🎓 Classroom Economics Activity
GOLD
SILVER
BITCOIN
A trading game about strategy, markets, and why people make the decisions they do.
🏇
Gold
Contrarian · 3 pts
🏈
Silver
Balanced · 2 pts
Bitcoin
High Risk · 5 pts
⏰ 45 MINUTES 👥 UP TO 100 STUDENTS 📱 NO TECHNOLOGY NEEDED 🃏 2 ROUNDS
What will students experience?
This is not a lesson about economics — it is economics. Every mechanic maps directly to a real concept.
Incentives
The rules don’t change between rounds — only the rewards do. Yet behaviour shifts dramatically.
📈
Markets & Scarcity
When everyone wants Bitcoin, it becomes scarce. Supply and demand emerges without explanation.
🧠
Game Theory
There is no single best asset. The optimal choice depends entirely on what everyone else holds. Nash Equilibrium in action.
🎭
Information
Keeping your card hidden is a strategy. Lying about it is a tactic. Information has value — asymmetry changes every negotiation.
⚖️
Risk vs. Reward
Bitcoin offers 5 points — the highest reward. Silver destroys it every time. That tradeoff is what investors face daily.
🔄
Trade
Trades happen because each side values what they receive more than what they give up — students feel this gap directly.
Print Cards
Discover Economics · Royal Economic Society · University of Surrey
· × A game developed by University of Surrey · SoSS-Economics
Gold · Silver · Bitcoin — Classroom Trading Game · 63×88mm · Cut on dashed lines

Gold · Silver · Bitcoin

Each sheet has its own 🖨 Print sheet button — opens an isolated print window for that page only. No mixing.

Card Exchange — Important

Within each round, students freely swap cards — this is the trading mechanic. Between rounds, the teacher collects ALL Round 1 cards and replaces with Round 2 cards. The two sets have different point values and are not interchangeable.

🥇 Round 1 · Gold
9 cards — print 4× for 100 students
🥈 Round 1 · Silver
9 cards — print 4× for 100 students
₿ Round 1 · Bitcoin
9 cards — print 4× for 100 students
🥇 Round 2 · Gold
9 cards — print 1× for 100 students (need 17)
🥈 Round 2 · Silver
9 cards — print 5× for 100 students (need 38)
₿ Round 2 · Bitcoin
9 cards — print 5× for 100 students (need 45)
📋 Round 1 · Rules Card
9 cards — print 2× for 100 students (18 copies)
📋 Round 2 · Rules Card
9 cards — print 2× for 100 students (18 copies)
Game Manual
Discover Economics · Royal Economic Society · University of Surrey
Discover Economics · Royal Economic Society
A game developed by
University of Surrey · SoSS-Economics
Teacher & Student Manual · Classroom Economics Activity
GOLD · SIL
VER
· BIT
COIN
A trading game about strategy, markets, and why people make the decisions they do.
45 minutes All ages Up to 100 players No technology needed 2 rounds Physical cards
🥇
Gold
Asset Card
One of three assets. Point values depend on which asset you face. Read your card — it tells you everything.
🥈
Silver
Asset Card
One of three assets. The win cycle is cyclic — like Rock-Paper-Scissors. Which card wins? Check the table.
Bitcoin
Asset Card
One of three assets. In Round 2 you can trade cards with other players. The game changes — figure out how.

"Every decision in this game depends on what everyone else decides. That's not just a game mechanic — it's how real economies work."

Discover Economics · Royal Economic Society
A game developed by University of Surrey
Discover Economics
Royal Economic Society × A game developed by
University of Surrey
SoSS-Economics

Welcome to Discover Economics — a programme by the Royal Economic Society that brings economics to students of all ages, wherever you are from, whatever school you go to.

What is this game?

A fast, physical card game. Each student gets one card. Find opponents. Reveal simultaneously. Score points. Win.

Gold · Silver · Bitcoin is a classroom card game for up to 100 players. Each student holds one card — Gold, Silver, or Bitcoin. They walk around the room, find opponents, and duel by revealing their cards at the same time. In Round 2 the point values change, and students can swap cards with each other before each duel.

🏇 Gold

One of three asset cards. Each has a different point value depending on which asset it faces. The card tells you everything you need to know.

