Many products are being sold that have substantial total production costs but very small marginal production costs, e.g. virtually all forms of digital entertainment, software, books (especially digital ones) etc.
Sellers of these products could set the product price such that the price for the (n+1)th instance of the product sold is cheaper than the price for the (n)th instance of the product sold.
They could choose a convergent series such that the total gains converge as the number of products sold grows large (e.g. price for nth item = exp(-n) + marginal costs )
They could choose a divergent series such that the total gains diverge (sublinearly) as the number of products sold grows large (e.g. price for nth item = 1/n + marginal costs )
Certainly, this reduces the total gains, but any seller who does it would outcompete sellers who don’t.
And yet, it doesn’t seem to exist.
True, many sellers do reduce prices after a certain amount of time has passed, and the product is no longer as new or as popular as it once was, but that is a function of time passed, not of items sold.
A psychological effect could be at play. If you pay $10 for a product and this causes the next person to pay $9 for it, it’s an incentive against being the first to buy it. You would wait until others have bought it before buying. Or you might think the product is being priced unfairly and refuse to buy at all.
It seems that to counter this, you’d need another psychological effect to compensate. Like, for instance, offering the first set of buyers ‘freebies’ that actually have zero or near-zero cost (like ‘the first 1000 people get to enter a prize-giving draw!’)
Snowdrift.coop is essentially trying to solve the same problem in a different way. Instead of changing the product price as more units are sold, they ask folks to finance its fixed component directly, using a game-theoretic mechanism that increases total contributions superlinearly as more people choose to contribute. (This boosts the effectiveness of any single user’s contributions through a “matching” effect). However, there is no distinction between “earlier” vs. “later” contributors; they’re all treated the same. The underlying goal is to generalize the successful assurance-contract mechanism to goods and services that do not have a well-defined ‘threshold’ of feasibility, especially services that must be funded continuously over time.
It’s an interesting idea but I’m not sure it has the psychology behind crowdfunding right. It seems to be constructed to minimize the risk donors carry in the event of a failed campaign, and to maximize the perceived leverage of small donations; but it does that at the expense of bragging rights and fine-grained control, which might make a lot of donors leery. I think you could probably tweak it to solve those problems, though.
It also does nothing at all to solve the accountability issues of traditional crowdfunding, but that’s a hard problem. I wouldn’t even mention it if they hadn’t brought it up in the introduction.
(Also, that’s some ugly-ass web design. I get that they’re trying to go for the XKCD aesthetic, but it’s… really not working.)
It also does nothing at all to solve the accountability issues of traditional crowdfunding, but that’s a hard problem. I wouldn’t even mention it if they hadn’t brought it up in the introduction.
Yes, crowdfunding is mostly based on trust, not accountability. But a service that’s funded continuously over time (the Snowdrift.coop model) ought to be inherently more accountable than a single campaign/project.
t seems to be constructed to minimize the risk donors carry in the event of a failed campaign, and to maximize the perceived leverage of small donations
I think it’s been constructed to maximize democracy—the crowdthink determines the flow of money. I can’t tell if the author considers the inevitable snowballing to be a feature or a misfeature (or even realizes it will happen).
Not sure how communism is relevant here. Snowdrift.coop’s mechanism is entirely private and voluntary, and assuming that it works properly, it’s incentive properties are superior to typical charities or governments.
I kept thinking: All of the funding that goes to proprietary software could, in principle, go to Free Software; all of the funding for copyright restricted music and educational resources could, in principle, go to works licensed with Creative Commons. The value to society would be greater if everyone has access and ability to build upon the work of others.
.
it’s incentive properties are superior to typical charities or governments
That remains to be seen. Its incentive properties are basically “winner take all”. Maybe they should have called the project Snowball, not Snowdrift.
All of the funding that goes to proprietary software could, in principle, go to Free Software; all of the funding for copyright restricted music and educational resources could, in principle, go to works licensed with Creative Commons.
How is this wrong? Kickstarter, IndieGogo and similar projects have boosted the funding of FLOSS software and CC artworks/educational works significantly. Snowdrift.coop is simply an extension of that model.
The ‘winner take all’ properties of Snowdrift.coop are overstated. If you think a project is raising ‘too much’, you’re free to compensate by reducing your stake, although this will nullify the incentive effect of your contribution. There is no way of escaping this—the same change in incentives happens on Kickstarter when “the goal” is reached. Here, the “goal” of contributions is fuzzy and entirely determined by funders’ choices.
