Zero-Sum Game

A zero-sum game is a contest in which the benefit received by the winner is equal to the deficit faced by the loser.

No time for losers

Many of us live in societies in which we are conditioned to think of competition as primarily a means of separating the winners from the losers. The former group enjoys the spoils of coming out on top, be it prizes, glory, power or wealth, while the latter (everyone else) is left to sulk and lick their wounds. Many types of contests are designed to result in a single winner and one or more losers.

A competition in which the gain enjoyed by the winner is equal to the loss suffered by the loser is known as a zero-sum gain. The name itself conveys the idea that the collective outcome of the winner and loser cancels itself out.

A pure zero-sum game

Imagine two contestants facing off in a game. It does not matter if the game relies on skill, strength, speed, luck or even some combination of these. Once the game is over, one of these two contestants will be deemed the winner, and the other the loser. Accordingly, the winner will receive some benefit (material compensation, standing or personal satisfaction), and the loser will be denied that same benefit in equal measure. This can be thought of as a standard zero-sum game.

Consider the various games that are familiar to you, and you will probably find that many of them appear to fit this description. But if we dig a bit more deeply, we can unearth many cases in which the math does not add up, and the overall result is non-zero.

Complications to the zero-sum game

The result of a game can only “nullify” if the immediate outcome of the competition (that is, the victory itself) is the only thing that matters. But once we examine what specific impact a win or loss may have on the individual contestants themselves, it becomes evident that winning and losing do not mean the same thing to everyone. Here we explore five ways in which the outcome of a competition, when viewed holistically, does not so easily zero out.

Unequal expectations

Two players who compete against one another who share equal hopes of winning stand to gain or lose just as much as their counterpart, thus finding themselves in a true zero-sum game. But this is often not the case. Consider two players who are mismatched in skill. The first player is exceptional, while their opponent is closer to average in abilities. A win for the superior is desirable but expected. But if the average player should come out on top, that outcome could prove far more rewarding, whereas the loss by the superior player may be treated as an annoyance, or dismissed as a meaningless fluke.

The importance of any given game within the wider context of a playing season or ranking hierarchy can vary from player to player and round to round. In a round-robin tournament a team facing elimination will greet a win much more cheerfully than might their opponent who has already earned enough points to pass through to the next round. Although each team stands to either win or lose (we will address the possibility of ties at the end), the doors that open or close as a result may not be same for each side.

Prevailing conditions

The impact of the aftermath of a competition may be retrospectively tempered when players take into account the particular circumstances in which they competed. If a player is unwell or faces a failure in their equipment, or if some outside force negatively influences their performance, they may adjust the emotional significance they place on losing. In the reverse situation, a player who enjoys good luck or otherwise benefits from an outside force that favors them might also moderate the degree of importance they place on the victory. (However, we humans probably tend to embrace excuses for failing to succeed, and to downplay the factors outside of our control that thrust us into the winner’s circle.)

The value of playing for its own sake

Winning, truly, is not everything. Junior competitors who are given opportunities to go head to head with people who who outclass them in experience and achievement may end up losing time and again. But the opportunity to test oneself against those of superior ability has its own intrinsic value, and is often a needed catalyst for a junior player to develop their own potential. In this case the notion of evaluating a contest through the dichotomy of wins and losses does not capture the whole picture.

More than two players

It becomes harder to classify a game with more than two players as fitting the definition of a zero-sum game because all of the complicating factors mentioned above are in effect, plus one more. A race may have numerous competitors, but there will only be one winner crossing the finish line first. The winner will receive some kind of reward, but it is often true that second place, third place and so on will claim diminishing rewards of their own. Does it stand to reason that the runner-up then receives a combination of benefits and deficits for placing second, for having performed extremely well, but for failing to surpass one single opponent? It becomes clear that the impact of earning a particular result will depend on the competitor’s own abilities and expectations. In fact, research suggests that competitors who place third tend to feel more positive about their result than those who come in second. Bronze medalists get to take the podium, while silver medalists are left to question what they might have done differently to win.¹

Strategic defeat

Sometimes a player or team may prefer to lose a given match. This could be done with a view to being paired up with a particular opponent in a later round over whom they think they have some advantage. Strategic losses upend expectations about which result (a win or a loss) is actually desirable, and they could even result in both competitors or teams being satisfied with the final score (such as when the losing team gets the upcoming matchup they were seeking while the winning team now earns enough points to advance to the next round). This may prompt ethical questions about fairness, and many sports have rules and norms that attempt to prevent teams from “throwing” a game, but it is very much a phenomenon that creeps into in elite competitions.

The question of ties

Is a game that ends in a tie also a zero-sum game? In short, it depends. All of the above concerns are at play, and there are many historical instances of ties being celebrated or bemoaned with nearly the same vigor as if they had been wins or losses.

Any game, whether it results in a win, a loss, or a tie, takes place within a wider context. A true zero-sum game, rather than being the normal state, may in fact be an exception.

1. Medvec, Victoria & Madey, Scott & Gilovich, Thomas. (1995). When Less Is More: Counterfactual Thinking and Satisfaction Among Olympic Medalists. Journal of Personality and Social Psychology. 69. 603-610. 10.1037/0022-3514.69.4.603. ↩︎