Zero Sum Game

Abstract

"Zero-sum" is a concept derived from game theory, a social theory based on the disciplines of mathematics and economics, which seeks to anticipate the rational decisions of people to a specific set of choices. Zero-sum includes all social processes that may be modeled as a game or a set of probabilities, in which the gain of any actor or group can only be acquired at the expense of the opposing party. The simplest version is modeled on two players, one of which wins all because the other party losses all. Created during the postwar years, game theory gained prevalence during the Cold War and continues to be influential.

Overview

The concept of zero-sum was first described in Oskar Morgenstern and John von Neumann's seminal book, The Theory of Games and Economic Behavior (1944). Game theory is concerned with the behavior of individuals and groups faced with win-lose situations. The basic premise of game theory is utilitarian and rational: When people must make a decision in the face of several possible outcomes, they are expected to choose the one that provides the maximum satisfaction. Zero-sum refers to the idea that there is a limited or finite amount of resources—such as land, food, money, status, power, and even game points—for which individuals or groups are in constant competition. The success of one side, in this view, depends on the loss of the other. At the end of the game, when all gains and losses are added up, the total sum should give a final balance of zero; hence its name. Zero-sum beliefs, then, drive individuals not only to work toward the success of their own group, or in-group, but also to undermine or debilitate the ability of the rival party or outgroup to succeed. In zero-sum theory, the gains won by one side are matched by corresponding losses to the other. Zero-sum is part of a spectrum of theories known collectively as game theory, much used to understand and manage competition, conflict, risk, and/or market situations.

As an ideology, zero-sum theory can resemble Social Darwinism, the theory proposed by followers of Herbert Spencer (1820–1903), who extrapolated his social theory from Charles Darwin's description of natural selection. Herbert and his followers believed that the competitive market, as viewed in classical economics, is akin to a natural law, that is, inevitable and immutable. Furthermore, wealth and success came to those who were better able, by nature, to adapt and survive in a competitive society. In modern terms, because life is a zero-sum game, the owners of wealth rightfully manage game elements so that it favors their group against the outgroup.

One of the most influential thinkers of zero-sum theory, prior to the modern inception of the Neumann-Morgenstern theories, was Thomas Robert Malthus (1766–1834). Malthus gained fame with the publication of An Essay on the Principle of Population (1798), which argued that in times of abundance of resources, the population increases. However, the population multiplies geometrically, while food production increases arithmetically, so that population grows faster than food production. In other words, for Malthus, the number of workers would grow more rapidly than the availability of food; this, in turn, would lead to a fall in earnings and, thus, in access to food, so that the poor would become poorer and their poverty would lead to illness, famine, and overall catastrophe.

Many thinkers who espouse zero-sum views of society consider well-being and wealth to be finite; society, therefore, in all aspects, works by some individuals taking away from others. This paradigm of individuals and groups of people in endless struggle, sees all society as a zero-sum game: Progress for some always comes at a cost to others. These views are foundational to some early political-economic models, such as feudalism and absolutism.

The Enlightenment brought seismic changes in political philosophy, and eventually developed democratic social models unimaginable to many Malthusians. Enlightenment ideas highlighted an ethical view of individual liberty and rights, with market dynamics based on processes of voluntary exchanges rather than antagonistic extraction. Enlightenment principles of "Liberty, Equality and Fraternity" viewed all "outgroups" as integral parts of society—as citizens rather than aliens or subservient classes. The idea of citizenship for all as normative for a democratic society helped erode ideas of inherently and inevitably antagonistic societies, generating—at least as an ideal—respect for multiple identities in a non-competing world.

On the other hand, the world can fall into zero-sum scenarios, which may run the gamut from international conflicts to competitive games. In fact, as some thinkers posit, some societies may be more prone to relying on zero-sum beliefs than others. Relations in a society—as well as within its institutions and organizations—work according to mainstream beliefs about the nature of the world. These beliefs are culturally socialized and become part of the matrix of social relations.

A generalized view of life as a zero-sum game would, theoretically, lead to more antagonistic social relations, as a society would be permeated by the conviction that the gains of one person—material or symbolic—must come at the expense or failure of another. The world, according to this view, is populated by rivals—a social condition that is highly incompatible with trust or social harmony. Holders of this view often point to war theaters, as well as to societies in civil strife or to post-conflict societies, as examples.

Interestingly, however, zero-sum beliefs usually do not necessarily isolate or shield groups from each other. They merely ensure more antagonist relationships. For instance, it is the premise of zero-sum games that each move will result in a win or loss for the players, depending on the move and who makes it. In a way, then, players on one side are involved in a relationship of dependency with the others.

