A tertius gaudens ("rejoicing third") is a third party who profits or benefits from competition amongst two others. The coining of this term is usually attributed to sociologist Georg Simmel, who was interested in how, when a dyad becomes a triad, the third party can gain tremendous power. The tertius gaudens is able to play one party off against the other for his or her own advantage, or gain favour with one party to the detriment of the other. The classic military strategy of divide and conquer is an example of creating a situation where a person or country can become a tertius gaudens by rendering a previously unified power into a divided pair of competitors; or the backstabbing version of this, where one party is encouraged by the tertius gaudens-to-be to betray another, who does so, only to find that the tertius gaudens has switched sides and now favours the competitor.
Note that this model only works if all three have equal and independent positions and relations; if the two parties join forces, the tertius gaudens' favourable position dissolves. In economic terms, the buying public can be seen as playing two producers off against each other and promoting for their own self interest by gaining the lowest price; if the producers join forces and become a monopoly, the tertius gaudens no longer has the upper hand and has to pay whatever the new big producer asks.