Pricing is a well-studied area. Price discrimination based on time and exclusivity of ‘first editions’ and the like is possible, but highly dependent on the market. Why would anyone be able to sell an item with a given pricing scheme like 1/n? If their competitor is undercutting them on the first item, they’ll never get a chance to sell the latter ones. And besides there’s no reason such a scheme would be profit-maximizing.
Why would anyone be able to sell an item with a given pricing scheme like 1/n?
On downloaded, digital goods, this would be simple.
If their competitor is undercutting them on the first item, they’ll never get a chance to sell the latter ones.
And besides there’s no reason such a scheme would be profit-maximizing.
Kickstarter is really sneaky, because I tend to assume (and I assume everyone assumes) that the preorders will get a better price than the postorders. But the only time I used kickstarter final cost was lower than what I paid. I don’t know if that it is typical. Probably one should charge more to preorders for price discrimination reasons: they are the principle fans. But that is a different reason.
Kickstarter implements dominant assurance contracts, e.g. it solves a coordination problem and takes a cut for doing so. It’s an example of doing well by doing good.
For the practical real-world analogue of this, look up price discrimination strategies.
Anyhow, this doesn’t work out very well for a number of reasons. In short antiprediction form, there’s no particular reason why price discrimination should be monotonic in time, and so it almost certainly shouldn’t.
One could note that natural markets are going to this direction. For example steam has pretty reliably games appear on sale year or two after their release. Savvy consumers already know to wait if they can. This can get so bad taht early access games hit sales before they are released!
I tired to bring this topic up at a LessWrong meeting I have been calling my thoughts on this direction as “contributionism”.
There is some additional even more radical suggestions. Instead of treating at each new sell as lesser amount, retroactively lower the price for already happened purchases (I am pretty sure they dont’ mind). Otherwise there is this contention that if two customers are about to buy the product they try to make the other guy buy first so they get the cheaper price (which leads to a mexican standoff that chills selling).
Also normally when a seller and a customer are negotiating for a price seller wants to make it high and the buyer wants it to go low. However if the seller fixes the total amount of money he wants form all of his products then the price negotiation is only about whether the buyers wants to opt in now that it is higher or later when it is lower. However if the price retroactively changes you are “ultimately” going to be spending the same amount of money. If you attach your money early you get earlier access and run the risk that the product never hits high sales numbers (ie that you do not get any returns on it).
However the more people attach money the more the instant price lowers and more money is prone to flow in. This can also be leveraged to overcome a coordination problem. Even if the current instant price too much for you the seller can ask you how much you would honestly be willing to pay for it. (Answering this question too high will not cost you (too much) money). Then when the next customer that doesn’t quite have enough buying willingness he might still promise the same level of sum of it. At some point that enough promisers have visited the sum of the promises actually covers for whaqt the seller wants to get for all of his products combined. At this point we can inform the promisers of each others existence—ie that a working sale configuration has been found. This might be a lot of people for a small sum of money each indivudally totalling up to a considereable sum.
Howeer this runs contary to a lot of curretn economical “ethos”. Essentially every seller is expected ot try make as much money with the products as possible, there is no sum that is “good enough” that he would settle for. There is also talk of profit motive and letting the pricing game go on is said to make the wheels of the economy run smoothly. However in practise sellers will settle at some price as they think the proabbility of getting more diminishes faster than the gain.
However instead of maximising profits we could set profits to be constant and minimise cost per user. Ie instead of trying to maximse the wealth transfer we try to make the sale happen with as little fuss as possible.
One of the current economys problems is also that advertising and such creates otherwise frivoulous needs that prodeucts can be marketed for. The customer is taken into the decision procees only in what product they choose from the super market self. The decision to build the factory and logistic chain is a money lord with a profit motive trying to be greedy.
However we start from the needs of the customer for example that “I want our village to be educated and I am willing to do 10 hours of work for that end”. When you got 100 of these kind of people someone might come suggest aplan to build a school that would take about 150 hours + 50 hours of someone teaching. It turns out that for contrucetion 1.5 hours of work on average is required per villager. Howevver the teacher is doing 50 hours of work when his “fair share” would have only be 1.5 hours. Probably the teacher has other desires beside wanting the village to be educated, the other promise to work on those projects for 48.5 hours. Divided evenly amongs the rest of the 99 willing villagers this amounts to 0.5 hours on those other projects.
That is in this village scenario the customer/investors put in 2 hours of effort 1.5 which most do themself and part is focused on one teacher.
