increase subscriber numbers, and increase MMORPG developer revenue.

Contents

• 1 Introduction
• 2 Player trade with complete rivalry
• 2.1 Assumptions
• 2.2 Constructing the model
• 2.2.1 Trade gains
• 2.2.2 Individual demand
• 2.2.3 Individual supply
• 2.2.3.1 First supply phase
• 2.2.3.2 Second supply phase
• 2.3 Conclusions
• 2.3.1 Trade decisions
• 2.3.2 Player population
• 2.3.3 Play time
• 3 Fiat sale
• 3.1 Fiat sale and player competition
• 3.2 Effect of fiat sale
• 3.3 The scarcity of fiat sale
• 4 Player trade with non-rivalry
• 4.1 Assumptions
• 4.2 Constructing the model
• 4.3 Conclusions
• 5 Further research

1 Introduction

Asymmetric trade — earlier defined as real-world trade that changes balances of game and non-game wealth — is perhaps the most controversial topic in MMORPG, with some claiming that it undermines the nature of game play, and even threatens the future of the genre. Setting these normative claims aside, what can be said about the effect of asymmetric trade on game worlds?

The following pages address this question by introducing several basic models of asymmetric trade. These are simplified representations of ideas that are themselves abstract and idealized. They are useful as conceptual aids, however, illustrating mechanisms that influence player decisions, if they do not always dictate them. The models build upon a number of basic assumptions. These mostly restate conclusions reached earlier, but in some cases, they simplify or ignore that work for the sake of convenience.

2 Player trade with complete rivalry

We will start with a simple model that assumes game goods are completely rivalrous in their consumption.

2.1 Assumptions

Assumption 1

Game play is a productive process; it takes player time as its input, and produces alienable output (game goods), and inalienable output (play experiences).

MMORPG are played because this output is valued by players. Rational players make consumption and production decisions by balancing costs with benefits. A good’s utility is the benefit it confers to its consumer. Its marginal utility is the benefit conferred by the last unit that is consumed from a given quantity. Marginal utility typically decreases as the consumption quantity increases. Cost and marginal cost measure what is lost when goods are purchased or produced. Marginal cost typically increases as the production quantity increases.

For a given player, let:

MU_g ≡ Marginal utility of play

MU_a ≡ Marginal utility of alienable output

MU_i ≡ Marginal utility of inalienable output

so that:

MU_g = MU_a + MU_i

Assumption 2

Every unit of play time yields the same quantity of output for all players at all times.

This assumption greatly simplifies the nature of play. It ignores content density variations encountered when camping or practicing character skills, and the fact that content is inevitably finite in quantity. It also ignores the role of power and fellowship as capital or durable goods. In keeping with the assertion that MMORPG challenge is primarily egalitarian, it further ignores differences in player ability. However, it allows play time to be used as a measure of play output, just as it measures the production cost of that output.

Assumption 3

Players divide their time between play, work, and non-game leisure. The marginal cost of play is therefore the player’s wage rate, or the marginal utility of non-game leisure, whichever is higher. Both costs vary among players.

This assumption ignores bandwidth and customer service costs, which are external to the player. Because existing MMORPG charge flat rates for unlimited play, subscription fees are also disregarded, as these are sunk relative to play time.

A nation that does not trade with others is said to practice autarky. We will apply the same term to players who do not engage in asymmetric trade.

Assumption 4

In autarky, all players are employed.

This assumption simplifies the definition of production costs, and it does describe most MMORPG players. Given:

w ≡ Player wage rate

MU_n ≡ Marginal utility of non-game leisure

t₀ ≡ Optimal play time in autarky

t_n ≡ Optimal non-game leisure

it follows that:

t₀ = t such that (MU_g = w)

t_n = t such that (MU_n = w)

Finally, given:

t_b ≡ Player time budget

t_gw ≡ t_b - t_n

the player’s optimal work time must be t_gw − t₀. Since we assume that players are employed, it is also true that t_gw > t₀.

Assumption 5

For all players, MU_g and MU_n decrease as consumption increases, but remain strictly positive.

