War of Attrition, explained.
A war of attrition is a contest where persistence costs resources and the participant who outlasts the other receives a prize. The winner's net payoff includes the cost of waiting.
Why it happens
Each extra round can preserve a chance to win, but it also consumes two tokens. The disclosed bot exits at a fixed patience limit. Because that rule is known, you can compare the prize with the total required cost without estimating a hidden opponent's strategy.
A war of attrition is a contest where waiting is costly and the player who outlasts the other receives the prize. Net gains depend on the cost of persistence.
Read the result
Track the cost already paid, your payoff from exiting now, and the net payoff from outlasting the bot. Continuing six rounds costs the entire 12-token prize. Beyond that, winning produces a negative net return. The cost already paid is visible so that local incentives and total returns are not confused.
A worked example
An eight-round rival in a twelve-token contest
The prize is 12 tokens and the disclosed rival waits until round eight before exiting.
Outlasting it requires eight Continue actions at a cost of two each, making your total cost 16.
You win the prize but finish at 12−16=−4. An immediate exit would yield zero; winning is not by itself a measure of success.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
Both start with zero cumulative cost. Exit concedes immediately and gives you minus accumulated cost. Continue charges 2 to both; when the resulting round reaches the disclosed bot patience, the bot exits and you receive 12 minus your total cost. Limits range from 1 to 8 rounds.
Where this idea is useful
A practical use
A costly dispute or delay can consume the value the participants were trying to secure.
A common misconception
“Persistence pays because the final survivor gets the prize.”
Receiving a prize is different from earning a positive net payoff. Waiting costs can exceed its value, even when the rules guarantee eventual victory.
What this explanation leaves out
- This finite, disclosed-cutoff bot is not the mixed-strategy evolutionary model in the source. There is no real money and no uncertainty about the bot's rule.
Is this the full equilibrium model of a war of attrition?
No. A fixed, known cutoff strips away strategic uncertainty so you can inspect costs. The source considers richer timing and evolutionary questions that this board does not solve.
What exit rule would you choose before entering a contest that charges you for every extra round?
Associated thinkers
Associations marked provisional are awaiting source review.
Further reading
Explore the original research or the teaching reference behind this experiment.