Snowdrift game

To illustrate the snowdrift game, imagine two drivers caught in a blizzard and trapped on either side of a snowdrift unable to communicate. They both want to get home and so they have the options to cooperate, i.e. to get out in the cold and start shovelling or to defect and stay in the cozy warmth of the car hoping the other guy would do the job. If both cooperate and shovel they have the benefit [math]\displaystyle{ b }[/math] of getting home while sharing the labor [math]\displaystyle{ c }[/math] ([math]\displaystyle{ b \gt c \gt 0 }[/math]). Thus [math]\displaystyle{ R = b - c / 2 }[/math]. Whereas if both stay in the car they don't get anywhere before spring arrives and therefore [math]\displaystyle{ P = 0 }[/math]. However, if only one shovels, then both get home but the one that stayed in the car avoids the trouble and gets [math]\displaystyle{ T = b }[/math] whereas the diligent one is left with the whole work [math]\displaystyle{ S = b - c }[/math]. The resulting rank ordering of the payoff values is similar to the Prisoner's Dilemma except that [math]\displaystyle{ P }[/math] and [math]\displaystyle{ S }[/math] have a reverse ordering: [math]\displaystyle{ T \gt R \gt S \gt P }[/math]. Nevertheless this leads to fundamental changes because now the best action depends on the behavior of the opponent: defect if the other cooperates but cooperate if the other defects.

As for the Prisoner's Dilemma, the payoff values can be again conveniently rescaled such that [math]\displaystyle{ R = 1 }[/math], [math]\displaystyle{ P = 0 }[/math], [math]\displaystyle{ T = 1 + r }[/math] and [math]\displaystyle{ S = 1 - r }[/math] where [math]\displaystyle{ r }[/math] denotes a slightly different cost-to-benefit ratio [math]\displaystyle{ r = c /(2b-c) }[/math]. This parametrization results in a single parameter and preserves the proper payoff ranking required for the Snowdrift game.