Game play and non-game leisure are therefore normal goods. This suggests a simple model of the decision to play. Given:

R₀ ≡ Consumer surplus from play, in autarky

the decision is shown by Figure 1. The consumer surplus is the utility of play, less its cost. If this area exceeds the subscription fee for period t_b, the player will gain by subscribing to and playing the game. Note that MU_n is reversed horizontally and displayed as MU_n'. This divides the player’s time budget geometrically into play, work, and non-game leisure.

Assumption 6

Players have varied preferences for alienable and inalienable output, and therefore receive different amounts of utility from given play quantities. However, for a particular player, the ratio α of MU_a to MU_g is constant at all times.

While there is no reason for the marginal utilities of play output to remain constant in proportion, this constraint simplifies without offending economic sensibilities. Since:

α ≡ MU_a / MU_g

it follows that:

MU_a = αMU_g

MU_i = (1 - α) MU_g

with 0 ≤ α ≤ 1.

Assumption 7

Alienable and inalienable output are both non-durable goods. These are goods that provide immediate, one-time value to their consumer.

This ignores the non-rivalrous nature of content, and the resemblance of power and fellowship to durable or capital goods. With this assumption, however, it is unnecessary to consider inventories of play output.

Assumption 8

Alienable output is perfectly fungible. The market for alienable output is perfectly efficient.

Assumption 9

Players are rational and self-interested with regard to asymmetric trade. The trade itself produces no externalities.

These assumptions — though far from realistic — allow for the transfer and consumption of alienable output at no cost.

2.2 Constructing the model

2.2.1 Trade gains

In autarky, the player’s only decisions are whether to play, and for how long. As shown in Figure 1, if their play surplus will exceed the subscription fee, the player subscribes plays until MU_g is equal to w. They will devote their remaining time to work and non-game leisure.

Asymmetric trade offers the player four more options. They can:

• Increase their alienable consumption by purchasing another player’s output;
• Use purchase as a substitute for their own alienable production;
• Sell alienable output they would have consumed; or,
• Produce additional alienable output specifically for sale. The practice of producing game goods for sale is sometimes called farming2.

To understand the player’s decisions, it is necessary to determine the costs and benefits of the goods they produce and consume.

Alienable output is produced with play time, and the cost of that time is the value of whatever else the time might have produced. However, just as accomplishment and fellowship complement the production of game goods, inalienable output complements the production of alienable output, partially offsetting its production cost. Therefore, if:

MC_a ≡ Marginal cost of alienable production

t_i ≡ t such that (MU_i = w)

then, for t ≤ t_i:

MC_a = 0

since MU_i > w in this range. Where t_i ≤ t ≤ t_gw:

MC_a = w − MU_i

= w − (1 − α) MU_g

Where t ≥ t_gw:

MC_a = MU_n - MU_i

= MU_n - (1 − α) MU_g

So, at small quantities, alienable output is free, because its production complements inalienable output that would have been produced for its own sake. At larger quantities, the cost of alienable output is the player’s wage, or the value of the non-game leisure they could enjoy, less the (now diminished) value of the inalienable output at those quantities.

Given:

U_a,0 ≡ Utility of alienable output, in autarky

C_a,0 ≡ Cost of alienable output, in autarky

U_a,M ≡ Utility of additional alienable output, at maximum production

C_a,M ≡ Cost of additional alienable output, at maximum production

Figure 2 shows the costs and benefits of alienable production, with marginal cost represented implicitly by w, MU_n, and MU_i. Figure 3 does the same with an explicit representation of marginal cost, equal to the play time opportunity cost, less MU_i.

At the autarkic production quantity t₀, MU_g = w. Since MC_a = w − (1 − α) MU_g at this point, and MU_a = αMU_g:

MC_a = MU_a = αw

This is to be expected. If MC_a and MU_a were unequal, the player could gain by producing at a level other than t₀. For a given player, αw will be called the autarkic price of alienable output, the price at which the player produces and consumes the same amount. At any other market price, the player will engage in asymmetric trade.

