SM-GT-CS-01 · Playing the Right Game · Sector Spotlights

Game theory on a Tuesday morning

Six everyday business problems from six industries — each one a game you now know how to read. No famous cases here: these are the situations you will actually meet. Read the story, find the game, try the exercise.

Mixed strategies · Screening · Adverse selection

Insurance: The Audit Game

You cannot audit every claim. You cannot audit none. What is the right rule?

The situation

Your claims unit receives 100,000 claims a year; about 3% are fraudulent. A full investigation costs $400 per claim. Fraudsters adapt to any rule you publish.

The game

This is an inspection game with no stable pure strategy. Never audit → fraud pays → fraud grows. Always audit → fraud stops → your audits are pure cost → you cut them → fraud returns. The answer is a mixed strategy: audit at a credibly RANDOM rate that makes fraud unprofitable on average. If a fraud gains G when paid and costs F when caught, fraud stops paying when the audit probability p is bigger than G ÷ (G + F).

Note the reversal: with partners, predictability builds trust (Tit-for-Tat). Against adversaries who exploit patterns, calibrated unpredictability is the equilibrium.

Also in this sector: deductible menus are screening — the policy a customer picks reveals their private risk type. And adverse selection is the sector’s life-or-death game: price for the average and the good risks leave first.

Course language:Mixed strategyInspection gameScreeningAdverse selection

Try it (10 min):

A claim profile gains a fraudster $5,000 if paid; being caught costs $20,000 (repayment plus fine). What is the minimum audit rate?
Your budget covers only half that rate. Find two levers that restore deterrence without a single extra audit.

Backwards induction · BATNA · Commitment devices

Supply Chain: The Hold-Up Problem

The squeeze that arrives eighteen months after you invest — and how to see it before you sign.

The situation

A customer asks you to invest $2M in tooling that fits only their product, against a three-year forecast at healthy margins. Eighteen months in — tooling sunk, volumes delivered — procurement requests an 8% price cut at renewal.

The game

Solve it backwards. Once the tooling is sunk, it is worth almost nothing elsewhere — your plan B has collapsed, and the customer knows it. The squeeze is visible before you invest. The deeper damage: expecting hold-up, rational suppliers under-invest or price in a risk premium — value is destroyed for both sides before anyone behaves badly. Structural, not moral.

The remedies are commitment devices signed BEFORE investing: multi-year contracts with price formulas, take-or-pay volumes, customer co-ownership of the tooling, termination penalties. Plus reputation: a customer known for honouring supplier investments gets better tooling, cheaper.

Also in this sector: dual sourcing is BATNA-building made routine. Lowest-price tenders are winner’s-curse machines — the “winning” bid is often the one that most underestimated the true cost, repaid later in delays and claims.

Course language:Backwards inductionSunk costBATNACommitment deviceWinner’s curse

Try it (10 min):

As the supplier, pre-investment: list four contract mechanisms that make the $2M safe.
Classify each one: does it raise the shadow of the future, change the payoffs, or commit the customer?

Coordination games · Mechanism design

Banking: The Bank Run

Why a healthy bank can die of a rumour — and how deposit insurance deletes an equilibrium.

The situation

A rumour spreads about a mid-size bank. Every depositor faces the same choice: leave the money in, or withdraw now.

The game

A coordination game with two equilibria. If everyone stays, the bank is fine and staying is best. If everyone runs, the bank fails and the last in the queue loses most — so running is the best reply to running. Panic is rational. The rumour does not need to be true; it only needs to be believed about what others believe.

You \ Everyone else	They stay	They run
You stay	3, 3 good equilibrium	0 last in the queue
You run	2 cash out, minus hassle	1, 1 bad equilibrium

Deposit insurance is mechanism design: it changes staying-while-others-run from 0 to safe. Once staying is safe whatever others do, running stops being a best reply — the bad equilibrium is deleted from the game, not talked away.

Also in this sector: credit rationing is adverse selection — raise loan rates and the safest borrowers exit first, so beyond a point, higher prices lower profit. That is why banks ration credit instead of just charging more.