Related to zero-sum beliefs is a social phenomenon known as zero-sum bias. Zero-sum bias refers to believing a situation to be zero-sum when it is not a zero-sum situation, or, as it is known in game theory, a non-zero-sum. A non-zero-sum can refer to a wide variety of situations, such as one in which both parties gain—known as a win-win situation—or when both parties lose. Even in situations of unlimited resources, for example, the belief may exist that the gains of some inevitably imply the loss of another; in other words, people may be prone to a zero-sum bias even in scenarios in which these are unwarranted. Studies show that conclusions of risk and unfairness may remain unchanged even when evidence is clear that there are enough resources for everyone.

Applications

There are many fields in which zero-sum theories are of use. They are used to explore scenarios of regional cooperation, international and maritime borders, economic zones, agreements of resource extraction, business negotiations, lawsuits, sports, and so on. During the Cold War, for example, many countries shaped their international policies in accordance with zero-sum principles, often at the expense of other nations. Foreign relations were managed, then, according to a worldview of distrust, rival claims, and competing interests; it was a commonplace perception that international peace was fragile and volatile, and that the world was closer to conflagration than to international agreements and integration.

In general, there are many applications to game theory overall, of which zero-sum is but a part. A great deal of it is highly complex and mathematics based, since it depends on probabilities. As such, it is quite useful in a wide variety of settings, such as that of gaming. In a sphere in which one player seeks to maximize his or her advantage at the expense of the other, it is useful to be able to calculate the sets of probabilities for either side, its reasonable outcomes, and its best solutions.

Another field in which these strategic principles are applied is in organizational management. Contemporary organizations understand the value of teambuilding, communication, and, in general, social integration in the workplace. For this to occur, workplace relations, even when vertical—top-down and hierarchical—must be based on trust, transparency, and availability of information. When people believe the environment is a zero-sum place, that is, one in which any gain for one worker comes at the expense of another, it is hard to develop the relationships necessary for an organization to function efficiently. To foster engagement and cooperation, organizations often employ game theory strategies in management, seeking to reduce any zero-sum scenarios and increase non-zero-sum feelings, ideally that of a win-win scenario. In fact, as many studies show, increasing employee trust and satisfaction results in reduced turnover and improved productivity and profits.

Zero-sum theory is often used in scientific endeavors, such as biology, forestry, and meteorology. For example, globalization has brought an increase in trade of exotic species around the world, causing problems of invasive species. With climate change, many of these species—having grown better able to adapt and survive in alien environments—are expected to thrive and to range in wider and higher latitudes. These species often thrive at the expense of native species, so that scientists study the ways in which the gains of some determine the cost of others.

Finally, zero-sum views are studied in social sciences, to understand such social phenomena as inequality, race relations, discrimination, and migration. One of the core reasons for the persistence of inequality, according to many experts, is that people embrace ideologies that justify inequality. Studies show that high status individuals in a society tend to blame low status groups for their own lower status in the hierarchy, finding their claims of being discriminated against as without merit.

For example, low status groups are frequently accused by high status individuals of clinging to their low status, arguing that discontented people could change their situation if they worked harder. The difficulties faced by members of out groups are disregarded by members of advantaged groups, so that, for example, men tend to downplay the extent to which women face discrimination. Moreover, well-resourced groups tend to see the world as zero-sum, that is, believing that any gains by lower status groups comes at the expense of higher status groups. Nevertheless, zero-sum is not an accurate representation of real social dynamics. People in societies integrate to different degrees in social, economic, and cultural spheres, and may be successful in some aspects while failing in others. Even unequal societies, in general, engage in negotiations, accommodations, and trade-offs rather than winner-take-all dynamics.

Issues

Individuals may develop zero-sum views based on the aggregate of personal experiences, both at the social level as well as with other individuals. On the other hand, culture shapes general beliefs and develop what some expert call "social axioms," that is, beliefs that constitute foundational premises that people support and use as a roadmap in a variety of situations, without bothering to test or challenge their validity. These axiomatic beliefs are the result of shared experiences in a culture and society; that is, people are socialized into them, and fully internalize them so that they become unquestioned tenets and taken for granted. The belief that life is a zero-sum game is a common social axiom.

While zero-sum as a concept can work as a cognitive mechanism in very specific situations, applied overall as a worldview, it fosters the idea that most life experiences are intractable conflicts. According to a multinational study (Adamska et al., 2015), these ideas foster attitudes that affect individuals at three levels: cognitive, emotional, and behavioral.

At the cognitive level, zero-sum buttresses antagonistic perceptions, a belief in the unlikelihood of shared aspirations and interests, a negative vision of the world, dependence on others, pessimism, an external center of control, and distrust of social systems. At the emotional level, it makes people prone to anxiety, rumination, sadness, fear or feelings of "being a loser," and a low level of personal satisfaction. At the behavioral level, people with a zero-sum outlook may withdraw from social interactions, avoid cooperation and exchange, and engage in many interpersonal conflicts. Other studies have compounded the findings that a zero-sum outlook leads to conflictive behavior, as opposed to positive outlooks leading to better and more stable social relations. The conviction that life is a zero-sum game leads to negative evaluations of people and organizations.

