SM-GT-CS-01 · Playing the Right Game · Student Toolkit

Learn game theory by playing with it

Five small labs. Each one teaches one big idea from the course. Follow the “Try this” steps, watch the explanations, then play freely. Simple English on purpose — the ideas are the hard part, not the words.

Lab 1 · Session 1

The Payoff Matrix Lab

A payoff matrix is a small table that shows what each player gets from every combination of choices. When you can read one, “irrational” behaviour suddenly makes sense.

Try this:
  1. Load the Samsung & Apple preset.
  2. Press Find dominant strategy — read the explanation slowly.
  3. Press Find Nash Equilibrium — the gold cell is where the game “rests”.
  4. Press Best for both — see the better outcome nobody reached. That gap is what negotiation is for.
  5. Now change some numbers yourself and press the buttons again. When does the equilibrium move?

Step 0 · Where do these numbers come from?

Students always ask: where do the 6s and 9s come from? Answer: you score each outcome 0–10 for its TOTAL value to that player — money, strategic position, reputation, future options. Try each cell yourself, then reveal the model’s reasoning.
Cell 1 · Samsung supplies + Apple litigates (what really happened). Samsung keeps its $7–8B yearly component revenue and absorbs legal costs. Apple keeps its supply chain and pressures Samsung in court. Score both players 0–10, like: 6, 6.
Your estimate:
Cell 2 · Samsung supplies + Apple settles. Peace, and the parts keep flowing. But Apple gives up its court pressure. Score both.
Your estimate:
Cell 3 · Samsung restricts + Apple litigates. Samsung cuts Apple off in the middle of the legal war.
Your estimate:
Cell 4 · Samsung restricts + Apple settles. The dispute ends, but so does the relationship.
Your estimate:
Preset:
Each cell shows: Row player’s points, Column player’s points (0–10). Higher = better for that player. Click any number to change it.
Ready.
Load a preset and press a button. I will explain every step in plain words.
Words to know: Payoff — what a player gets (not only money: reputation and relationships count too) Dominant strategy — a choice that is better no matter what the other player does Nash Equilibrium — a resting point: nobody can do better by changing alone
Lab 2 · Session 2

The BATNA & ZOPA Lab

Your BATNA is your best plan B — what you really do if there is no deal. The ZOPA is the space where a deal is possible. Watch how the space moves when a plan B changes.

Try this:
  1. Move the two sliders. The green bar is the ZOPA — where a deal can happen.
  2. Push the seller’s minimum above the buyer’s maximum. The bar turns red: no deal is possible.
  3. Press the three Disney & Fox story buttons in order and watch $18.9 billion of movement.
  4. Use the Plan B calculator: a big plan B with a small chance is a small plan B.

Step 0 · Where do these numbers come from?

Where do the wall numbers come from? Each wall is the value of the alternative behind it. Estimate each one, then reveal.
Wall 1 · Fox’s minimum, December 2017. Disney offers 52.4 (in $ billions) and is the only serious buyer. Fox’s alternative is staying independent, with an uncertain streaming future. Where is Fox’s wall?
Your estimate:
Wall 2 · The Comcast effect, June 2018. Comcast bids 65 in cash. Nothing about Fox’s business changed that day. Where is Fox’s wall now?
Your estimate:
Wall 3 · Risk-adjusting the two bids. Comcast: 65 cash, heavier regulator risk (say ~60–65% chance of completing). Disney: 71.3 at ~90%+. Which bid is really worth more?
Your estimate:
52
75

The Disney & Fox story (numbers in $ billions, simplified)

The walls can move.
The edges of the ZOPA are made by the two plan Bs. Change a plan B → the wall moves → the deal changes.

Plan B calculator (risk adjustment)

My plan B is worth million if it works.

The chance it really works is %.

The four steps (write them down!)

1 · Brainstorm all plan Bs — even uncomfortable ones.
2 · Develop the best one: get the real quote, make the real call.
3 · Risk-adjust: value × chance (use the calculator).
4 · Write it down. A plan B that is only an idea is only a hope.
Words to know: BATNA — Best Alternative To a Negotiated Agreement (your plan B) ZOPA — Zone Of Possible Agreement Risk-adjust — multiply value by the chance it happens
Lab 3 · Session 2

The Repeated Game Lab

Play the Prisoner’s Dilemma six times against the computer. Points each round: both cooperate = 3 each · both defect = 1 each · you defect against a cooperator = you 5, they 0. Watch how the future changes behaviour.

Try this:
  1. Play 6 rounds against Tit-for-Tat. Try defecting once — see what happens next round.
  2. Play against Grim Trigger and defect in round 2. Watch the rest of the game. That is why some betrayals can never be repaired.
  3. Turn on the round-4 warning (“the game may end soon”) and notice your own thinking change. That feeling is your discount factor falling.
  4. Best total score usually comes from cooperation. Check if that is true for you.

