Zero-sum in game theory is the direct correlation between one player's gain and the other player's loss. For example, in a hand of poker one Player A's take of the pot is directly equal to the loss of Player B .When the gain and the loss are added together; it is a zero sum result. In a zero sum game one player cannot win unless the other player loses. For example, taking a piece of a pie reduces the amount of pie available for others. This is the way that many people operate in the real world. The competitive nature of our society is based on zero-sum games. These games are played out in sports, business and within many social constructs- including monogamy. The conventional thought within monogamy is that you cannot give to another person without taking away from your partner. You see this exemplified in every jealous lover on every day time talk show. Polyamorous people, those who have chosen to share their emotional resources should be outside such zero-sum games, but that is seldom the case.
It may seem crass to refer to interpersonal relationships as a game but most people are firmly rooted in their competitive nature. Because of the framework of our society it is the usual mode of operation for all of us; the gains of time, attention, love, affection…etc are to the loss of another 'player' or partner. For many people in poly situations this will seem like a ludicrous way to operate but it happens all the time.
To pull an all too common resource of a zero-sum situation in poly we will use sex. For the purposes of this example we will define sex as "intimate physical contact to include penetration (toy, penis, or any random object lying around the room), manual stimulation and oral to genital contact." Jane and Mandy are in a poly relationship and Mandy is dating Billy. Billy and Mandy are close and have had sex many times. This fact upsets Jane who believes that some act or action by Billy and Mandy takes from her the intimate closeness that she and Mandy share. Billy and Mandy have a falling out and stop their physical relationship. Jane's perception of the situation is that, now that Mandy is only having sex with her, she has regained some of that intimate closeness that she and Mandy had. The truth is that Jane and Mandy never lost touch but because of the zero-sum game Jane was playing, the actually gain and the perceived gain were not the same. All gains in this situation are perceived gains and there for immeasurable and highly subjective.
What Jane did was create an unnecessary conflict that didn't benefit her or the group as a whole but kept the situation static. If Jane had instead used a strategy of equilibrium to resolve her perceived loss, the outcome would have been consistently at least Pareto optimal i.e. the gains for all players are equitable. She should have examined what she was getting, what Mandy was getting, what Billy was getting and created a strategy that improved her situation, the situation of the group and the individuals in the group. This does not always yield the largest gains for anyone involved but it does create the optimal situation.
Approaching poly and relationships from a zero-sum mentality is damaging to both the relationship and your own psyche. In addition it creates conflict and strife in what already is going to be a hard situation, as all interpersonal relationships are. What others gain does not necessarily correlate to a loss for you and often there is a balance that can be reached that doesn't involve the deprivation of anyone's gain.