Apples to Apples is a popular party game; as Wikipedia previously explained it:
Each player is dealt seven “red apple” cards; on each is printed a noun or noun phrase (Madonna, Lightning, Socks, Mahatma Gandhi, Street Gangs, London, The Universe, A Locker Room, The San Andreas Fault, Science Fiction, etc.).
One player is appointed as the first “judge”. She draws a “green apple” card on which is printed an adjective (Scary, Smelly, Patriotic, Rich, Aged, etc.), and places it face-up. Each of the other players places (face down) one of his red apple cards which he feels matches the green apple card. The judge shuffles the red apple cards then turns them face up (without knowing who submitted each) and chooses the one she feels is the best match for the green apple card. The player who submitted that red apple card wins the round, and takes the green apple card to signify the win.
(by Fritzlein, Vicki Rosenzweig, Zandperl, Fsufezzik, and Brian Kendig)
Cards Against Humanity is a Creative-Commons-licensed game along the same lines with blacker humor.
In Scrum, there’s a “planning poker” that is sort of structured as a game, allowing the project to be planned based on estimates of costs, but it doesn’t provide incentives for providing good estimates; consequently the way a selfish player would keep their job or get promoted is to spend as little effort as possible on estimates, with the predictable result that the estimates are terrible. Perhaps “Planning Apples” or “Planning Against Humanity” could provide correct incentives, so that people who put the right amount of effort into estimation would instead keep their job or get promoted. How would that work?
The first attempt is the jellybean-jar-game approach: each person’s estimate of a task is anonymously recorded, and then when the task is done, whoever had the closest estimate wins a point. The estimate used for planning is some sort of average of the estimates; perhaps the median is the best average to use, or perhaps a median weighted by people’s scores.
However, this creates a perverse incentive: if you get assigned a task, you have an incentive to take the exact amount of time you estimated. There’s a second-order perverse incentive: you have an incentive to pad your estimate so that you’re pretty sure that, if you get the task, you can sandbag your work to hit the estimate. This can be ameliorated by disqualifying the performer’s guess if it happens to be closest, assigning the point to the next-closest estimate, just as the “judge” in A2A doesn’t get to play a red apple card. Then two different people have to collude (against the interests of the rest of the team) to win these points. In some social contexts that is a sufficient control.
Perhaps the perverse incentive can be solved entirely by giving a bigger prize for beating the estimate that was used for planning. In the case where that estimate was the median, this prize should be awarded when the actual time taken was lower than the highest estimate that was less than the median. So, for example, if the estimates were 2, 4, 7, 11, and 13, the median is 7, but you only win the prize if you completed it with 4 units of work or less.
That way, if you expect to be assigned the task, and you know what the other players’ estimates are, by choosing your estimate adversarially you can only push the estimated time up to the next higher estimate.
In the above example, suppose the estimates on the table are 2, 4, 11, and 13; this gives you the freedom to set the estimate to anything between 4 and 11 by choosing a number in that range, or to set it to 4 or 11 by picking a number lower than 4 or higher than 11. If the real difficulty of the task is in the 4-11 range, you aren’t going to be able to get the fast completion prize by picking a number in that range, but you can win the estimation prize by doing the best job possible at estimating the difficulty, taking the estimation prize away from the 4 guy and the 11 guy. If you pick a number below 4, such as 3, you set the estimate to 4 and forfeit the estimation prize, but you’d have to beat your own estimate of 3 to win the early completion prize, which is unlikely. But if you pick a number over 11, like 12, you set the estimate to 11, but the early completion prize threshold to 4, which, again, you probably can’t beat, and again you’re forfeiting the estimation prize. So, even in that extreme case, your best strategy is to estimate as honestly as you can.
If the estimates on the table are 2, 4, 7, and 11, then the same holds, but even more strongly. You can under some circumstances nudge the median up to the next partition but you don’t win anything by doing so.
How do we measure completion times? Because of course if they’re entirely self-reported you could claim that every task took you 0 units or 1 unit and thus win an early-completion time for every task you complete. If the other players judge your completion time, they can try to push it closer to their estimate. Perhaps we could assign each player a fixed number of points to allocate during the iteration, or assign them in proportion to their billable hours. There are additional tricky incentive-design problems there, but they may be tractable.