Asymmetric purchase is often said to distinguish ‘casual’ gamers from their ‘hardcore’ peers, with the implication that casual players are less committed to the game, yet somehow more greedy for game wealth3. If casual and hardcore players are distinguished only by their play time, this view may be justified. Because game play is more costly for high-wage players, they will necessarily play less. Such players will also have higher autarkic prices, and thus be more disposed to asymmetric purchase. However, if hardcore players are those who receive the most utility from play, then this claim must be discarded. Neither total nor marginal utility determines a player’s entry into the market for asymmetric trade (though they do influence trade quantities for those who choose to trade). In this model, participation is determined solely by the player’s preferences and wage rate.

It is possible to determine the exact effect of asymmetric trade on the player’s production and consumption. If:

t_y ≡ Alienable production

t_c ≡ Alienable consumption

then the player’s asymmetric trade balance equals t_y - t_c. As demonstrated above, in autarky:

t_y = t_c = t₀ = t such that (MC_a = MU_a)

However, given:

p_a ≡ Market price of alienable output

the following opportunities are also available to the player:

• Where p_a < MU_a, the player can gain by purchasing output for consumption;
• Where p_a < MC_a, they can economize on production costs by purchasing output;
• Where p_a > MU_a, they can gain by selling output instead of consuming it; and,
• Where p_a > MC_a, they can gain by producing output specifically for sale.

Therefore, with asymmetric trade:

t_y = t such that (MC_a = p_a)

t_c = t such that (MU_a = p_a)

The effect of asymmetric trade on player production, consumption, and welfare is shown in Figures 4 and 5.

In both cases, R_s + R_t is the player’s gross benefit from the asymmetric exchange. For buyers, this is the consumption value of the goods, less their market value. For sellers, it is their market value, less their production cost. R_s is the benefit that is ‘sunk’ with respect to trade; this portion would be realized even in autarky, through ordinary play. Therefore, R_t is the player’s net gain from trade. Naturally, both buyer and seller benefit from the exchange.

Although the player’s alienable production decreases with p_a, it never falls below t_i, where the MC_a curve begins. As shown in Figure 2, this where MU_i matches the player’s wage. Even if the player cared nothing for alienable output, they would invest this quantity of play time for the inalienable output alone.

2.2.2 Individual demand

Having defined the player’s production and consumption choices, it is now possible to derive their demand for and supply of alienable output.

Consider the player’s demand. As shown in Figure 4, the player’s purchase at price p_a is the horizontal distance between MU_a and MC_a. These are functions that convert quantities to prices, so their quantity difference must be expressed with function inverses, MU_a^-1 - MC_a^-1.

If supply and demand were also functions of quantity, it would be necessary to invert this difference. However, though economists graph prices on the vertical axis, and quantities on the horizontal, supply and demand are conventionally presented as functions that convert prices to quantities. Therefore the demand:

D_a ≡ Player’s demand for alienable output

can be expressed without inverting the quantity difference:

D_a = MU_a^-1 - MC_a^-1

Since t_gw was assumed to exceed t₀, and since MC_a = w - (1 - α) MU_g for t_i ≤ t ≤ t_gw:

D_a = (αMU_g)^-1 - [w - (1 - α) MU_g]^-1

Its exact shape varies with the definition of MU_g, but generally, the demand curve starts at αw (at which price the player purchases nothing) and slopes downward thereafter. The player’s demand for asymmetric trade is shown in Figure 8.

2.2.3 Individual supply

Like demand, the player’s supply of asymmetric trade is defined by MU_a and MC_a. However, MC_a has an inflection point at t_gw, so the player’s supply is produced in two phases, according to the prevailing market price.

The inflection is shown in Figure 6. The significance of:

p_a:gw ≡ MC_a at t_gw

t_a ≡ t such that (MU_a = p_a:gw)

will be demonstrated below.

