Prevolio
Game theoryClassroom · multi-user

Bertrand Competition — Price Wars

Paired as two firms, you both set a price each round. The cheaper firm captures the whole market, so undercutting spirals the price toward marginal cost — the Bertrand paradox: just two competitors can behave almost like perfect competition.

You’ll learn: See how price competition between just two firms can drive the price all the way down to marginal cost, leaving almost no profit.

Teacher guide

Students will learn to

  • Experience price competition as one of two firms setting prices each round.
  • See why undercutting is always tempting — and where that spiral ends.
  • Connect the Bertrand paradox to why some markets are fiercely competitive with only a few sellers.

Before the session — ask

  • If you and one competitor sold identical products, how would you set your price?
  • Where does undercutting your rival stop being worth it?

After the session — discuss

  • How close did prices fall to marginal cost over the rounds?
  • Did any pair sustain high prices — and how? What broke it down?
  • Why can two price-competing firms end up acting almost like perfect competition?

Timing

  • Briefing & pairing3–5 min
  • Five pricing rounds6–10 min
  • Reveal & discussion8–10 min

Run it with your class

Students join with a code or QR — no account needed. Teachers start a session from the dashboard.

Join with a codeFor teachers

What is Bertrand competition?

Bertrand competition models how two firms selling an identical product compete by setting prices. Because buyers simply pick whichever is cheaper, the firm that sets even a slightly lower price captures the entire market. That creates a relentless incentive to undercut: whatever price your rival sets, you can win everything by shaving a fraction below it. This undercutting spirals down until price hits marginal cost — the cost of producing one more unit — where there's no room left to cut without losing money. The striking result is the Bertrand paradox: with just two competitors, the market can reach the same outcome as perfect competition (price equal to marginal cost, essentially zero economic profit), even though there are only two firms rather than many. The Nash equilibrium is both firms pricing at marginal cost, each playing a best response to the other. It shows how powerful price competition is — but also why firms work so hard to escape it, through differentiating their products, building brands, or tacitly colluding, since head-to-head price competition on an identical good is ruinous for profits.

How the simulation shows it

Paired as two firms, each round you both set a price and the cheaper firm captures the whole market. Trying to undercut your rival yourself shows the trap: every round the price ratchets down toward marginal cost, and the profit you were chasing evaporates — the Bertrand paradox in action.

Common misconceptions

Frequently asked questions

What is Bertrand competition?
A model of oligopoly where firms compete by setting prices for an identical product. The cheaper firm takes the whole market, so undercutting drives the price toward marginal cost.
What is the Bertrand paradox?
The surprising result that just two price-competing firms selling an identical good can reach the perfectly-competitive outcome — price at marginal cost and near-zero profit — despite there being only two of them.
Why does the price fall to marginal cost?
Because each firm can capture the whole market by pricing just below its rival, both keep undercutting until price equals marginal cost, where cutting further would mean selling at a loss.
What is the Nash equilibrium?
Both firms pricing at marginal cost. Given that the rival prices at marginal cost, neither can profit by charging more (it loses all sales) or less (it loses money), so it's a best response.
How do firms escape Bertrand competition?
By avoiding head-to-head price competition on identical goods — differentiating their products, building brands and loyalty, or tacitly colluding — since pure price competition erases profit.