🏈 Silver

One of three asset cards. Point values are printed on the card. Same win cycle applies in both rounds — only the numbers change in Round 2.

₿ Bitcoin

One of three asset cards. Can be traded in Round 2 — but you don't have to. Keeping your card is always a valid choice.

The win cycle

There is a rule printed on every card that tells you which asset beats which. Read your card — it has everything you need to play.

What's in the pack?

Card typeQty for 100 studentsWhen used
🥇 Gold, 🥈 Silver, ₿ Bitcoin — Round 1~34 / ~33 / ~33Round 1 only
🥇 Gold, 🥈 Silver, ₿ Bitcoin — Round 2~34 / ~33 / ~33Round 2 only
📋 Rules Card — Round 1~18 cardsReference during Round 1
📋 Rules Card — Round 2~18 cardsReference during Round 2

Print 4 sheets of each asset card type (9 per A4) and 2 sheets of each rules card type. Total: ~216 asset cards + 36 rules cards.

Discover Economics · Royal Economic Society
A game developed by University of Surrey

How to Allocate Cards

Round 1 and Round 2 use different distributions — for mathematical reasons, not arbitrary ones.

Round 1 — Why equal thirds?

In Round 1 all wins are worth 2 points. The Nash Equilibrium for equal payoffs is exactly ⅓ each. Starting the room at that distribution means no asset has a structural advantage, and final scores cluster together — which is the direct, felt demonstration of equilibrium.

Round 2 — Why seed at Nash Equilibrium?

With asymmetric payoffs the equilibrium shifts to Gold ~17% · Silver ~37% · Bitcoin ~46%. Seeding at that distribution creates immediate, realistic trading pressure from the first duel rather than waiting for imbalance to develop. Students experience the market in motion from the start.

The rounding rule — no arbitrary "+1"

Round 1 formula

Divide the class size N by 3. The remainder (0, 1, or 2) is distributed as follows:

N mod 3GoldSilverBitcoin
0 (e.g. 30)N ÷ 3N ÷ 3N ÷ 3
1 (e.g. 40)N ÷ 3N ÷ 3N ÷ 3 + 1
2 (e.g. 32)N ÷ 3N ÷ 3 + 1N ÷ 3 + 1

The spare card(s) go to Bitcoin first, then Silver — never Gold — because Bitcoin dominates in Round 2 anyway, and this creates better opening trading tension.

Round 2 formula

Compute Gold and Silver by rounding to the nearest whole number. Bitcoin always gets the remainder — this guarantees the total is exactly N with no leftover cards.

AssetFormula
Goldround(N ÷ 6)
Silverround(N × 3 ÷ 8)
BitcoinN − Gold − Silver

Bitcoin is calculated last as the remainder so rounding errors never accumulate. The result stays within 1–2 cards of the true NE proportions for any class size.

Discover Economics · Royal Economic Society
A game developed by University of Surrey

Class Size Reference

Quick-lookup table — how many of each card to print per round.

Quick-lookup table — common class sizes

Students (N) Round 1 — Equal thirds Round 2 — Nash Equilibrium seed
🥇 Gold🥈 Silver₿ Bitcoin 🥇 Gold🥈 Silver₿ Bitcoin
15555 267
20677 389
24888 4911
25889 4912
3010101051114
3511121261316
4013131471518
4515151581720
5016171781923
60202020102228
75252525122835
100333334173845

Practical tip — print a small surplus

Print 2–3 extra cards of each type per round. Cards get lost, torn, or pocketed during trading. Spare cards also let you correct the distribution mid-session if a card goes missing and one asset becomes noticeably scarce.

Discover Economics · Royal Economic Society
A game developed by University of Surrey

Card Exchange — What's Allowed?

Understanding which cards can be swapped, and when, is essential to running the game correctly.

The core rule

Round 1 cards and Round 2 cards have different point values printed on them. They are two separate sets. You cannot mix them. The teacher manages the transition between rounds by collecting all Round 1 cards and replacing the full deck with Round 2 cards.