I am interested if anyone wants to talk start-up or similar thingies, or just plainly would be okay purchasing some kind of services in this manner. The most challenge I have faced that people don’t like it when a product doesn’t cost a fixed amount of money even if they could argue that it’s a fixed cost + free money afterwards however it comes back. Also it reminds of a ponzi scheme. However you can never go into a negative price ie you can’t profit by buying a product. At most you get the product for (practically) free.
I would like to point out that kick starter uses clever methods in making sure taht the donation amount doesn’t degenerate into nothingness. Ie it has perks where you get something when you enough. I am not sure whether being the “not profit making version” of kickstarter is a big enough difference to go compete with such recognised thing. But it has other alluring properties. However it is hard to pitch as a venture capital idea because it is “anti-profit” the most close is that sellign in this way would slightly outcompete with a profit maker because the profit makes has to guess beforehand the price point right to exact digits in order to have similar performance. In practise sales deviate somewhat from projected sales, contributionistic sale is sure to make econimcal sense at whatever scale but a beforehand fixed pricepoint will always live in a slightly uncompatible scale.
This is also a good counter point to how market does serve good, but good is made to serve the market. That is if you choose your nominal ultimate goals so that a spesific intrumental goal is the chosen method to archieve it, the nominally instrumental goal is your main objective. In that way sellers don’t want to serve the customers needs they just want them to be okay on chipping in the money because they are perfectly satisfied on creating a new problem for the customers so that they can sell cures for them.
The decreasing price for prior buyers is an interesting notion.
There are specific auction and pre-commitment and group-buying schemes that evoke certain behaviors, and there’s room for a lot more start-ups and businesses taking advantage of these (blockchains and smart contracts in particular have a lot of potential).
I don’t think we’ll ever get rid of marketing though.
this reduces the total gains, but any seller who does it would outcompete sellers who don’t
Why would the dynamic-price seller outcompete other sellers who are making more money?
Besides, he would have the classic takeoff problem—this first items would be (relatively) very expensive and nobody will buy them (the flat-price sellers are selling the same thing much cheaper).
Because the parasite is drawing less blood from the host. While various pressures make seller go near the tipping point of economical viability usually the sales are a little past that. Ie there is some amount of the price could have been lower and the total amount of sales would have been the same. If customers would be offered this price they would prefer it to the original price. However such a venture will make 0 profit. In economic lecture i saw this pharsed in the way that there is some X amount of profit the company wants to make if it’s profits will fall to x-1 it will voluntarily go out of business or change to a more lucrative business “no one will bother to do it as a charity”. Usually this “bookkeeping profit” is actually included in the production costs so that 0 profit means the point where the firm still stays in business.
The idea of competition comes that if X is the painthreshold for you and the current market price is X+20 you can sell at X+10 to be +10 on the confortable side. Ie the most modest greed will win.
Suppose 2 movies have been produced, movie A by company A and movie B by company B. Suppose further that these movies target the same audience and are fungible, at least according to a large fraction of the audience. Both movies cost 500 000 dollars to make.
Company A sells tickets for 10 dollars each, and hopes to get at least 100 000 customers in the first week, thereby getting 1000 000 dollars, thus making a net gain of 500 000 dollars.
Company B precommits to selling tickets priced as 10 f(n) dollars, with f(n) defined as 1 / ( 1 + (n-1)/150000 ) , a slowly decreasing function. If they manage to sell 100 000 tickets, they get 766 240 dollars. Note that the first ticket also costs 10 dollars, the same as for company A.
200 000 undecided customers hear about this.
If both movies had been 10 dollars, 100 000 would have gone to see movie A and 100 000 would have seen movie B.
However, now, thanks to B’s sublinear pricing, they all decide to see movie B. B gets 1270 000 dollars, A gets nothing.
The movie industry actually does this, more or less. It’s not a monotonic function, which makes analysis of it mathematically messy, but it’s common (albeit less common now than twenty years ago) for films to be screened for a while in cheaper second-run theaters after their first, full-priced run; and then they go to video-on-demand services and DVD, which are cheaper still.
Wouldn’t surprise me if similar things happened with 3D projectors and other value-added bells and whistles, but I don’t have any hard data.
Certainly, this reduces the total gains, but any seller who does it would outcompete sellers who don’t.
If they have less gains, then in what way are they outcompeting other sellers? If they want to sell the most copies, they should just give them away, or better yet, pay people to take them.
Why would sellers doing this outcompete sellers who don’t? Sellers reducing prices whenever they want, rather than precommitting to a set function, will have more information to base their prices on at the time they set each price, so I’d expect them to do better.