2.2.3.1 First supply phase

The first supply phase starts where the demand curve ends: at the player’s autarkic price, where the trade quantity is zero. Suppliers will economize on costs as much as possible — in this case, the opportunity cost of play time, and the utility they would enjoy by consuming the output themselves (another opportunity cost). Play is less costly when it generates more inalienable utility, and when alternative uses for time generate less value. The last unit of alienable output becomes less valuable as the consumption quantity (whatever production is not sold) increases. This implicates the range between t_a and t_gw, where MU_a is relatively low, and MU_n is less than w. Output in this range will be sold when p_a is close to αw. The most that can be produced here is:

t_gw-a ≡ t_gw − t_a

The last unit in this range will not be sold for less than p_a:gw, so the first supply phase extends from (0, αw) to (t_gw-a, p_a:gw).

Like demand, supply in the first phase is defined by MU_a and MC_a. If:

S_a ≡ Supply of alienable output

it follows that, for t ≤ t_gw-a:

S_a = MC_a^-1 - MU_a^-1

= [w - (1 - α) MU_g]^-1 - (αMU_g)^-1

Throughout this phase, as p_a increases, the supplier forgoes increasing quantities of alienable consumption, and substitutes play time for work.

2.2.3.2 Second supply phase

When p_a exceeds p_a:gw, the player stops working outside the game, and works instead as a MMORPG farmer. Henceforth, the player can supply asymmetric trade only by forgoing non-game leisure, or by selling portions of their remaining alienable output, equal to t_a. This situation is shown in Figure 7.

The player’s choices are much what they were in the first phase, except that MC_a is here equal to MU_n − MU_i. Since MU_i = (1 − α) MU_g:

S_a = [MU_n − (1 − α) MU_g]^-1 − (αMU_g)^-1

for t ≥ t_gw-a. The second phase starts where the first left off, at (t_gw-a, p_a:gw), and slopes upward thereafter. The supplier can produce no more than t_b, whatever the market price4.

The two supply phases are shown in Figure 8, along with the player’s demand.

2.3 Conclusions

2.3.1 Trade decisions

The model offers some common-sense conclusions about who engages in asymmetric trade, and with whom. Each player’s autarkic price marks the origin of their personal demand and supply curves. If two players have different autarkic prices, the demand curve of the player with the higher price must somewhere exceed the other player’s supply, and a price exists at which the two will trade. Autarkic prices are entirely determined by wages and preferences for alienable or inalienable consumption; therefore, high-wage players will buy game goods from low-wage players5, and those who prefer power and content will purchase from those who prefer accomplishment and fellowship. The quantity of trade will be determined by the amount of variation in these factors.

Since autarkic prices will vary considerably, the model predicts that nearly every player will trade, a conclusion that is obviously incorrect. In fact, only 9.7% of EverQuest players report having purchased an item on eBay (Yee 2001). This prediction rests on assumptions of rationality and market efficiency that describe reality abstractly, at best. A more defensible interpretation is that — given low transaction costs — most players could gain by trading.

2.3.2 Player population

Trade has broader effects on the game and its players. As demonstrated in Figures 4 and 5, asymmetric trade increases the play surplus of those who participate. Presumably, this includes some who would not otherwise have played, thus increasing the player population and developer revenues.

Asymmetric trade is particularly advantageous for players whose wages or preferences vary significantly from the norm. Trade is therefore likely to diversify the player community by attracting both high-wage and low-wage players, and those with relatively extreme preferences for alienable or inalienable output. High-wage players who prefer power and content, and low-wage players who prefer accomplishment and fellowship will be especially favored6.

2.3.3 Play time

As shown in Figures 4, 5, and 7, trade prompts players to produce until MC_a equals p_a. For some, this yields an alienable production quantity that is less than their consumption, creating a deficit that drives asymmetric demand. Others produce more than they consume, creating a surplus that is the source of asymmetric supply. For all players, the change in play time induced by market price p_a is determined by:

MC_a-0 ≡ Marginal cost of alienable production beyond autarkic level

which is MC_a shifted left by t₀:

MC_a-0 = (MC_a^-1 - t₀)^-1

The boundaries and inflection point are also shifted left:

t_i-0 = t_i - t₀

t_gw-0 = t_gw - t₀

t_b-0 = t_b - t₀

The effect of asymmetric trade on individual play time is shown in Figure 9, along with individual demand and supply.

