The price war
Compare the incentives to undercut when a commitment carries a penalty and monitoring costs both firms.
Dilemma
An interactive game theory lab. Make a move in one of six economic games and see how your payoff depends on the other player’s choice. Change the rules and see which outcomes hold up.
Why do both firms cut prices?
In the price war game, undercutting pays more whichever action your rival takes. Both firms undercut at the Nash equilibrium, even though both would earn more by maintaining prices. At an equilibrium, neither player can improve their payoff by switching alone.
Set the commitment penalty to 5 points with full enforcement and zero monitoring cost. Now both firms maintaining prices is the only pure equilibrium. The scenario flags effects on consumers and entrants separately from the firms’ payoffs.
Try the price war| B maintains | B undercuts | |
|---|---|---|
| A maintains | 8, 8 | 1, 12 |
| A undercuts | 12, 1 | 4, 4 Nash equilibrium |
Six games with rules you can change
A field in common
Two farmers share a grazing field. Adjust the expansion charge, monitoring reliability, or damage from each extra herd.
Who funds the network?
Turn on all-or-nothing funding to refund a lone contributor. Under that contract, both contributing and both declining are stable outcomes.
The tariff response
Change the weight governments give to producers or add a trade agreement penalty. See how the policy choices shift.
Invest into the boom?
Leave the starting relative profit advantage in place and set a 4-point loss for joint expansion. Each side now prefers the opposite move to its rival.
The credit coordination game
Full rescue coverage lifts a lone expander’s payoff from −4 to 2 before insurance charges. Both banks holding steady and both expanding remain pure equilibria.
What changes when you meet again?
The payoff table marks the equilibria for a single encounter. Repeated play shows what happens over time when players follow the strategies you select.
Play a round
Choose your move and pick an opponent strategy. A reciprocating opponent starts with the first action, then copies your move from the previous round.
Run an experiment
Set both strategies and run up to 100 rounds. Add accidental moves and keep the same random seed to reproduce them.
Compare rules
Pin a baseline and change a rule. The comparison uses the same strategies, number of rounds, chance of mistakes, and seed for both runs.
Build your own game
Start with a template or name two players and give each two choices. Edit the four payoff pairs and see how the live analysis changes. It shows pure equilibria, dominant choices, and an interior mixed equilibrium when the game has one.
Keep your experiments
Save a scenario with its rules and experiment settings in your browser’s notebook. Export the notebook to back it up or reopen it on another device.
How do you split a shared taxi fare?
Alice gets out at €6, Ben at €10 and Chloë at €18. All three use the first leg. Chloë alone uses the last one.
The Shapley value averages the extra cost each passenger adds across all six possible joining orders. That assigns €2 to Alice, €4 to Ben and €12 to Chloë. Move the final stop to see the shares change.
Try the taxi illustration