Course language:Coordination gameMultiple equilibriaMechanism designAdverse selection

Try it (10 min):

Using the matrix, explain in one sentence why a solvent bank can still die.
Design three interventions that make “stay” the only equilibrium. For each: which payoff cell does it change?
Mobile banking moves money in seconds and rumours travel on social media. Which parameter of the game changed — and what should regulators conclude?

Repeated games · Commitment · Shapley value

Airlines: The Fare War and the Alliance

Two games at 10,000 metres: the discounting trap, and the fair split of a network.

Game 1 · The fare war

Two carriers on one route: discounting steals share; matched discounting ruins margins for both — a repeated Prisoner’s Dilemma. The twist: capacity announcements are commitment devices. Publishing next season’s extra frequencies is a visible, hard-to-reverse escalation made before the pricing game even starts.

Game 2 · The alliance split

A trunk carrier (A) earns 30 alone ($M per year in this market); a regional feeder (B) earns 20 alone; connected under one code the network earns 70. Fair split? Average each partner’s added value over both joining orders: A first — A brings 30, B adds 40; B first — B brings 20, A adds 50. Shapley: A = 40, B = 30. The “small” feeder deserves 30, not its standalone 20 — its feed creates much of the joint gain.

Watch the focal points fight the maths: A will argue “proportional to size” or “proportional to standalone revenue” — both feel fair and both under-pay B. B’s defence is one sentence: “without our feed, your network earns 30, not 70.”

Course language:Repeated PDCommitment deviceShapley valueFocal point

Try it (10 min):

Compute the Shapley split, showing both joining orders.
Role-play the split negotiation: A anchors on proportionality; B defends with marginal contribution. Who wins the room — and why?

Commitment devices · Payoff engineering

Retail: The Price-Match Paradox

“We’ll match any price” sounds like war. It is usually peace — paid for by the customer.

The situation

A chain announces: “Find it cheaper anywhere and we will match it.” Consumers cheer. Should the rival worry?

The game

Without the guarantee, two chains sit in a discounting trap — each tempted to cut, both ending at ruined margins. WITH a public, automatic match, a rival’s discount wins them no customers: every cut is matched instantly. The temptation payoff is deleted, and holding prices becomes the equilibrium.

Without guarantee	Rival holds	Rival cuts
You hold	3, 3	0, 5
You cut	5, 0	1, 1 equilibrium

With automatic matching	Rival holds	Rival cuts
You hold	3, 3 equilibrium	2, 2 cut is matched
You cut	2, 2 you get matched	1, 1

Also in this sector: loyalty points raise customers’ switching costs — payoff engineering that softens price competition without a single meeting between rivals. Understanding the mechanism is not a licence to collude: agreements with competitors are where illegality begins.

Course language:Commitment deviceTemptation payoffEquilibrium shiftSwitching costs

Try it (10 min):

Find the equilibrium in each matrix. In one sentence: what did the guarantee change?
Debate: pro-consumer promise, or tacit coordination a regulator should study? Where exactly is the line?

Coordination · Tipping · Costly signals

Platforms: The Standards War

When the fight is not over the product — it is over what everyone believes everyone will choose.

The situation

Two firms launch incompatible standards — payment QR codes, EV charging connectors, messaging protocols. Users, merchants and developers must pick a side.

The game

A coordination game with conflict: both firms prefer one winning standard to a fragmented market — but each prefers its own. Users add tipping: each adopter joins the standard they expect to win, so expectations self-fulfil and small early leads compound into winner-take-most.

That turns the war into a battle over beliefs. Preannouncements, launch subsidies and flagship partnerships are costly signals saying “we will win — join us now”. Test each one: does it actually cost the sender something (credible), or is it cheap talk? Subsidy wars between platforms are a war of attrition — chicken with a burn rate.

The design lens: standards wars often end by mechanism design, not victory — a regulator or industry body imposes interoperability, converting the war into a committee game. The trailing player should usually WANT that intervention; the leader should fear it.

Course language:Coordination gameTippingCostly signalWar of attritionMechanism design

Try it (10 min):

Pick a live standards fight in a market you know (mobile payments, EV charging, mini-programmes). Map the two-equilibrium structure and each side’s tipping lever.
Identify one costly signal each side has sent — and one piece of cheap talk pretending to be one.
Who could act as mechanism designer here — and which player should want them to?