The Rare Earth Game | QSnxt Education

What it is

This is a design, not a product. There is nothing to play yet. The scenario, the mechanics and the case below are complete enough to run as a paper exercise or a seminar discussion, and they are published here for comment.

You govern Aster. Aster builds things (motors, turbines, drives, optics), and every one of them needs a small quantity of separated rare-earth oxides. Aster has almost no workable deposits and no separation capacity at all. Everything in the basket arrives from somewhere else, and it arrives separated, which matters more than it sounds.

Ore is not the scarce thing. Rare earths are not geologically rare; what is scarce is the plant that separates the mixed concentrate into individually usable oxides, and the willingness to host that plant. So the map has two distinct chokepoints, and they are in different places.

The five polities

Aster: You. A large manufacturing economy. Negligible deposits, no separation capacity, the highest demand per capita in the game.
Nyra: The other large manufacturer. Wants substantially the same basket you do, on substantially the same timetable. Your principal competitor for every tonne that reaches the open market.
Belmar: Holds the largest workable deposits, and very little capacity to separate them. Exports concentrate and captures the smaller share of the value.
Corvane: Holds most of the separation capacity and moderate deposits. The chokepoint through which most of the basket passes, whoever dug it up.
Tavena: Some deposits, some separation capacity, and the ability to expand either given time and demand. The swing supplier, and the polity whose choices move the others most.

Note that no single polity holds both chokepoints, and that separation is split. That is deliberate, and it is not how any real supply chain is arranged. The scenario is built to make the incentive structure legible rather than to model a particular country, and the conclusions do not depend on who stands where.

What makes it a puzzle

Securing your own supply is straightforward: sign exclusive contracts for future output, and hold a stockpile against interruption. Both work. Both are what a careful government does. The difficulty is that they work by removing tonnes from the pool everyone else draws on, and the other four polities are as careful as you are.

So the round after you lock up Belmar's output, Nyra bids harder for Tavena's, the residual open market thins, and the price of what is left rises for both of you. You each end up paying more for the same coverage than you would have paid for more coverage bought together. Nobody in that sequence made a mistake.

There is a better arrangement available, and the game makes it available: a shared reserve that members fund jointly and may draw on under agreed conditions. It gives more expected security per unit of capital than five national stockpiles do, for a reason worth understanding precisely: shocks are imperfectly correlated, so not every member needs the buffer in the same round. Pooling exploits that. It is a statistical property, not a reward for goodwill.

The catch is that the pool is least credible exactly when it is most valuable. A shock that hits one member is what pooling is for. A shock that hits everyone at once is when holding your own inventory looks wise and drawing down the shared one looks urgent. Whether you join, and whether you stay, is the game.

Rules of play

What you decide each round

You divide a finite budget across six instruments. They differ in how fast they pay off, how certain the payoff is, and how much of the cost they push onto the other polities.

Offtake contracts: Buy the right to a share of a named polity's future output. Fast, certain, and priced at a premium. Removes those tonnes from the open market for the duration.
Domestic extraction: Open a mine at home. Comes online only after a lag, costs more per tonne than importing, and carries a domestic siting cost that rises the more you build.
Separation capacity: Build your own plant. The slowest instrument and the most expensive, and the only one that removes the chokepoint rather than paying to pass through it.
Recycling and substitution: Research that permanently lowers how much of the basket you need per unit of output. Pays off late, and whether it pays off at all is uncertain.
National stockpile: Buy now, hold against interruption. Immediate coverage, capital sits idle, and the act of buying moves the price against you and against everyone else.
Shared reserve: Contribute to a pooled buffer any member may draw on when a shortage is declared. Cheaper coverage per unit of capital than the national stockpile, conditional on enough members remaining in it.

What the other polities do

The four simulated polities are not scripted and they are not trying to punish you. Each pursues its own supply security given its position on the map, its own read of the shock environment, and what it observes you doing. Two consequences follow that students should be told in advance: they will sometimes cooperate with you when it suits them, and they will sometimes take the tonnes you were counting on without any hostility being involved.

How a round resolves

You commit your allocation for the round. Commitments are simultaneous: you do not see the other polities' choices first.
Contracted volumes are delivered, subject to the reliability of each source.
Remaining supply clears on the open market among whoever still needs it, and the price reflects how thin the residual is.
The round's event, if any, is applied.
If a shortage is declared, the shared reserve pays out to members according to the drawing rules in force.
Coverage, spend and the state of the reserve are reported to you, and the next round opens.

Events

Events are drawn rather than scheduled, and they differ in whether they hit one polity or all of them at once. That distinction is the point of the whole design, so it is worth stating plainly: an idiosyncratic shock is the case pooling handles well, and a systemic shock is the case in which pooling is hardest to sustain.

A separation plant goes offline, and the queue for the remaining capacity lengthens.
A polity introduces licensing on separated exports, throttling volume to non-partners.
Demand jumps as a new product class scales.
A new deposit is confirmed, and prices ease, after the lag needed to bring it into production.
Freight or insurance is interrupted on a major route.
A member of the shared reserve draws heavily, or leaves it.

