Police are treating the three incidents, all of which happened in the early hours of yesterday morning, as linked and believe two teenagers are responsible.
At around 4.45am on Sunday a 38-year-old man and a 26-year-old woman were sitting talking in Blackfriars Street when two men approached and threatened the man before punching him and stealing his phone and wallet. They then fled along New Skinner’s Close.
Around 20 minutes later a 22-year-old man was sitting outside Waverley Station on Market Street when a group of individuals attacked him and stole his personal belongings.
Just after 5.30am, a 20-year-old man was on Montrose Terrace when two males approached armed with a broken bottle and threatened the victim.
He was also robbed of his phone and wallet.
Officers are treating the incidents as linked and they are keen to hear from any witnesses.
One of the suspects is described as white, around 16-years-old with a defined jaw and blond curly hair, which was swept back over his forehead. He spoke with a local accent.
Another of the suspects is described as white, around 16 or 17-years-old, 5ft 6ins tall with brown eyes and wearing a dark blue baseball cap worn backwards. He also spoke with a local accent.
Detective Sergeant Lynsey Thomson said: “We believe the main suspects for each of these attacks were part of a larger group, who may have assisted in robbing the victims of their property.
“We are therefore keen to hear from anyone who can help us identify these individuals and I would ask that those with information contact police immediately.
“In addition anyone who remembers seeing any suspicious activity in these locations during the early hours of Sunday morning is also asked to come forward.”
Inspector Nicola Page from the City Centre Policing Team said: “Thankfully, incidents such as this are rare and none of the victims sustained any serious injury.
“In addition to the ongoing investigation we will have high-visibility patrols throughout busy city centre areas as part of our Festival policing operation.
“To help keep the public safe throughout the summer we offer a range of crime prevention advice on our website. This can be obtained by visiting www.scotland.police.uk.”
Those with information in relation to these incidents can contact Police Scotland on 101 or alternatively, the charity Crimestoppers on 0800 555 111.