Life often seems to resemble a type of game where there are losers and winners. People and whole societies often seem locked in business, war, political, and relationship games. If you have often wondered if there is a scientific way to reason about these ‘games,’ read on.

A net sum zero or zero-sum game is a highly competitive interaction where the winning participant’s gains are precisely equal to the loser’s losses. The overall net payoff is said to be zero because if you add the winners (+X) winnings to the loser’s (-X) losses, you get: +X – X = 0

Economists and social scientists study how humans compete for scarce resources and how they interact or what games they play to obtain them. A better understanding may lead to less destructive business and political decisions.

Is Business Competition Always A Zero-Sum Game?

Conclusion

Zero-Sum Game is a term used in anapplied branch of mathematicscalled Game Theory. ‘Game’ in this sense doesnot directly referto recreational sports matches such as football, card games such as Poker, and board games such as monopoly.

Game Theory uses mathematics tomodeltherational decisionoptionsagents have in competitive situations, where agents need to bestrategicbecause decisions are based on predicting the moves and reactions of opponents. This science of decision-making is now widely used in Economics and Social Science.

In 1921, the French mathematician, Emile Borel, wondered whether it was possible to mathematically model how competing agents such as Poker players can best bluff and second guess each other when very little information is available. He was curious to know if a ‘best’ strategy exists for any game.

The game of Poker inspired Von Neumann. He realized that who won or lost did not depend on luck alone and hence could not be adequately modeled using probability theory alone. He was interested in how a rational player could skillfully counter an opponent’s best moves in a zero-sum game like Poker to minimize their losses under uncertainty.

Many board games such as chess, card games such as Poker, and sports such as football are zero-sum games. These games have very well-defined rules and scoring systems, which make it clear who wins and who loses.

Recreational games are played within well-defined boundaries and neatly isolated from life’s problems, which are not allowed to encroach on the playing field or game board. Because competitive behavior in real-life pursuits such asbusiness, politics,andwarare so often andpoorly defined, it is challenging to identify zero-sum outcomes in these activities.

Now, if they found a packet of chips instead, assuming the brothers are friends, it would be a win-win since they could share the chips equally. The ticket is, unfortunately, rendered useless if torn in half.

Deciding to flip a coin, John calls out heads, and Peter calls out tails. Assuming tails wins, we can technically only call this situation zero-sum if John’s loss precisely cancels out Peter’s happiness. Now let’s assume that we could measure happiness inunits of satisfactioncalledutils (from utility)and measure their happiness levels before finding the ticket as 10 Utils.

Since 10utils +10Utils (before) = 15Utils + 5 Utils (after), the total satisfaction has been conserved and there hasn’t been a net change because thenet change cancels to zerobecause +5Utils - 5Utils = 0Utils.

What if Peter feels guilty and so strongly empathizes with his brother that he tears up the ticket so that neither of them goes? How does this affect the total happiness score now? Will the total Utils, still be conserved at 20?

John may validly ask Peter if he felt so guilty, why did he not give him the ticket instead? Now, none of them can benefit. If John now makes Peter realize his guilt is silly, he may regret tearing the ticket. The total happiness could quickly plummet because of Peter’s embarrassment for being silly and John’s resentment due to the wasted ticket.

Since the requirement that satisfaction must perfectly cancel dissatisfaction is highly improbable, John and Peter are likelier to experience a non-zero-sum outcome.

Theperfect symmetrybetween John’s loss and Peter’s gain is a veryspecial and unique case. In contrast, there are many non-unique ways in which John’s loss is non-symmetrical to Peter’s gain. For example, John may only ‘like’ Justin Beaver (+1Util), but Peter may be a hardcore fan (+5Utils).

Being wise, John may realize thatcooperating, rather than competingwith his brother and losing 1Util, so that his brother may gain 5 will result inmore happiness overallsince John’s Utils (10 - 1) added to Peter’s Utils (10 + 5) = 24Utils. That’s 4Utils above the present 20, making it anet-positive-sum game.

In contrast, if John decided to play a more competitive game, the brothers would collectively lose happiness: (10 + 1) + (10 – 5) = 16Utils, -4 from 20. Suppose John and Peter were strangers instead of brothers, and John knew he would never run into Peter again. In that case, he may decide to gain 1Util at Peter’s expense.

Since Peter and John are brothers and run into each other daily, John may reason that Peter mayhold a grudgeagainst him if he went, which may not be in his long-term interest. Sometimes in the future, John may need Peter’s cooperation and support.

This is why true zero-sum games are mostly playedamongst strangersand in situations where thestakes are quantifiable, such as in money. If that is true, why are many fun children’s games, such astic-tac-toeandrock-paper-scissor, zero-sum, played amongst friends and siblings?

While it is true that these games are Zero-sum in the sense that there is always a clear winner and loser (except in tic-tack-toe, where there is often a draw), children’s games are never played for high stakes, such as for money or property. They are played purely for fun, where the zero-sum competitive element merely enhances the thrill.

When adults play games such asBridgeandPokerfor high financial stakes, then winning and losing is not just a formality, and the zero-sum nature of the game has very real consequences.

When Businesses compete for a larger share of a small limited market, then outcomes are generally zero-sum if a business can only increase their market share at the expense of their rivals. However, if only a few small firms are selling in a market vast enough to absorb their collective maximum output, then outcomes could be win-win and positive-sum.

However, suppose the rival firms miscalculate, with none having a clear scale or cost advantage. In that case, they could bankrupt each other, and the price war could turn out to be a lose-lose and a negative-sum game. To avoid a costly price war, many firms compete regarding non-price factors.

Zero-sum outcomes are easily identifiable in well-defined recreational games. However, they are less identifiable in real-life competitive behaviors, such as wars, business, and politics.

References

https://en.wikipedia.org/wiki/Minimax_theorem

https://cs.stanford.edu/people/eroberts/courses/soco/projects/1998-99/game-theory/neumann.html

https://en.wikipedia.org/wiki/Zero-sum_game

https://www.quora.com/Who-invented-the-term-zero-sum-game

https://study.com/academy/lesson/game-theory-positive-negative-zero-sum-games.html

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