"The American convention is to use full stops (periods) at the end of almost all abbreviations and contractions. The British convention is to use full stops after abbreviations - eg, abbr., adj., co. - but not after contractions - eg, Dr, Mr, Mrs, St."
source: The Economist Style Guide (2005)
This is strange because I would say "e.g." is an abbreviation, but they use "eg" without full stops throughout the whole document.