The ultimatum game, along with the dictator game
is a favorite among behavioral economists
who want to demonstrate that simple models of self-interested behavior
don't explain everything.
In the ultimatum game, there are two players, a "Proposer" and a "Responder". There is a pot of money which the two players can split (say it's $20, in $1 bills). The Proposer gets to propose a split of the money, and the Responder gets to either accept or reject the proposal. If the Responder rejects it, then neither player gets any money.
According to the simplest applications of game theory, the Proposer should propose a split of $19 for themself, and $1 for the Responder. The reason for this is that the Responder will be choosing between $1 and nothing for themself, and so will choose $1, which means accepting the proposal.
In practice, of course, it doesn't work out that way. Responders tend to reject very uneven splits. Anticipating this, Proposers tend to propose fairly even splits.
Economists and psychologists are fiddling with a number of different ways of dealing with this, including altruism, inequality aversion, reciprocity (including negative reciprocity or spite).