As expected, demand for alienable output correlates with decreased play time, and supply with increased play. Like supply, MC_a-0 increases in slope at p_a:gw — and more drastically, since it is not affected by the distance to and curvature of MU_a. t_i-0 marks the greatest possible decrease in play time, since at quantities less than t_i, play is worthwhile for its inalienable output alone. Similarly, t_b-0 shows the greatest possible increase, since the player’s time budget is exhausted at t_b.

It is impossible to make broad statements about play time changes without defining MU_g and MU_n, but a few conclusions can be drawn.

In the case where two players have similar tastes and different wages, the better-paid player will have a higher autarkic price, and a lower autarkic production level. Since MU_i is likely to be more steep at lower quantities, MC_a (which equals w - MU_i) and MC_a-0 will be steeper also. Consequently, the change in play time at prices below p_a:gw will be less for the high-wage player than it is for their lower-paid counterpart. Trade based on wage variation will probably increase aggregate play time.

A similar method applies to trade that arises from preference variations. Given two players with similar wages, similar MU_g, and different preferences for alienable output, the player with the stronger preference will have a higher value for α, and a higher autarkic price. Since MU_i is necessarily less steep when α is high (MU_i being equal to (1 − α) MU_g), MC_a and MC_a-0 will be less steep as well. The play time change will be greater for the high-α player, and therefore, where the price is less than p_a:gw, trade based on preference variation will likely decrease aggregate play time.

As ever, the player’s production is limited by their time budget, and by their desire for non-game leisure, which varies less with price at high production levels. For these reasons, MC_a and MC_a-0 will be quite steep above p_a:gw, and asymmetric trade in this range is likely to decrease aggregate play time.

Finally, while asymmetric trade was assumed to produce no externalities, changes in play time will affect the developer’s bandwidth, server, and customer service costs.

3 Fiat sale

We have focused on trade between players, but fiat sale is also a form of asymmetric trade, since it alters balances of game and non-game wealth. What happens when developers use their fiat power to produce goods for asymmetric trade?

3.1 Fiat sale and player competition

Developers have little ability to prevent asymmetric sale7, so those who enter this market must do so as competitors rather than monopolists. This competition can be modeled in a simple way by assuming two player types, each with different supplies of and demands for alienable goods. Given:

AD_af ≡ Aggregate demand for alienable output, including fiat production

AS_a ≡ Aggregate player supply of alienable output

α_Dw_D ≡ Autarkic price of demanders

α_Sw_S ≡ Autarkic price of player suppliers

t_a ≡ Asymmetric trade by players, without fiat sale

R_c,a ≡ Consumer surplus from asymmetric trade, without fiat sale

R_y,a ≡ Player producer surplus from asymmetric trade, without fiat sale

the situation before the developer enters the market is shown by Figure 10. Note that R_c,a and R_y,a are the benefits specifically resulting from trade; other player surpluses are not relevant here.

Player supply and demand quantities are equal at p_a, so only below this price can the developer hope to sell fiat goods. As the fiat price drops, player suppliers are forced to lower their prices as well; their supply quantities decrease, the quantity supplied by the developer increases, and the total demand quantity rises. Given:

p_f ≡ Price of fiat goods

t_ay ≡ Asymmetric sale by players, with fiat sale

t_ac ≡ Asymmetric purchase by players, including fiat goods

R_f ≡ Developer revenue from fiat sale

R_c,f ≡ Consumer surplus from asymmetric trade, with fiat sale

R_y,f ≡ Player producer surplus from asymmetric trade, with fiat sale

The effect of fiat sale is shown in Figure 11. The fiat sale quantity is t_ac − t_ay, so the developer’s revenue from fiat sale:

R_f = p_f (t_ac − t_ay)

Every player supplier is also (at market prices below their autarkic price) a demander. This is represented in Figure 11 by a flattening of the demand curve at α_Sw_S. Below this price, fiat production converts player suppliers from competitors to customers8. The developer gains a measure of monopoly control by pricing below the lowest autarkic price, but — in games with many thousands of players — the lowest autarkic price may be very low indeed.