Sublinear pricing.
Many products are being sold that have substantial total production costs but very small marginal production costs, e.g. virtually all forms of digital entertainment, software, books (especially digital ones) etc.
Sellers of these products could set the product price such that the price for the (n+1)th instance of the product sold is cheaper than the price for the (n)th instance of the product sold.
They could choose a convergent series such that the total gains converge as the number of products sold grows large (e.g. price for nth item = exp(-n) + marginal costs )
They could choose a divergent series such that the total gains diverge (sublinearly) as the number of products sold grows large (e.g. price for nth item = 1/n + marginal costs )
Certainly, this reduces the total gains, but any seller who does it would outcompete sellers who don’t. And yet, it doesn’t seem to exist.
True, many sellers do reduce prices after a certain amount of time has passed, and the product is no longer as new or as popular as it once was, but that is a function of time passed, not of items sold.
A psychological effect could be at play. If you pay $10 for a product and this causes the next person to pay $9 for it, it’s an incentive against being the first to buy it. You would wait until others have bought it before buying. Or you might think the product is being priced unfairly and refuse to buy at all.
It seems that to counter this, you’d need another psychological effect to compensate. Like, for instance, offering the first set of buyers ‘freebies’ that actually have zero or near-zero cost (like ‘the first 1000 people get to enter a prize-giving draw!’)
Reminds me of kickstarter.
Snowdrift.coop is essentially trying to solve the same problem in a different way. Instead of changing the product price as more units are sold, they ask folks to finance its fixed component directly, using a game-theoretic mechanism that increases total contributions superlinearly as more people choose to contribute. (This boosts the effectiveness of any single user’s contributions through a “matching” effect). However, there is no distinction between “earlier” vs. “later” contributors; they’re all treated the same. The underlying goal is to generalize the successful assurance-contract mechanism to goods and services that do not have a well-defined ‘threshold’ of feasibility, especially services that must be funded continuously over time.
It’s an interesting idea but I’m not sure it has the psychology behind crowdfunding right. It seems to be constructed to minimize the risk donors carry in the event of a failed campaign, and to maximize the perceived leverage of small donations; but it does that at the expense of bragging rights and fine-grained control, which might make a lot of donors leery. I think you could probably tweak it to solve those problems, though.
It also does nothing at all to solve the accountability issues of traditional crowdfunding, but that’s a hard problem. I wouldn’t even mention it if they hadn’t brought it up in the introduction.
(Also, that’s some ugly-ass web design. I get that they’re trying to go for the XKCD aesthetic, but it’s… really not working.)
Yes, crowdfunding is mostly based on trust, not accountability. But a service that’s funded continuously over time (the Snowdrift.coop model) ought to be inherently more accountable than a single campaign/project.
Yeah, it’s more accountable than Kickstarter funding, but not more accountable than Patreon funding.
I think it’s been constructed to maximize democracy—the crowdthink determines the flow of money. I can’t tell if the author considers the inevitable snowballing to be a feature or a misfeature (or even realizes it will happen).
I don’t think Snowdrift understands why communism failed (or economics in general).
Not sure how communism is relevant here. Snowdrift.coop’s mechanism is entirely private and voluntary, and assuming that it works properly, it’s incentive properties are superior to typical charities or governments.
To quote from Snowdrift’s site:
.
That remains to be seen. Its incentive properties are basically “winner take all”. Maybe they should have called the project Snowball, not Snowdrift.
How is this wrong? Kickstarter, IndieGogo and similar projects have boosted the funding of FLOSS software and CC artworks/educational works significantly. Snowdrift.coop is simply an extension of that model.
The ‘winner take all’ properties of Snowdrift.coop are overstated. If you think a project is raising ‘too much’, you’re free to compensate by reducing your stake, although this will nullify the incentive effect of your contribution. There is no way of escaping this—the same change in incentives happens on Kickstarter when “the goal” is reached. Here, the “goal” of contributions is fuzzy and entirely determined by funders’ choices.
I don’t get what you’re getting at.
Pricing is a well-studied area. Price discrimination based on time and exclusivity of ‘first editions’ and the like is possible, but highly dependent on the market. Why would anyone be able to sell an item with a given pricing scheme like 1/n? If their competitor is undercutting them on the first item, they’ll never get a chance to sell the latter ones. And besides there’s no reason such a scheme would be profit-maximizing.
On downloaded, digital goods, this would be simple.
