Thinking Beyond Zero

“There are a couple of watersheds in human evolution. Most people are comfortable thinking about tool use and language use as watersheds. But the ability to play non zero sum games was another watershed.”

– Jonathan Haidt

Why do nations indulge in trade when it forces a particular section of their labour force out of work? Does a nation trying to learn a new language jeopardise the chances of survival of its own languages? Why is protecting the environment crucial for sustaining an economy’s growth? The answer lies in a concept that has unknowingly come to rule every facet of our lives. All decisions that are taken after a lot of consideration boil down to non zero sum thinking.

Before we delve into what is a non zero sum game, we need to understand what a game is. In the context of game theory, a game is any situation that has players of the game, information and actions available to each player at each decision point, and the payoffs or the returns for each outcome. Every situation that we deal with in life can be reduced to this definition of game as we continuously make strategic decisions with the hope of receiving some payoff. Every game is either a zero sum or a non zero sum game.

A zero sum is a situation in game theory in which one person’s gain is equivalent to another’s loss, so the net change in wealth or benefit is zero. Politics is the best example of a zero sum game. One candidate can win only if the others lose. The payoff is constant and the winner takes it all. On the other hand, a non zero sum game is a situation where one decision maker’s gain (or loss) does not necessarily result in the other decision makers’ loss (or gain). When put colloquially, it means one need not win at someone else’s expense.

Most of the games that we play are non zero in nature and they require co-operation. In non zero sum games, the fortunes of the participants are correlated. They win together or lose together. So, the final payoff can either be positive or negative for all the participants collectively. Group projects are a great example of non zero sum games. Here, one member’s gain doesn’t come at the expense of the other’s. Rather, the payoffs are correlated. Non zero sum games can be further divided into positive and negative sum games. If everyone cooperates in a group project , there’s a positive payoff of good marks which makes it a win-win situation. But if no one puts in effort, then no one gets good marks making it a lose-lose situation.

In this game, there are two players: A and B with two strategies- study for an exam or play. In each cell, the first number represents the payoff of A and the second number, the payoff of B.

A, B Study Play
Study 10,5 3,3
Play 1,1 5,10

A prefers to study while B prefers to play but both would prefer to do stuff together than to do it alone. The strategy pairs (study, study) and (play, play) are the two Nash equilibria (optimal strategies) because neither of them can gain by deviating if the other player doesn’t change her strategy.

To check for mixed strategy Nash equilibria, we must run the mixed strategy algorithm. To do so, first we assign probabilities (p) and (1-p) for A studying and playing respectively, and (q) and (1-q) for B studying and playing respectively. Next we multiply the expected payoffs with the respective probabilities to find the expected value.

10p + 3(1-p) = 1p + 5(1-p)

7p + 3 = -4p + 5

p = 2/11

That is, B plays study with probability 2/11 and play with probability 9/11. Similarly, it can be calculated that A plays study with probability 9/11 and play with probability 2/11.

Trade truly captures the essence of a non zero sum game. It consists of a set of strategies that the nations choose to act on. The nations are the players while the benefits received by them are the payoffs. Both the countries stand to benefit from trade. Importing countries receive positive payoff as the citizens get to enjoy a variety of high quality products at lower prices. Apart from that, trade promotes efficiency and innovation thereby paving the path for further progress. It helps the countries to satisfy their needs which wouldn’t have been possible without trade. The exporting countries receive positive payoff as they get a bigger market for their products and thus a way to capitalize on their comparative advantages. They get to rid themselves of the surplus production.

Learning languages can also be seen as a non zero sum game. A lot of critics feel the language issue is a zero sum game wherein one language can win only at the expense of the other. This feeling is predominant in countries with linguistic diversity and this issue is a bone of contention. Today, a lot of non English speaking countries are voicing their dissent against the growing onslaught of the English language. So does it make sense to give up learning a language in order to protect the culture?

In China, a country which ranks towards the bottom in proficiency of English language internationally, service sector accounts for a mere 9% of its $ 2.4 trillion exports

Actually, it doesn’t. There’s no need for any language to downplay some other language’s importance. Learning different languages better the trade opportunities among nations and the refusal of the nations to embrace another language can come at a huge cost to them. Britain’s stubbornness to let go of its attachment to the English language and unwillingness to significantly invest in learning other languages, has been estimated to be as high as £48 billion a year, or a staggering 3.5 percent of GDP. Recent World Bank Data reveals that in India service sector accounts for 38% of the $ 488 billion worth exports. On the other hand, in China, a country which ranks towards the bottom in proficiency of English language internationally, service sector accounts for a mere 9% of its $ 2.4 trillion exports. Thus having a common language helps ease the trade barriers. Moreover, learning each other’s language provides the nations with an opportunity to showcase their culture and promote their language at a global platform .

Climate change is a problem that is grappling the world. Environment and economy are always pitted against each other but they aren’t mutually exclusive. The real solution lies in reframing the problem from a zero sum game to a non zero sum game. Environment and economy can and do often work in tandem and efforts in the right direction can create synergistic value. Environment policies, if formulated properly, can actually stimulate economic growth.

Humans keep playing these games as we keep finding ourselves in situations where we need to make strategic decisions. We can either compete or cooperate thereby benefiting everyone involved. We have been participating in non zero sum games even before we became aware of the concept. Understanding how non zero sum games work can be the key to a stable and better future. When we understand how our fortunes are correlated, we will be better equipped to make decisions that are beneficial to all the parties involved. Armed with this knowledge, no wonder the world is choosing cooperation over Pyrrhic victories. Luckily for us, not all decisions sum up to zero.

-Durga Vitthal Shirsat FYBA

Scope for further reading

Language is no zero-sum game

Photo Credits

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