3.2 Effect of fiat sale

Like other asymmetric trade, fiat sale decreases purchaser play time, but it does this without a corresponding increase in supplier play. Therefore, it can only decrease aggregate play time9. For developers, this reduces the costs associated with play time: bandwidth, server load, and customer service.

Since it depresses the price of alienable output below the player trade level, it adds to the buyer’s consumer surplus, as shown by the difference between R_c,a and R_c,f. Presumably, this attracts certain players, particularly those with high wages or strong preferences for alienable output. However, by lowering prices, fiat sale diminishes the supplier’s producer surplus from R_y,a to R_y,f, prompting some players with low wages or strong inalienable output preferences to leave the game. The buyer’s gain is greater than the seller’s loss, since their gain is equal to that loss, plus the area between AS_a, AD_af, and p_f. This perhaps suggests a net gain in population, with the attendant increase in subscription revenue. When fiat revenue itself is considered, the change in total developer revenue is presumably positive.

3.3 The scarcity of fiat sale

If fiat sale increases developer revenue, why is it so rare? Many players dislike asymmetric trade on principle; these probably outnumber the 9.7% of players who participate, and they are certainly more vocal. A developer who gives official sanction to this practice could face significant backlash from players.

If fiat sale were more common, developers would face difficult pricing decisions. Fiat goods are produced at no cost, and players (especially new ones) are likely to view power and content in different games as close substitutes. This suggests that developers would soon be forced into fiat price competition.

This competition could drive market prices for alienable output to low levels, largely or completely displacing player supply. Player production would not stop, since (as explained earlier) every player has a minimum production quantity t_i that complements their production of inalienable output. Players would not produce much beyond this level, however, and most would offer nothing for sale. The decrease in play time would also reduce the production of fellowship.

Fiat prices have no lower limit, so fiat revenues could drop to very low levels. It does not seem possible for developers to differentiate the power offered by one game from that offered by others. In the long run, therefore, they will benefit from fiat sale only if they can differentiate their content very effectively. If they succeed in this, fiat sale and the PvE power that accompanies it could provide a more direct way for them to ration and profit from the content they produce. If they cannot differentiate their content, it may be better for them to leave asymmetric trade to the players.

4 Player trade with non-rivalry

The player trade model can be made more realistic and only slightly more complex by treating parts of the play experience as non-rivalrous.

4.1 Assumptions

Assumption 10

A player’s alienable output is partly rivalrous and partly non-rivalrous. Because they lose none of its utility, the sale of non-rivalrous output incurs no opportunity cost for the player.

Given:

MU_r ≡ Marginal utility of rivalrous alienable output

MU_nr ≡ Marginal utility of non-rivalrous alienable output

if follows that:

MU_r = MU_a - MU_nr

Developers regulate the consumption of content by associating content access with PvE power, which inheres to the goods that players trade. Power is rivalrous in consumption, but content itself is not. This allows a player to produce a quantity of power, enjoy the content access it confers, and then transfer both to another player. Only the rivalrous portion of the goods’ utility contributes to the opportunity cost of the sale.

Assumption 11

For a given player, the ratio of MU_r to MU_a is constant at all times.

This claim is a convenience, like Assumption 6. Given:

ρ ≡ MU_r / MU_a

it follows that:

MU_r = ρMU_a = ραMU_g

MU_nr = (1 - ρ) MU_a = (1 - ρ) αMU_g

for 0 ≤ ρ ≤ 1.

