Zero-sum and non-zero-sum games in game theory

¶ … Zero-Sum Game and Non-Zero Sum Game

Zero-sum games are games, or operations that satisfy the property 'one's gain equals another's loss.' Taking, for instance, two players A and B; a zero-sum game is said to have occurred if A's gain implies that B. loses, with an equal magnitude. This means that player A's loss or gain exactly balances B's losses or gains. If A has a payoff of 1, then B. has -1. The implication is that the aggregate of both participants' gains and losses is equal to zero. Chess and tennis, for instance, can be considered "zero sum, in the sense that one player wins (+1), and the other loses (-1), so the sum is zero" (Baumeister & Bushman, 2011, p. 312).

In non-zero-sum games, on the other hand, the sum of all, parties' gains and losses is either greater, or less than, but not equal to zero. In these games therefore, one person's gain does not necessitate another's detriment (Bernstein, 2004). An example is the prisoner's dilemma; where two people are "questioned separately after being caught with stolen goods, and can either confess to theft (I1, II1), or keep quiet (I2, II2)" (Thomas, 2012, p. 55). The payoffs are as shown in the matrix below;

II1( confess)

II2(Not confess)

I1(Confess)

-9,-9

0,-10

II2(Not confess)

-10,0

-1,-1

(Source: Thomas, 2012, p. 55)

The implication is that if both I and II choose to confess, they each get a 9-year jail term. However, if one confesses, and the other does not, the confessor is freed, while the one who declines to confess gets a 10-year jail term. If both do not confess, they each just get a 1-year jail term. The player's objective comes to play in this scenario, whether "to do what is best for him as an individual or him as part of a group?" (Thomas, 2012, p. 55). Confessing would be good for an individual because if the opponent does not confess, you get freed, an if he/she does, then you both get just light sentences. However, confessing is seen as betrayal. The most suitable outcome is achieved if both cooperate (do not confess). The context of non-zero-sum games is literally "the dilemma of human cultural life in a nutshell: whether to selfishly pursue your own impulses, regardless of the rules and other people's welfare, or instead to do what is best for all" (Baurneister & Bushman, 2011, p. 312).

The theme of cooperation and betrayal in our social interactions forms the basis of Carol Gilligan's work. Gilligan holds the opinion that the difference in societal upbringing is the cause of the difference between the female and male morality views (Bernstein, 2008). Males believe in dominance, rules, rights, and justice; whereas females believe in caring and naturally prefer cooperation to competition. Gilligan compares the caring nature of women to close relationships such as mother-child, and "takes these relationships as the foundation of morality" (Bernstein, 2004, p. 178).