A new paper by Fu, Lu, and Pan called “Team Contests With Multiple Pairwise Battles” analyzes this kind of competition and shows that they exhibit no discouragement effect. The intuition is straightforward: if I win the second match, the additional effort that would have to be spent to win the third match will be spent not by me, but by my teammate. I internalize the benefits of winning because it increases the chance that my team wins the overall series but I do not internalize the costs of my teammate’s effort in the third match. This negative externality is actually good for team incentives.The leading example of a squash game resonated with me because I play racquetball twice per week in a group size that ranges from 2 to 5. If the number of players is odd, we usually start by playing cutthroat. If the number of players is even, we usually play one-on-one games. There are other strategic incentives in a cutthroat game, but it can be viewed as a series of three overlapping team games where one team size is 1 (the person serving at the time) and the other is 2 (the other two players). Should one expect less discouragement in a cutthroat game versus a one-on-one game? If we can swing the logic of team-shared effort into a match with unbalanced team sizes, the answer would be yes, but there are certainly some details to work out.
The implied empirical prediction is the following. Comparing individual matches versus team matches, the probability of a comeback victory conditional on losing the first match will be larger in the team competition. A second prediction is about the very first match. Without the discouragement effect, the benefit from winning the first match is smaller. So there will be less effort in the first match in the team versus individual competition.
In another vein, our racquetball matches have a weird property in that the discouragement effect seems to be masked by what I'll call the supreme victory effect. An implicit assumption in the discouragement argument is that winning is all that matters, but if you break this assumption by allowing supreme victories to matter more (say in racquetball games among friends), I'll bet one can get some interesting competitive dynamics.