First, it's your turn, and you're contributing. This is assigned a value of p.
Then, it's not your turn, and you're receiving. This is preferable, and is assigned a value of -p.
If it's not your turn, but you must contribute, this is less preferable, and given a value of p+q, where initially, q
And, if it is your turn, but you have no one to contribute to, you must still participate. This isn't preferable, and since no contribution = no arrangement, let us say this value is approximately (q).
Now, if all players (n) take their turns (d) equally, then ∆p = p•d - (-p•d/n), so then, if you replace p with (p+q)•d for the number of turns missed... then divide that by n...
This is exactly why the key to happiness at work is finding an easy-going carpool. So that when your vacation days overlap your days to drive, you can just settle everything with rock-paper-scissors.