✅ Allowed Swapping a Round 1 card for another Round 1 card during Round 1's trading phase. All three asset types are valid to hold.
✅ Allowed Swapping a Round 2 card for another Round 2 card during Round 2's trading phase. All three asset types are valid to hold.
❌ Not allowed Trading a Round 1 card for a Round 2 card (or vice versa). Different point values would create unfair scoring and confusion.
❌ Not allowed Carrying a Round 1 card into Round 2. When Round 2 begins, all Round 1 cards are collected and replaced.

Why two separate card sets?

The whole point of Round 2 is that the same game with different rewards produces different behaviour. If students held Round 1 cards (showing 8 pts per win) while others held Round 2 cards (showing 3 or 5 pts), they'd be playing a different game — and the lesson about incentives shaping behaviour would be lost.

Trading rules within Round 2

Voluntary

Both students must agree. No one can be forced to trade. Refusing a trade is a valid strategic choice.

One-for-one

You swap your card for their card. You cannot hold two cards at once, and you cannot trade without getting something back.

Hidden until reveal

During the trading window, do not show your card. Negotiation is verbal only. You may say what you hold — truthfully or not.

Bluffing is allowed

You may lie about what you're holding during negotiations. This is intentional — it mirrors real markets where information is incomplete and not always trustworthy.

No trading in Round 1

Round 1 is pure strategy. Cards are fixed. Students can only choose who to challenge — not what to hold. The trading mechanic is exclusively a Round 2 feature.

After trading closes

When the teacher signals trading is over, everyone keeps whatever card they currently hold. Find an opponent and reveal simultaneously.

Discover Economics · Royal Economic Society
A game developed by University of Surrey

Round 1 — Pure Strategy

No trading. No negotiation. Just you, your card, and your read on the room.

Setup

Hand each student one Round 1 card — roughly equal thirds of Gold, Silver, and Bitcoin. Students should not compare cards yet. Distribute a Round 1 Rules card to each group for reference.

How a duel works

1
Find any opponent
2
Cards face-down
3
3–2–1, flip together
4
Score & record
5
New opponent

Round 1 — no card swapping

Cards are fixed throughout Round 1. Students keep their assigned card. Strategy means choosing who to challenge, not what to hold.

Can you refuse a duel?

No. If someone challenges you, you play. You can choose who you approach — but you cannot turn down a challenge. Sitting out scores zero. Inaction is still a choice, and it has a cost.

Duration

Let students play freely for 5–8 minutes, circulating the room. Encourage them to play different opponents each time.

The win cycle

🥇
Gold
beats
🥈
Silver
beats
beats
Bitcoin

Cyclic — like Rock–Paper–Scissors.

Scoring

OutcomePoints
Win+8 points
Lose0 points
Draw (same asset)+1 point each

Discussion after Round 1

  • How did it feel when you won? When you lost? Did luck play a part?
  • Did you try to read your opponent before revealing? What gave them away?
  • Did you wish you had a different card? Did anyone try to get a different card? (Spoiler for Round 2.)
Discover Economics · Royal Economic Society
A game developed by University of Surrey

Round 2 — Trade & Reveal

Same game. Different rewards. Now you can trade. Everything changes.

Before Round 2 begins — teacher action

Collect all Round 1 cards. Hand out one Round 2 card to each student — again roughly equal thirds. Do not allow students to carry Round 1 cards into Round 2. Distribute the Round 2 Rules cards.

New point values

Win with…Points
🥇 Gold beats Silver+3 pts
🥈 Silver beats Bitcoin+8 pts
₿ Bitcoin beats Gold+5 pts
Any draw (same asset)+1 each

⚠ Critical — Bitcoin draws

Bitcoin vs Bitcoin = +1 point each. Not 5. The draw rule applies to all assets equally. Write this on the board.

Which card should you trade for?

That is for you to figure out. Read your card, look at who wins around you, and decide. The scoring table above tells you everything you need — the rest is your call.

The trading phase

Before each duel, a 45-second trading window opens. Students may swap cards with anyone willing.

Trading rules (summary)

Voluntary — both must agree
One-for-one — swap your card for theirs
Hidden — no showing cards, verbal only
Bluffing allowed — you may lie
Trades: refusable. Duels: not. Once trading closes and you face an opponent, the reveal happens. No one can turn down a duel.

