A new study also indicates that inequality within groups can actually help to ensure everyone contributes sufficiently to the group.
The results could help policy-makers who are responsible for ensuring continuing support for public goods and services such as taxes, healthcare and education, researchers say.
Scientists discovered that in a very unequal society, people with higher incomes were less inclined to contribute their proportional share towards public goods and services.
This, in turn, also led people on the lowest incomes to contribute less.
This breakdown of cooperation under equality has impacts funding for essential services for society.
Co-first author Dr Oliver Hauser from the University of Exeter, said: “To ensure our public goods are maintained we need to understand what impact inequality plays.
“Many people view inequality as either categorically bad or good, but our research demonstrates that it is more complicated than that.
“We looked at it in a slightly different way – under what conditions does inequality become harmful and are there cases where it can also be beneficial?
“The main take-away from our research is that if inequality runs away with us, we are threatening the maintenance of public services.
“Eventually, too much inequality negatively affects everyone’s outcomes – both for the poorest but even the rich.”
According to the research, high inequality reduces the willingness to cooperate in groups of two people with unequal incomes.
Yet when people had different productivities, some inequality in incomes can be beneficial to ensure they both continue to contribute.
Dr Christian Hilbe of the Institute of Science and Technology Austria, said: “We found that when there is some inequality, both people still have enough influence to hold each other accountable for their contributions.
“We also discovered that those who are highly productive in the task are more motivated to contribute.
“They will give more of their income, even if that is a large amount.
“But there is a limit: once the inequality between the two people becomes too large, the influence over the other person is lost and the poorer player is at the mercy of the more powerful rich player.
“Neither of them has much incentive to cooperate anymore and cooperation breaks down quickly.”
In the study published in the Nature journal, researchers developed a mathematical theory, which took into account to what extent people with differing incomes and productivities were able to cooperate with one another.
Their willingness to contribute part of their income to the public good was measured.
The research was also carried out by Professor Martin Nowak of Harvard University, and Professor Krishnendu Chatterjee of IST Austria.
The team used game theory, computer simulations and a behavioural experiment to develop their model and find empirical support for its conclusions.