The event set, the probabilities and whether you are warned in advance are part of what has not been fixed yet.

How you are scored

Scoring rewards coverage achieved per unit of capital spent, across the whole run rather than at the end of it: a buffer that saw you through round three counts even though it is empty by round nine. The design deliberately does not score you against the other polities. A relative score would teach that the object is to finish ahead of Nyra, and the thing worth learning here is that you and Nyra can both finish behind where you could jointly have been.

Teaching material

What a student should be able to do afterwards

Distinguish an outcome that is bad because someone behaved badly from an outcome that is bad because of the structure of the incentives, and say which one they are looking at.
Explain why pooling a reserve raises expected coverage per unit of capital, in terms of the correlation between members' shocks rather than in terms of trust or goodwill.
Identify the condition under which the coordinated arrangement stops being sustainable, and say what would have to change for it to hold.
Recognise that a strategy can be individually correct and collectively self-defeating at the same time, and that this is not a contradiction.
Defend a resource-security allocation made before knowing which shock arrives, using only the information available at the time.

The distinction to insist on

Students reach for "prisoner's dilemma" immediately, and it is the wrong label. In a prisoner's dilemma defection dominates: you defect whatever you expect the other to do, and cooperation is not an equilibrium at all. That is not this game.

Here, if you believe enough others will stay in the shared reserve, staying in is your best reply; if you believe they will leave, leaving is. Both are equilibria, and the coordinated one pays everyone more. That is a stag hunt, and the difference matters enormously in practice: a prisoner's dilemma needs the payoffs changed by enforcement, whereas a stag hunt can sometimes be resolved by nothing more than credible information about what others intend to do. Getting students to see which structure they face is the most transferable thing in the exercise.

There is a commons problem layered on top. Each polity's stockpiling raises the price faced by all of them, and no polity bears the whole cost of its own buying. That part does behave like a standard externality, and it is worth separating from the stag hunt rather than blending the two.

Running it

Single-player, so it can be assigned as homework and debriefed in class. Unlike a multi-team simulation, nobody needs to be scheduled.
Have students commit an allocation in writing, with reasons, before they see the outcome. The reasoning is the assessable artefact; the score is not.
Run it twice. The second run, with the shock structure understood, produces the interesting behaviour and the interesting discussion.
A productive variant: require the second run to be played as though the other polities can read the student's intentions. It changes the answer, and asking why is the lesson.

Debrief questions

At the moment you chose the national stockpile over the shared reserve, what did you believe about the other polities? What would have had to be true for the other choice to be right?
Name the point in your run where your own coverage improved and total system coverage fell. What did you do, and who paid for it?
If every polity had joined the reserve in round one and stayed, would anyone have been worse off? If not, why did it not happen?
You are told a shock is systemic rather than idiosyncratic. Which of your instruments becomes more valuable, and which becomes less? Explain in terms of correlation.
Suppose the pooled reserve could not be exited once joined. Would you have joined? What does your answer say about what the exit option is actually worth?
Identify an assumption in this scenario that you think is wrong about the real world, and say whether fixing it would change the conclusion or only the numbers.

For instructors

Instructor material. Published openly for now. Session parameters, scoring keys and solved case answers are not on this site. Write to us from an institutional address and we will send them.

The design has no fixed parameters yet: no round count, no budget, no prices, no shock probabilities, no payoff table. What follows is guidance on the shape of the exercise, not a key.

Where students go wrong

Labelling it a prisoner's dilemma and stopping. Push for the best-reply reasoning; the label follows from that, not the other way round.
Treating the simulated polities as adversaries with motives. Nothing in the model is hostile. Students who read hostility into it conclude the problem is bad actors, which is the conclusion the exercise exists to dislodge.
Concluding that coordination is naive. The pooled reserve genuinely pays more; the reason it fails is structural fragility under correlated shocks, not softheadedness. Both errors (that cooperation always works, and that it never does) are worth naming.
Optimising the score. The scoring is deliberately non-relative to make this less rewarding, but strong students will still try. Redirect to the written reasoning.

Keeping it out of current affairs

Students will map the polities onto real countries within about a minute. It is worth getting ahead of this: point out that separation capacity and deposits are split differently here than anywhere real, and that the argument is about positions rather than occupants. The exercise is more useful, and considerably easier to teach, when the discussion stays on the incentive structure. Whether a particular real government is behaving well is a different conversation and not one this simulation can settle.

Assessment

Quality of the pre-commitment reasoning, judged against the information available at the time rather than against the outcome.
Whether the student correctly identifies the game structure and justifies the identification.
Whether the correlation argument for pooling is stated in terms of covariance rather than trust.
Whether the student can state the condition for coordination to hold without describing anyone as good or bad.

Case studies

CASE 01

One round, one budget, and a reserve that needs three members

A single decision with enough structure to have a defensible answer, and enough uncertainty that the answer depends on a belief the student has to state out loud.

It is the round before a shock window opens. You have budget for one of two things, not both: you can fund Aster's national stockpile to a level that covers a moderate interruption, or you can buy into the shared reserve.