How a Round 2 duel works

1 Teacher opens 45-second trading window
2 Negotiate verbally — swap cards if you want
3 Trading closes — find an opponent, cards face-down
4 Count 3–2–1 — reveal simultaneously
5 Score and record — new trading window opens

Market freeze rule (if needed)

If everyone holds Bitcoin and no one will trade, introduce: "No player may hold Bitcoin for more than 3 consecutive duels." Frame it as a regulatory intervention — itself a real-world lesson.

Discover Economics · Royal Economic Society
A game developed by University of Surrey

Score Sheet

One box per duel. Fill in your points as you go. Total at the end.

Name: _______________________________________________
School: _____________________________

ROUND 1 — Equal Payoffs · Win = 8 · Draw = 1 · Lose = 0 · No trading

Points per duel
Running total
Round 1 Total: ________ Asset held all round:   🥇 Gold   /   🥈 Silver   /   ₿ Bitcoin   (circle one)

ROUND 2 — Asymmetric Payoffs · Trading allowed · Gold=3 · Silver=2 · Bitcoin=5 · Draw=1

Points per duel
Running total
Round 2 Total: ________ Cards traded: _______ → _______ → _______ → _______
Grand Total   (R1 + R2) ____________

Tips for players

  • Before challenging someone, try to read what asset they might hold. Who have they been challenging? What are they saying during trades?
  • Your information is your leverage. In Round 2, do not immediately reveal your card when someone asks during the trading window.
  • If everyone around you is chasing Bitcoin, that might be the worst time to hold Bitcoin — because Silver players are about to do very well.
  • A draw still earns 1 point. Never refuse a duel just because you might draw — 1 point is always better than 0.
Discover Economics · Royal Economic Society
A game developed by University of Surrey

Teacher Guide & Debrief

Run the game first. Reveal the economics after. This page is for your eyes only before play begins.

Session structure (45 mins)

1

Introduction (5 mins)

Hand out cards. Explain only the rules printed on the cards. Do not discuss strategy, optimal choices, or what beats what beyond what is already printed. Let students discover.

2

Round 1 (10 mins)

Distribute Round 1 cards — equal thirds. 5–8 minutes of free duelling. Collect top scores. Brief debrief using the experiential questions on page 5.

3

Round 2 (12 mins)

Collect all Round 1 cards first. Distribute Round 2 cards. Announce the new point values. Open 45-second trading windows before each duel. Run 4–5 windows. Keep energy high.

4

Debrief (15 mins)

Now reveal the economics. Use the questions and explanations on this page. This is where the concepts land — after students have felt them.

What to watch for during play

The Bitcoin Rush

In Round 2, students will chase Bitcoin (5 pts). This is understandable — it looks best. Do not correct them. Let the room discover what actually happens.

The Quiet Silver winners

As Bitcoin becomes common, Silver holders will quietly accumulate points. Don't point this out during play. Save it for the debrief — it lands much harder when students work it out themselves.

The Contrarian Few

A handful of students may hold Gold throughout. If Silver becomes common (as it should at equilibrium), Gold earns 3 pts per duel — the highest reward. These students are doing second-order reasoning without knowing it.

Market Signalling

"Everyone is going Bitcoin!" — true, false, or a deliberate bluff. Notice who says it and whether it changes behaviour. This is pure market dynamics.

Market Freeze (if needed)

If everyone holds Bitcoin and refuses to trade, invoke: "No player may hold Bitcoin for more than 3 consecutive duels." Frame it as a regulatory intervention — itself a lesson worth noting.

Can a student refuse a duel?

Trading: yes. Refusing a trade is a valid strategic choice — that is what voluntary exchange means.
Duels: no. Once trading closes and you face an opponent, the reveal happens. You cannot opt out.
If a student refuses to play, they score zero for that round. Frame it as their decision: "Sitting out is a choice — but it has a cost." That is itself an economics lesson: inaction is still a decision, and markets do not wait for you.

Discover Economics · Royal Economic Society
A game developed by University of Surrey

The Economics Reveal

Ask each question after both rounds. Let students answer first, then read the explanation aloud.

Why did behaviour change in Round 2 even though the rules were identical?

Debrief: The payoffs changed — and payoffs are incentives. When you reward something differently, people do it differently. This is the foundation of how economists think about policy, taxes, and market design.

