Strategy lab / shared costs

The Snowdrift

The road benefits both of you. The shovel costs whoever uses it. Change the conditions and watch the sensible response switch sides.

Shared benefit6

Points each person receives if the road opens.

Clearing cost3

Points lost if one person does all the shovelling; shared equally if both shovel.

Chance the other traveller shovels50%

Estimate how often the other traveller would contribute across similar encounters.

Expected payoff

Compare the two moves

The balance point is 66.67%.

Each cell gives your points first, then the other traveller's points.
Your move	They shovel	They wait
You shovel
You wait

Script-free model

Why the incentives cross

Let the benefit of an open road be B and the clearing cost be C, with B greater than C. If the other person shovels, waiting gives you B while helping gives B − C/2. If the other person waits, shovelling gives B − C while waiting gives 0.

Your move	They shovel	They wait
Shovel	B − C/2	B − C
Wait	B	0

So your best response is to wait when you expect them to shovel, and to shovel when you expect them to wait. That crossed response is what allows a mixture of contribution and non-contribution to persist.

Compare the structures

Snowdrift is not the Prisoner's Dilemma

Both travellers want the road cleared. Each wants the other person to freeze, strain and pay the cost of clearing it. The game asks when exploitation is rational—and why somebody may still choose to do the work.

Prisoner's Dilemma

If the other player defects, your one-shot payoff is still higher when you defect. Mutual defection is bad, but unilateral cooperation is worse for the cooperator.

Play the repeated dilemma

Snowdrift

If the other traveller waits, shovelling still leaves you better off than remaining blocked. Mutual waiting is worse than paying the cost alone.

That reversal changes the equilibrium.