# Snowdrift game

The snowdrift game is a scenario sometimes used in game theory. The scenario involves a set of drivers is confronted with a road blocked by a snowdrift. The easiest option for all of the drivers is when other drivers shovel the snow out of the road. The worst outcome for all drivers: no one shovels the road. The question proposed:

Which drivers will volunteer to shovel the road (the "volunteer drivers"), and which drivers will be the "freeloader drivers", sitting comfortably in their cars while the road is cleared by the volunteer drivers?

The scenario is sometimes used as an alternative to the more famous "prisoner's dilemma" as described on English Wikipedia (see "Prisoner's dilemma")

## Sources

This scenario is described in several online sources:

1. Snowdrift.coop wiki description (https://wiki.snowdrift.coop/about/snowdrift-dilemma) This description provides a simplified two-person version of the game, paraphrased below:
• 2 drivers
• choice: shovel or wait
• Maximum of 4 points allocated
• scoring:
• 3 points for the freeloader driver who relies on the other driver to clear the road
• 2 points for each of the two drivers who share the work
• 1 point for the volunteer driver who clears the road without help from the freeloader driver
• 0 points allocated if nobody shovels
2. Paper by Rolf Kümmerli, Caroline Colliard, Nicolas Fiechter, Blaise Petitpierre, Flavien Russierand Laurent Keller
University of Lausanne and University of Edinburgh
Summarized by Phys.org: https://phys.org/news/2007-10-snowdrift-game-tops-prisoner-dilemma.html
The summary quotes the paper (doi:10.1098/rspb.2007.0793) as follows:

The situation of the Snowdrift game involves two drivers who are trapped on opposite sides of a snowdrift. Each has the option of staying in the car or shoveling snow to clear a path. Letting the opponent do all the work is the best option (with a pay-off of 300 used in this study), but being exploited by shoveling while the opponent sits in the car still results in a pay-off of 100. (The other two possibilities, both shoveling and both sitting, have pay-offs of 200 and 0, respectively.)

There is almost certainly at least one other scholarly paper that describes the "snowdrift game"

## Iterated snowdrift

Researchers from the University of Lausanne and the University of Edinburgh have suggested that the "Iterated Snowdrift Game" may more closely reflect real-world social situations. Although this model is actually a chicken game, it will be described here. In this model, the risk of being exploited through defection is lower, and individuals always gain from taking the cooperative choice. The snowdrift game imagines two drivers who are stuck on opposite sides of a snowdrift, each of whom is given the option of shoveling snow to clear a path, or remaining in their car. A player's highest payoff comes from leaving the opponent to clear all the snow by themselves, but the opponent is still nominally rewarded for their work.

This may better reflect real-world scenarios, the researchers giving the example of two scientists collaborating on a report, both of whom would benefit if the other worked harder. "But when your collaborator doesn't do any work, it's probably better for you to do all the work yourself. You'll still end up with a completed project."[1]

Example snowdrift payouts (A, B)
A
Cooperates Defects
Cooperates 500, 500 200, 800
Defects 800, 200 0, 0
Example PD payouts (A, B)
A
Cooperates Defects
Cooperates 500, 500 -200, 1200
Defects 1200, -200 0, 0
1. Kümmerli, Rolf. "'Snowdrift' game tops 'Prisoner's Dilemma' in explaining cooperation". Retrieved 11 April 2012.