Who held Bitcoin? Did the high reward always pay off?

Debrief: Bitcoin earns 5 pts against Gold — but Silver beats Bitcoin every time for 2 pts. As more people chased Bitcoin, Silver became the rational counter. Bitcoin is high risk, high reward: it only works if you are not facing Silver.

Who held Silver? Was it boring — or quietly effective?

Debrief: Silver earns 2 pts against the most popular card (Bitcoin). In a Bitcoin-heavy room, Silver is the rational choice — not glamorous, but consistent. In real markets, this is called a contrarian strategy: not chasing what everyone else wants.

Who held Gold? Why is the 3-pt card the least popular?

Debrief: Gold earns 3 pts against Silver — the highest win reward — but Bitcoin (held by ~46% of players) beats Gold for 5 pts. The risk of losing to Bitcoin outweighs the reward of beating Silver. Rational players avoid Gold when Bitcoin is common.

The Nash Equilibrium — the key teaching moment

In Round 2, there is a mathematically stable mix: Gold ~17% · Silver ~37% · Bitcoin ~46%.

At this distribution, no player can improve their average score by switching assets — because the room is already balanced against every strategy. This is a Nash Equilibrium: the point where individual decisions, taken independently, produce a stable collective outcome.

Ask: did your class drift toward these proportions during Round 2? Usually yes — without being told.

Did anyone lie during trading? Did it work?

Debrief: Information was hidden and unverifiable. This is called information asymmetry — when one side of a transaction knows more than the other. It is how real financial markets, job markets, and negotiations work.

Closing message

"Economics is not just about money. It is about decisions — especially when your outcome depends on what everyone else decides. Every time you traded, predicted, bluffed, or held your nerve in this game, you were doing economics."

Discover Economics · Royal Economic Society
A game developed by University of Surrey

Glossary

Plain-English definitions for every concept in this game.

Asset
Something with value that can be owned or traded. In real life: shares, property, gold, cryptocurrencies. In this game: your card.
Trade
Swapping one thing for another. Trades happen because each side values what they're getting more than what they're giving up. That gap in perceived value is why trade exists at all.
Incentive
A reward (or penalty) that shapes behaviour. Changing the points in Round 2 changes incentives — which is why behaviour changes even though the underlying game is the same.
Risk vs. Reward
The tradeoff between the size of a potential gain and the likelihood of a loss. Bitcoin offers a huge reward — but Silver destroys it every time. Evaluating this is what investors do every day.
Supply & Demand
When many students want Bitcoin but few hold it, demand exceeds supply. In a real market, Bitcoin's price would rise until fewer people wanted it. In the game: you can't get the card you want.
Game Theory
The study of how people make decisions when outcomes depend on what others decide. The entire game is a game-theory problem — your best move depends entirely on what everyone else is doing.
Strategic Game
Any situation where your outcome depends on the choices of others, not just your own. Chess, negotiations, auctions, elections, and financial markets are all strategic games.
Info. Asymmetry
When one side in a negotiation knows more than the other. Keeping your card hidden creates information asymmetry — just like in many real markets.
Contrarian
Someone who does the opposite of the crowd. Gold is the contrarian card — it earns the highest win reward (3 pts vs Silver) but is held least often at equilibrium (~17%), because the most popular asset, Bitcoin (~46%), beats it. Gold only pays off when Silver is common — a second-order bet against the crowd.
Market Signalling
Communicating (or mis-communicating) information to change how others behave. "Everyone is going Bitcoin!" may be true, false, or a deliberate bluff — but it can change decisions either way.
Specialisation
Focusing on what you are best at, then trading for what you need. Countries, companies, and people specialise — it is the foundation of why trade exists at all.

Quick Reference — Round 1

Match-upWinnerPts
Gold vs SilverGold+8
Silver vs BitcoinSilver+8
Bitcoin vs GoldBitcoin+8
Same assetDraw+1 each

No trading in Round 1. Cards are fixed.

Quick Reference — Round 2

Match-upWinnerPts
Gold vs SilverGold+3
Silver vs BitcoinSilver+2
Bitcoin vs GoldBitcoin+5
Same assetDraw+1 each

Bitcoin vs Bitcoin = +1 each, not 5. Trading allowed within Round 2 only.

