Matthijs van Veelen studies the evolution of altruism, fairness and morality. His main tool is evolutionary game theory – the 'blind' sidekick of classical game theory, which describes strategic interactions mathematically. He developed a unified theory for the evolution of cooperation. This theory subsumes two classic results – one from theoretical biology and one from classical game theory – for the evolution of cooperation and altruism. Van Veelen's previous research focused on comparisons of income levels, in which he formulated and proved the 'apples and oranges theorem', which sets out the inherent shortcomings of attempts to compare incomes. 

Van Veelen has worked as a researcher at the UvA's Center for Research in Experimental Economics and Political Decision Making (CREED) since 2004, where he also collaborates with scientists from the UvA's Institute for Biodiversity and Ecosystem Dynamics (IBED). In 2009, 2011 and 2013 he was a guest researcher at the Program for Evolutionary Dynamics at Harvard University (US), and in 2012 he was named a member of The Young Academy of the Royal Netherlands Academy of Arts and Sciences (KNAW). His results have been published in Econometrica, the American Economic Review, the Proceedings of the National Academy of Sciences (PNAS) and the Journal of Theoretical Biology.