Other studies have shown that a zero-sum outlook may result in inappropriate reactions to some scenarios, such as encountering the judicial system. There is a common belief that criminal investigations and court interactions are two-sided competitive endeavors in which the judge must maintain a balance on both sides. The judicial process, then, is considered as a zero-sum game, with the law on one side and wrongdoers on the other. In reality, however, the relationship between the law and defendants is more complicated. The justice system is not an arena for competition, because the law deals with fundamental and inalienable rights of the people involved, including law enforcement, victims, witnesses, and defendants. The issues of rights is not very amenable to considerations of cost-benefit. This does not mean that, to a certain extent, considerations of game theory are not applicable to, for instance, some cases such as tort law. But the law is often meant to deal with the balance of rights and meting out justice, and zero-sum principles prove inadequate for such analyses.

Terms & Concepts

Axioms: A statement or principle accepted as a general truth.

Cost-benefit: Related to analyzing or calculating a situation by taking into consideration all its costs and its benefits.

Game Theory: A mathematics-based theory used to predict outcomes based on the rational choice of individuals involved in competitive scenarios.

Utilitarian: A philosophy meant to guide individuals to make pragmatic decisions and in this manner achieve the greatest good for all.

Winner-take-all: A competitive strategy or set of actions intended to win the most outcomes ensuring the losing side scores none.

Zero-Sum: In game theory, a situation in which whatever is won by one player is lost by another.

Bibliography

Adamska, K., Jurek, P., & Różycka-Tran, J. (2015). The mediational role of relational psychological contract in belief in a zero-sum game and work input attitude dependency. Polish Psychological Bulletin, 46(4), 579–586.

Garrett, A. (2015). Is integration a zero-sum game? Negotiating space for ethnic minorities in Europe. French Politics, Culture & Society, 33(3), 116–130.

Jackson, J. E., Mach, B. W., & Miller-Gonzalez, J. L. (2016). Attitudes about EU expansion and zero-sum thinking. Economics of Transition, 24(3), 481–505. Retrieved January 1, 2018 from EBSCO Online Database Business Source Ultimate. http://search.ebscohost.com/login.aspx?direct=true&db=bsu&AN=116145551&site=ehost-live

Martin, K., & Flynn, A. (2015). Anthropological theory and engagement: A zero-sum game? Anthropology Today, 31(1), 12–14.

Simmons, R. (2013). Ending the zero-sum game: How to increase the productivity of the Fourth Amendment. Harvard Journal of Law & Public Policy, 36(2), 549–604. Retrieved January 1, 2018 from EBSCO Online Database Business Source Ultimate. http://search.ebscohost.com/login.aspx?direct=true&db=asn&AN=87434430&site=ehost-live

Stephens, A. A., Stringer, L. D., & Suckling, D. M. (2016). Advance, retreat, resettle? Climate change could produce a zero-sum game for invasive species. Austral Entomology, 55(2), 177–184.

Stone, J. (2015). Under-labourer or ϋber-labourer—a zero sum game? Ethnic & Racial Studies, 38(8), 1413–1416.

Wellman, J.D., Liu, X., & Wilkins, C.L. (2016). Priming status-legitimizing beliefs: Examining the impact on perceived anti-White bias, zero-sum beliefs, and support for Affirmative Action among White people. British Journal of Psychology, 55(3), 426–437.

Suggested Reading

Boitano, A., Lagomarsino, R., Schockman, H.E. (2017) Breaking the zero-sum game: transforming societies through inclusive leadership. Bingley, UK: Emerald Publishing.

Cheng, E. (2017, November 18). Fruit, veggies and how to depict the universe. Wall Street Journal—Online Edition. p. 1. Retrieved January 1, 2018 from EBSCO Online Database Business Source Ultimate. http://search.ebscohost.com/login.aspx?direct=true&db=bsu&AN=126304437&site=ehost-live

Lidbetter, T. (2017). On the approximation ratio of the Random Chinese Postman Tour for network search. European Journal of Operational Research, 263(3), 782–788. Retrieved January 1, 2018 from EBSCO Online Database Business Source Ultimate. http://search.ebscohost.com/login.aspx?direct=true&db=bsu&AN=124355265&site=ehost-live

Neyman, A. (2012). The value of two-person zero-sum repeated games with incomplete information and uncertain duration. International Journal of Game Theory, 41(1), 195–207. Retrieved January 1, 2018 from EBSCO Online Database Business Source Ultimate. http://search.ebscohost.com/login.aspx?direct=true&db=asn&AN=70431342&site=ehost-live

Ruthig, J., Kehn, A., Gambin, B., Vanderzanden, K., Jones, K., (2017). When women's gains equal men's losses: Predicting a zero-sum perspective of gender status. Sex Roles, 76(1/2), 17–26.