Discover Economics
Royal Economic Society
Bringing real economics into the classroom
A game developed by
University of Surrey
SoSS-Economics
Score Tool
Discover Economics · Royal Economic Society · University of Surrey

Win Count Analyser

Enter the number of wins per asset after a round. Updates live.

Blog
Discover Economics · Royal Economic Society · University of Surrey
Discover Economics · University of Surrey · Teaching Blog

Gold · Silver · Bitcoin

Why the Rules of the Game Reveal the Rules of the Economy
NASH EQUILIBRIUM TAXATION CURRENCY POWER

You have just played two rounds of the same game with the same three assets — Gold, Silver, and Bitcoin. Same cyclic win rule. Same opponents. Yet behaviour almost certainly changed between the rounds. That shift is not a coincidence. It is the core mechanism of modern economics.

In this blog we unpack what happened in each round, why it happened, and what two powerful ideas from economics it mirrors: one ancient — the search for equilibrium — and one very modern — how taxes and currency strength reshape who wins even before the game begins.

Round 1: The Symmetric Game and Nash Equilibrium

Why did everyone get 8 points for a win?

In Round 1, every win earns 8 points regardless of which asset you hold. Gold beats Silver for 8. Silver beats Bitcoin for 8. Bitcoin beats Gold for 8. The three assets are perfectly symmetric in their payoffs.

The key question: If all wins pay equally, what is the “right” way to distribute Gold, Silver, and Bitcoin across the room?

The Nash Equilibrium — a level playing field finds its own balance

John Forbes Nash Jr. showed in 1950 that in any finite game — any game with a limited number of players and strategies — at least one equilibrium point always exists. An equilibrium is a state where no individual player can improve their expected score by switching asset, given what everyone else is doing. Nash's proof earned him the Nobel Prize in Economics in 1994.

👤 For students

Imagine everyone in your class is holding a Rock, Paper, or Scissors card. If you hold Scissors and nearly everyone has Rock — you keep losing. So you switch to Paper. But once lots of people switch to Paper, Scissors become good again. The chase never ends, unless everyone lands on a mix where nobody can do better by switching. That resting point is the Nash Equilibrium.

Because Round 1 is a symmetric game — every asset earns exactly the same reward per win — the mathematics of mixed-strategy equilibria guarantees a unique stable point:

Round 1 Nash Equilibrium
GOLD
SILVER
BITCOIN

This is the only distribution where no student, knowing the composition of the room, has a reason to switch cards. If Gold falls below a third, Gold-holders win more often against the now-abundant Silver, making Gold attractive again — automatically restoring balance. Each asset self-corrects the same way.

Why ⅓ each? The maths behind the intuition

Let p be the fraction of players holding Gold, q Silver, r Bitcoin, with p + q + r = 1. A Gold-holder beats Silver (probability q) for 8 pts, so their expected score per duel is 8q. A Silver-holder scores 8r. A Bitcoin-holder scores 8p. For no asset to offer a better expected return — the Nash indifference condition — we need:

8q  =  8r  =  8p   ⇒   p = q = r =

The equal payoffs force the room to split evenly. This is the unique mixed-strategy Nash Equilibrium of the symmetric game.

Round 2: When the Payoffs Change, Everything Changes

In Round 2, wins become asymmetric: Gold earns 3 pts for beating Silver, Silver earns 2 pts for beating Bitcoin, Bitcoin earns 5 pts for beating Gold. The cyclic win rule is identical. But the rewards have changed dramatically — and so has the equilibrium.

Asset Round 1 win Round 2 win NE share (R2)
🏇 Gold +8 pts +3 pts ~17%
🏈 Silver +8 pts +2 pts ~37%
₿ Bitcoin +8 pts +5 pts ~46%

The new Nash Equilibrium shifts to approximately Gold 17% · Silver 37% · Bitcoin 46%. Bitcoin now needs to be the most common card before the others become rational, because its 5-point reward makes it so attractive that only abundance makes it dangerous.

Incentives shape strategy. That is the first great lesson of economics, and your class just felt it.