The reserve pays out only if at least three of the five polities are still members when a shortage is declared. Its coverage per unit of capital is meaningfully better than the stockpile's: that is the whole reason it exists.

What you know

Belmar and Corvane have both signalled they intend to remain members. Neither has broken such a signal in the run so far.
Nyra has left the reserve in every previous round where the shock turned out to be system-wide, and stayed in every round where it did not.
Tavena has not signalled either way. As the swing supplier it is the least dependent on the pool, and the most able to expand its own capacity instead.
You do not know whether the coming shock is idiosyncratic or systemic. You know that both are possible and that systemic shocks are the rarer of the two.

The question

Do you join, or do you stockpile? Commit to one before reading further, and write down the single belief that your answer most depends on.

Why it is not a coin flip

The structure does most of the work. With Belmar and Corvane in, the reserve needs exactly one more member to pay out, and there are two candidates. Nyra is a conditional member: reliable precisely in the states of the world where you need the pool least, and absent in the states where you need it most. So Nyra's membership contributes almost nothing to the outcome you actually care about, even though it counts toward the threshold in the rounds where nothing much happens.

That reduces the problem to Tavena. If Tavena stays, the reserve holds under a systemic shock and dominates the stockpile. If Tavena leaves, you hold a claim on a pool that fails in exactly the state you bought it for, and you would rather have had the inventory.

So the belief your answer depends on is not "will people cooperate" and not "is the pool a good idea". It is narrower and more answerable: how likely is Tavena to remain a member conditional on a systemic shock? Most students discover they had been reasoning about the wrong quantity. That reframing is the point of the case, more than whichever choice they made.

The second-order move

There is a move better than either option, and a minority of students find it: do something this round that raises the probability Tavena stays. Tavena is the least dependent member and therefore the cheapest to retain: a contracted commitment to buy from its expanded capacity, or support for that expansion, changes its payoff from staying. You would be spending part of your budget on someone else's incentives rather than on your own inventory. Notice how counterintuitive that is as a resource-security policy, and how well it works.

Discussion

Nyra's behaviour is perfectly rational given its position. Describe it without using any word that implies a judgement, then say whether doing so changed how you think about it.
You identified one belief your answer hinged on. How would you go about actually estimating it, if this were a real portfolio and not a game?
Why does a member who is reliable in ordinary conditions and absent in a crisis add so little value to a pool? Give the general principle, not the example.
The second-order move spends your security budget on another polity's incentives. Under what conditions is that the highest-return use of the money? Under what conditions is it a waste?

Written as a design exercise. When the simulation exists, this case should be re-checked against the built model, in particular that the three-member threshold and the conditional-membership behaviour are real mechanics and not just plausible ones.

CASE 02

The year every polity improved its coverage and the system got worse

A short case on why five actors can each correctly raise their own security while collectively lowering it, and why the usual advice to diversify does not help here.

Look at a run in which all five polities behaved sensibly. Each raised its coverage ratio. Each could show a board a chart trending in the right direction. Then a systemic shock arrived and four of the five could not meet demand.

Nothing went wrong in the sense of an error being made. What went wrong is that every polity measured its coverage against its own demand in an ordinary year, and bought that coverage from the same thin flow of separated material. Five buffers sourced from one bottleneck are not five independent buffers. They are one buffer, counted five times, and the count is only correct as long as no more than one polity draws at a time.

Why diversification did not save them

Each polity did diversify. Aster contracted across two suppliers; Nyra spread across three. The standard advice was followed, and it failed, because diversification protects against idiosyncratic risk and everyone diversified into the same place. When the constraint is separation capacity rather than ore, buying from more mines does not help if the concentrate from all of them queues at the same plants.

This is a general result and it is worth naming as one: when every actor hedges into the same asset, the hedge becomes correlated with the thing it was meant to hedge against. It appears in bank funding, in airline fuel, in supplier qualification, and in the composition of sovereign reserves.

What would have worked

Funding the shared reserve, which is the only instrument whose payout does not depend on the same bottleneck being available at the moment of the shock.
Building separation capacity, which is slow and expensive and removes the constraint rather than queueing at it. In the run, the polity that started this earliest did worst in the middle rounds and best overall.
Recycling and substitution, which lower the requirement instead of securing the supply. The only instrument that is not zero-sum against the other polities.

Note what those three have in common: each is worse than stockpiling on the measure a polity is most likely to be judged on in the short term, and better on the outcome that actually matters. That gap is not a modelling artefact. It is most of the reason the coordinated outcome stays available and unchosen.

Discussion

Write down a coverage metric that would have revealed the problem before the shock. Then say why an organisation might reasonably decline to adopt it.
The three instruments that would have worked all look worse in the short run. Who inside a government is rewarded for the short-run measure, and what behaviour does that produce?
Give an example from another domain where everyone hedged into the same asset. What broke the correlation there, if anything did?
Is the aggregate outcome here anyone's fault? Answer carefully, and say what work the word "fault" is doing in your answer.

The mechanism described here (correlated buffers sourced through a shared bottleneck) is the load-bearing claim of this case. Confirm it holds in the built model before this page is presented as an account of the simulation rather than of the design.