4.2 Constructing the model

Non-rivalry requires few changes to the original model. Non-rivalrous output benefits producers whether they sell the associated game goods or not; from their standpoint, only the rivalrous utility is lost. Given:

MC_r ≡ Marginal cost of rivalrous alienable output

MU_i+nr ≡ MU_i + MU_nr

= (1 - α) MU_g + (1 - ρ) αMU_g

= (1 - ρα) MU_g

t_i+nr ≡ t such that (MU_i+nr = w)

it is seen that, for t ≤ t_i+nr:

MC_r = 0

MC_r has an inflection point for the same reason that MC_a does. Where t_i+nr ≤ t ≤ t_gw:

MC_r = w - MU_i+nr

= w - (1 - ρα) MU_g

Where t ≥ t_gw:

MC_r = MU_n - MU_i+nr

= MU_n - (1 - ρα) MU_g

The costs and benefits of rivalrous production are shown in Figures 12 and 13. A seller’s reservation price is the lowest price they are willing to accept for some good. When ρ < 1, the net production cost and reservation price of alienable output decrease relative to complete rivalry. As before, MU_g = w at t₀, so, at this point:

MC_r = ραw = MU_r

ραw will be called the non-rivalrous autarkic price of alienable output10.

Once again, suppliers produce in two phases. Given:

S_r ≡ Supply of rivalrous alienable output

p_r:gw ≡ MC_r at t_gw

t_r ≡ t such that (MU_r = p_r:gw)

t_gw-r ≡ t_gw - t_r

it is seen that, for t ≤ t_gw-r:

S_r = [w − (1 − ρα) MU_g]^-1 − (ραMU_g)^-1

Where t ≥ t_gw-r:

S_r = [MU_n − (1 − ρα) MU_g]^-1 − (ραMU_g)^-1

The player’s supply of rivalrous output is shown in Figure 14. While suppliers forgo only the rivalrous portion of their sales, buyers benefit from both rivalrous and non-rivalrous output, and their demand remains unchanged.

4.3 Conclusions

Non-rivalry has straightforward effects on the conclusions drawn earlier.

With complete rivalry, trade gains derive from variations in preferences or wages. With non-rivalry, even identical players gain by trading with each other, as demonstrated by the fact that each player’s supply curve S_r crosses their own demand curve D_a at a non-zero quantity.

Who sells and who buys when such players meet? The rivalrous model defines an autarkic price αw for each player, at which they forgo trade. With complete rivalry, if the market price exceeds this value, MC_a exceeds MU_a, and the player enters the market as a seller. If the market price drops below this price, MU_a exceeds MC_a, and they enter as a buyer.

When alienable output is partially non-rivalrous, trade gains from asymmetric purchase are defined by MU_a and MC_a, as before, but gains from sale are not. These are determined by MU_r and MC_r, reflecting the fact that non-rivalrous utility is retained when the goods are sold. The new curves meet at a second autarkic price ραw. So, at market prices above αw, the player sells, while at prices below ραw, they buy.

What happens between αw and ραw? The curves cross in this range, showing that the player can gain by selling or buying. These options generate different trade gains, however, with prices close to αw rewarding sellers more than buyers, and prices close to ραw rewarding buyers more than sellers. The break-even point will be found at the price that divides the region above S_r and below D_a into two equal areas.

By lowering net production costs, non-rivalry lowers market prices, increases the quantity of asymmetric trade, and increases both consumer and producer surpluses. This increases player surpluses, player population, and ultimately developer revenue. The change is most pronounced when the proportion of non-rivalrous utility (1 − ρ)α is greater.

Finally, non-rivalry redefines the relationship between preferences and market roles, since players with strong content preferences no longer favor purchase over sale. Instead, when wages are identical, players who prefer accomplishment and fellowship will supply goods, while those who prefer power will demand them.

5 Further research

The greatest shortcoming of these models is the assumption that play output is a non-durable good. As argued in an earlier work, this is largely incorrect. Fellowship and PvP power are more like durable goods, since they add to the utility of future play time. PvE power is more like a capital good, since it facilitates the production of additional power. A more accurate model would account for the persistence of certain play outputs, and the future returns that result from current game play decisions. That approach would consider MMORPG play as an alternative to real-world investment, just as this work presents it as an alternative to labor and non-game leisure.

The possibility of stockpiling play output suggests trade motives beyond simple consumption, including price speculation and game entry or exit. Player population changes also become significant. If play output persists, aggregate game wealth and player population will vary independently. More complex models might show the effect of population changes on the price and quantity of asymmetric trade, and on the play experience in general.