Step 0 · Where do these numbers come from?

Where do 3, 0, 5 and 1 come from? From a business story you already know: the price war. Estimate each payoff, then reveal.
Payoff 1 · Both hold prices (cooperate). Picture two rival suppliers, each deciding privately: hold prices, or secretly discount. Payoffs are profit in $M. If both hold, what does each earn?
Your estimate:
Payoff 2 · One discounts alone. One firm secretly discounts while the other holds. What do they each earn?
Your estimate:
Payoff 3 · Both discount. Both firms discount. Market shares end up unchanged. What does each earn?
Your estimate:
Opponent:
You: 0
Computer: 0
Round: 1 / 6
Round 1.
Make your first choice. Remember: this is not a one-time game.
Words to know: Defect — choose yourself and hurt the other player Discount factor (δ) — how much you care about future rounds Tit-for-Tat — start nice, then copy the other player’s last move Shadow of the future — tomorrow’s punishment keeps today honest
Lab 4 · Session 4

The Fair Shares Lab (Shapley Value)

Three companies can work together. How should they split the profit? “Equal thirds” feels fair — but the Shapley value measures what each partner really adds. It averages each player’s contribution over every possible joining order.

Try this:
  1. Load the Consortium preset (the class capstone) and press Calculate.
  2. Read the orderings table: each row asks “if partners join in this order, how much does each one add when they arrive?”
  3. Compare the bars: Shapley share vs equal thirds. Who is under-paid by an equal split? That partner will cause trouble later.
  4. Try the Vaccine partnership preset: two partners who are worth almost nothing alone.

Step 0 · Where do these numbers come from?

The scenario: three companies consider a smart-energy joint venture, “Meridian Grid”. Each value below is the yearly operating profit (in $ millions) that a group could earn on its own. Read each story, write your own estimate first, then reveal the model’s number. Disagreeing with the model is allowed — arguing about these values is exactly what real partners do.
A alone — the Platform (software and data). Sells analytics subscriptions to utilities on good margins — but with no hardware of its own, its data feed is limited and sales are slow.
Your estimate ($M per year):
B alone — the Maker (hardware manufacturer). Sells generic smart meters. Big factory, big revenue — and brutal price competition against identical rivals.
Your estimate ($M per year):
C alone — the Distributor (channel and services). Resells other firms’ equipment through its sales network and earns service fees. No product of its own.
Your estimate ($M per year):
A + B — product without channel. Meters with built-in analytics: a differentiated, premium product. But no distribution network — they must sell direct.
Your estimate ($M per year):
A + C — channel without hardware. The platform flows through the Distributor’s channel and service network — analytics retrofitted onto meters customers already own.
Your estimate ($M per year):
B + C — hardware without brains. Generic meters pushed through the channel: wider reach for an undifferentiated product.
Your estimate ($M per year):
All three together — the full stack. Premium product, full channel reach, service revenue — everything connected.
Your estimate ($M per year):
Preset:
Why this matters.
When a partner’s real contribution is bigger than their official share, the structure is under tension — expect renegotiation or conflict. Check every joint venture this way.
Words to know: Coalition — a group of players working together Marginal contribution — how much value you add when you join Shapley value — your average contribution over all joining orders = your fair share
Lab 5 · Session 4

The Auction Game (Winner’s Curse)

A licence is for sale. Its true value is the same for everyone — but nobody knows it exactly. You and three rivals each get a different estimate. Highest sealed bid wins and pays its bid. Profit = true value − your bid.

Step 0 · Where do these numbers come from?

One question before you bid.
Why do the four bidders bid differently?. The licence has one true market value (near 100 points) — the same for whoever wins it. So why does every bidder act differently?
Your estimate:
Try this:
  1. Play round 1 naturally. If you bid close to your estimate and win — check your profit.
  2. Ask: why did I win? Usually because your estimate was the most optimistic one.
  3. Play again and shade your bid (bid clearly below your estimate). Compare your results over 5 rounds.
  4. Rule of thumb: shade more when uncertainty is high and when there are many bidders.
Your analyst’s estimate
—
True value is somewhere near this — could be higher or lower. 3 rivals have their own estimates.
Your sealed bid:
Your results
Rounds: 0
Wins: 0
Total profit: 0
A professional bidder’s goal is profit, not winning. Winning at a loss is the curse.
Round 1.
Look at your estimate, choose your bid, and press Bid. I will show everyone’s cards afterwards.
Words to know: Sealed bid — everyone bids secretly at the same time Winner’s curse — the winner is usually the most optimistic — and often over-pays Shading — bidding below your estimate on purpose, for safety
SM-GT-CS-01 · Playing the Right Game · Sigma Mentoring / Dagda Media © 2026 · Companion to the one-day course
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