Reading Round 2 as Taxation

The payoff change as an asymmetric tax

One scientifically valid way to interpret the move from Round 1 to Round 2 is as the introduction of asymmetric taxation on different assets. In Round 1, all wins earn 8 points — a perfectly flat system with no distortions. In Round 2:

  • Gold's reward falls from 8 to 3 pts — a cut of 62.5%.
  • Silver's reward falls from 8 to 2 pts — a cut of 75%.
  • Bitcoin's reward stays at 5 pts — relatively favoured in the new landscape.

A government that imposes a higher capital gains tax on one type of investment (say, gold bullion) than another (say, equities) does not change the underlying assets — it changes the rewards for holding them. Investors reallocate. The Nash Equilibrium moves. Exactly as your class moved.

👤 For students

Imagine the school canteen taxes chocolate bars more than crisps. Even if you like both equally, you buy fewer chocolate bars — not because they changed, but because the rules around them did. Taxes change choices without changing the things themselves.

A key result in public economics is that taxes drive a wedge between the private reward of an activity and its social benefit. When that wedge is the same for all activities — as in Round 1 — no distortion occurs. When the wedge is asymmetric — as in Round 2 — players move away from what they would have chosen in a neutral market. Economists call the lost value a deadweight loss.

The academic literature on asymmetric tax competition — particularly Bucovetsky (1991) and the extensive work surveyed by Wilson (1999) — shows precisely this: when markets apply differential tax rates, capital flows toward lower-taxed assets and the equilibrium allocation shifts away from the socially optimal one. Your classroom reproduced this in under ten minutes.

Reading Round 2 as Currency Competition

Gold, Silver, and Bitcoin as currencies

The names in the game are not accidental. The three assets can stand for three types of national currency competing on global markets:

🏇 GOLD  ≈  BRITISH POUND (GBP)

Historically dominant, high prestige — Gold earns +3 pts against Silver, the highest single-match reward. But it is vulnerable to Bitcoin (the reserve currency). The pound was the world's reserve currency for over a century before the dollar displaced it after World War II.

🏈 SILVER  ≈  SWISS FRANC (CHF)

The “safe haven” currency. Silver reliably beats Bitcoin (+2 pts every time). It does not deliver the highest returns, but it is the most consistent. In periods of global uncertainty, investors flock to the Swiss franc exactly as Silver-holders profit when everyone chases Bitcoin.

₿ BITCOIN  ≈  US DOLLAR (USD)

The dominant reserve currency. Bitcoin's 5-point reward mirrors the structural advantages of the dollar: seigniorage, geopolitical leverage, lower borrowing costs. Over 60% of global foreign exchange reserves are held in dollars (IMF, 2024) — mirroring Bitcoin's 46% Nash share. But it is also the most targeted card in the room.

Purchasing Power Parity — and why it is not enough

The standard economic theory for valuing currencies is Purchasing Power Parity (PPP), which holds that, in the long run, exchange rates should adjust so that a basket of goods costs the same in every country (Cassel, 1918; Taylor & Taylor, 2004). PPP is like Round 1: a world where the rules are neutral and symmetric, and no currency should persistently outperform another.

👤 For students

PPP is the idea that a cup of hot chocolate should cost roughly the same “effort” wherever you buy it. If it is much cheaper in Switzerland, people would buy it there and sell it at home — until prices balanced out. That automatic balancing is purchasing power parity. The Economist tracks this every year using the Big Mac Index.

But PPP consistently fails in the short and medium run, and often in the long run too (Rogoff, 1996). Why? Because other factors create asymmetric advantages — exactly like Round 2's asymmetric payoffs:

  • Safe-haven status (Swiss Franc, USD): Investors flee to these currencies in crises, pushing their value above PPP — just as Silver rises rationally in a Bitcoin-heavy room.
  • Reserve currency demand (USD): Countries must hold dollars to trade in oil and many commodities. This structural demand keeps the dollar strong regardless of PPP — like Bitcoin's 46% equilibrium share, higher than “fair” because its rewards make it the default choice.
  • Interest rate differentials & the Balassa–Samuelson effect: Higher interest rates attract capital that strengthens a currency beyond PPP. Richer, more productive countries have currencies that trade above PPP because their service sectors are more expensive (Balassa, 1964; Samuelson, 1964).
  • Trade restrictions and transaction costs: Tariffs and barriers prevent goods being freely arbitraged across borders, allowing persistent deviations from PPP (Krugman & Obstfeld).