Please see the numerical example in this comment
I think you could probably model Kickstarter as a sneaky version of this.
Kickstarter is really sneaky, because I tend to assume (and I assume everyone assumes) that the preorders will get a better price than the postorders. But the only time I used kickstarter final cost was lower than what I paid. I don’t know if that it is typical. Probably one should charge more to preorders for price discrimination reasons: they are the principle fans. But that is a different reason.
Kickstarter is an excellent example of how to monetize affective biases :-D
Kickstarter implements dominant assurance contracts, e.g. it solves a coordination problem and takes a cut for doing so. It’s an example of doing well by doing good.
For the practical real-world analogue of this, look up price discrimination strategies.
Anyhow, this doesn’t work out very well for a number of reasons. In short antiprediction form, there’s no particular reason why price discrimination should be monotonic in time, and so it almost certainly shouldn’t.
One could note that natural markets are going to this direction. For example steam has pretty reliably games appear on sale year or two after their release. Savvy consumers already know to wait if they can. This can get so bad taht early access games hit sales before they are released!
I tired to bring this topic up at a LessWrong meeting I have been calling my thoughts on this direction as “contributionism”.
There is some additional even more radical suggestions. Instead of treating at each new sell as lesser amount, retroactively lower the price for already happened purchases (I am pretty sure they dont’ mind). Otherwise there is this contention that if two customers are about to buy the product they try to make the other guy buy first so they get the cheaper price (which leads to a mexican standoff that chills selling).
Also normally when a seller and a customer are negotiating for a price seller wants to make it high and the buyer wants it to go low. However if the seller fixes the total amount of money he wants form all of his products then the price negotiation is only about whether the buyers wants to opt in now that it is higher or later when it is lower. However if the price retroactively changes you are “ultimately” going to be spending the same amount of money. If you attach your money early you get earlier access and run the risk that the product never hits high sales numbers (ie that you do not get any returns on it).
However the more people attach money the more the instant price lowers and more money is prone to flow in. This can also be leveraged to overcome a coordination problem. Even if the current instant price too much for you the seller can ask you how much you would honestly be willing to pay for it. (Answering this question too high will not cost you (too much) money). Then when the next customer that doesn’t quite have enough buying willingness he might still promise the same level of sum of it. At some point that enough promisers have visited the sum of the promises actually covers for whaqt the seller wants to get for all of his products combined. At this point we can inform the promisers of each others existence—ie that a working sale configuration has been found. This might be a lot of people for a small sum of money each indivudally totalling up to a considereable sum.
Howeer this runs contary to a lot of curretn economical “ethos”. Essentially every seller is expected ot try make as much money with the products as possible, there is no sum that is “good enough” that he would settle for. There is also talk of profit motive and letting the pricing game go on is said to make the wheels of the economy run smoothly. However in practise sellers will settle at some price as they think the proabbility of getting more diminishes faster than the gain.
However instead of maximising profits we could set profits to be constant and minimise cost per user. Ie instead of trying to maximse the wealth transfer we try to make the sale happen with as little fuss as possible.
One of the current economys problems is also that advertising and such creates otherwise frivoulous needs that prodeucts can be marketed for. The customer is taken into the decision procees only in what product they choose from the super market self. The decision to build the factory and logistic chain is a money lord with a profit motive trying to be greedy.
However we start from the needs of the customer for example that “I want our village to be educated and I am willing to do 10 hours of work for that end”. When you got 100 of these kind of people someone might come suggest aplan to build a school that would take about 150 hours + 50 hours of someone teaching. It turns out that for contrucetion 1.5 hours of work on average is required per villager. Howevver the teacher is doing 50 hours of work when his “fair share” would have only be 1.5 hours. Probably the teacher has other desires beside wanting the village to be educated, the other promise to work on those projects for 48.5 hours. Divided evenly amongs the rest of the 99 willing villagers this amounts to 0.5 hours on those other projects.
That is in this village scenario the customer/investors put in 2 hours of effort 1.5 which most do themself and part is focused on one teacher.
I am interested if anyone wants to talk start-up or similar thingies, or just plainly would be okay purchasing some kind of services in this manner. The most challenge I have faced that people don’t like it when a product doesn’t cost a fixed amount of money even if they could argue that it’s a fixed cost + free money afterwards however it comes back. Also it reminds of a ponzi scheme. However you can never go into a negative price ie you can’t profit by buying a product. At most you get the product for (practically) free.
I would like to point out that kick starter uses clever methods in making sure taht the donation amount doesn’t degenerate into nothingness. Ie it has perks where you get something when you enough. I am not sure whether being the “not profit making version” of kickstarter is a big enough difference to go compete with such recognised thing. But it has other alluring properties. However it is hard to pitch as a venture capital idea because it is “anti-profit” the most close is that sellign in this way would slightly outcompete with a profit maker because the profit makes has to guess beforehand the price point right to exact digits in order to have similar performance. In practise sales deviate somewhat from projected sales, contributionistic sale is sure to make econimcal sense at whatever scale but a beforehand fixed pricepoint will always live in a slightly uncompatible scale.
“One of the current economys problems is also that advertising and such creates otherwise frivoulous needs that prodeucts can be marketed for. ”
This is an excellent summation of a point that gets bandied about a lot in certain circles. Do you mind if I shamelessly steal this?
It’s all yours, my friend
This is also a good counter point to how market does serve good, but good is made to serve the market. That is if you choose your nominal ultimate goals so that a spesific intrumental goal is the chosen method to archieve it, the nominally instrumental goal is your main objective. In that way sellers don’t want to serve the customers needs they just want them to be okay on chipping in the money because they are perfectly satisfied on creating a new problem for the customers so that they can sell cures for them.
The decreasing price for prior buyers is an interesting notion.
There are specific auction and pre-commitment and group-buying schemes that evoke certain behaviors, and there’s room for a lot more start-ups and businesses taking advantage of these (blockchains and smart contracts in particular have a lot of potential).
I don’t think we’ll ever get rid of marketing though.
Why would the dynamic-price seller outcompete other sellers who are making more money?
Besides, he would have the classic takeoff problem—this first items would be (relatively) very expensive and nobody will buy them (the flat-price sellers are selling the same thing much cheaper).
Because the parasite is drawing less blood from the host. While various pressures make seller go near the tipping point of economical viability usually the sales are a little past that. Ie there is some amount of the price could have been lower and the total amount of sales would have been the same. If customers would be offered this price they would prefer it to the original price. However such a venture will make 0 profit. In economic lecture i saw this pharsed in the way that there is some X amount of profit the company wants to make if it’s profits will fall to x-1 it will voluntarily go out of business or change to a more lucrative business “no one will bother to do it as a charity”. Usually this “bookkeeping profit” is actually included in the production costs so that 0 profit means the point where the firm still stays in business.
The idea of competition comes that if X is the painthreshold for you and the current market price is X+20 you can sell at X+10 to be +10 on the confortable side. Ie the most modest greed will win.
I imagine the following:
Suppose 2 movies have been produced, movie A by company A and movie B by company B. Suppose further that these movies target the same audience and are fungible, at least according to a large fraction of the audience. Both movies cost 500 000 dollars to make.
Company A sells tickets for 10 dollars each, and hopes to get at least 100 000 customers in the first week, thereby getting 1000 000 dollars, thus making a net gain of 500 000 dollars.
Company B precommits to selling tickets priced as 10 f(n) dollars, with f(n) defined as 1 / ( 1 + (n-1)/150000 ) , a slowly decreasing function. If they manage to sell 100 000 tickets, they get 766 240 dollars. Note that the first ticket also costs 10 dollars, the same as for company A.
200 000 undecided customers hear about this.
If both movies had been 10 dollars, 100 000 would have gone to see movie A and 100 000 would have seen movie B.
However, now, thanks to B’s sublinear pricing, they all decide to see movie B. B gets 1270 000 dollars, A gets nothing.
Wolfram alpha can actually plot this! neat!
The movie industry actually does this, more or less. It’s not a monotonic function, which makes analysis of it mathematically messy, but it’s common (albeit less common now than twenty years ago) for films to be screened for a while in cheaper second-run theaters after their first, full-priced run; and then they go to video-on-demand services and DVD, which are cheaper still.
Wouldn’t surprise me if similar things happened with 3D projectors and other value-added bells and whistles, but I don’t have any hard data.
If movie A sells for 9 dollars, people able to do a side-by-side comparison will never purchase movie B. Movie A will accrue 1.8 million dollars.
I don’t see what sublinear pricing has to do with it unless the audience is directly engaging in some collective buying scheme.
If they have less gains, then in what way are they outcompeting other sellers? If they want to sell the most copies, they should just give them away, or better yet, pay people to take them.
Why would sellers doing this outcompete sellers who don’t? Sellers reducing prices whenever they want, rather than precommitting to a set function, will have more information to base their prices on at the time they set each price, so I’d expect them to do better.