The economic insight: Currency strength, like card strength in Round 2, is relative to the distribution of everyone else's choices. A currency can be objectively powerful and still be strategically vulnerable when too many people depend on it. China holds over $800 billion in US Treasury bonds — a position that gives it strategic influence, mirroring the Silver player who beats Bitcoin precisely because Bitcoin is so common.

What Your Game Actually Modelled

Together, the two rounds recreate three ideas that span centuries of economic thought:

1
Nash Equilibrium (Round 1)

In a level playing field, rational agents self-sort into a stable mixed distribution. No one has to be told what to do; the incentive structure finds its own balance. Nash (1950, 1951) proved this is always true for finite games.

2
Incentive Distortion (Round 2 as taxation)

Changing relative rewards — even without changing the rules — shifts the equilibrium. This is the economic case for why asymmetric tax systems distort investment and allocation. Ramsey (1927), Diamond & Mirrlees (1971).

3
Beyond Purchasing Power (Round 2 as currency)

In a neutral world all assets are equal — PPP holds, all wins pay the same. In the real world, structural asymmetries create persistent deviations. Cassel (1918), Balassa (1964), Samuelson (1964), Taylor & Taylor (2004).

“The rules of the game are the rules of the economy. Change the rules and you change what rational people do — without changing the people at all.”

References

Academic

[1] Nash, J.F. (1950). Equilibrium points in n-person games. Proceedings of the National Academy of Sciences, 36(1), 48–49.
[2] Nash, J.F. (1951). Non-cooperative games. Annals of Mathematics, 54(2), 286–295.
[3] von Neumann, J. and Morgenstern, O. (1944). Theory of Games and Economic Behavior. Princeton University Press.
[4] Cassel, G. (1918). Abnormal deviations in international exchanges. The Economic Journal, 28(112), 413–415.
[5] Balassa, B. (1964). The purchasing-power parity doctrine: A reappraisal. Journal of Political Economy, 72(6), 584–596.
[6] Samuelson, P.A. (1964). Theoretical notes on trade problems. Review of Economics and Statistics, 46(2), 145–154.
[7] Ramsey, F.P. (1927). A contribution to the theory of taxation. The Economic Journal, 37(145), 47–61.
[8] Diamond, P.A. and Mirrlees, J.A. (1971). Optimal taxation and public production I–II. American Economic Review, 61(1/3).
[9] Rogoff, K. (1996). The purchasing power parity puzzle. Journal of Economic Literature, 34(2), 647–668.
[10] Taylor, A.M. and Taylor, M.P. (2004). The purchasing power parity debate. Journal of Economic Perspectives, 18(4), 135–158.
[11] Bucovetsky, S. (1991). Asymmetric tax competition. Journal of Urban Economics, 30(2), 167–181.
[12] Wilson, J.D. (1999). Theories of tax competition. National Tax Journal, 52(2), 269–304.
[13] Harsanyi, J.C. (1973). Games with randomly disturbed payoffs. International Journal of Game Theory, 2(1), 1–23.
[14] IMF (2024). Currency Composition of Official Foreign Exchange Reserves. International Monetary Fund.

For further reading — accessible for students

Dixit & Nalebuff (1991) — Thinking Strategically. W.W. Norton. The classic introduction to game theory for non-economists. Clear, funny, and packed with real examples.
The Economist's Big Mac Index — economist.com/big-mac-index — A live, interactive tool showing PPP deviations for currencies worldwide, updated annually.
Quanta Magazine (2018) — “Why Winning in Rock-Paper-Scissors (and in Life) Isn't Everything.” An excellent accessible explanation of Nash Equilibrium in cyclic games.
Yale Open Courses — ECON 159, Lecture 10 — oyc.yale.edu — Professor Ben Polak explains mixed strategies in everyday contexts, including taxes. Free to watch.
Osborne, M.J. (2004) — An Introduction to Game Theory. Oxford University Press. More formal, but free online at economics.utoronto.ca — ideal for older students ready for the maths.
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