Sony has stepped up its efforts to address customer anger after a data breach led to the theft of personal information belonging to 78 million users of its PlayStation Network.
The consumer electronics giant is offering some free content, including 30 days of free membership to a premium service to existing users.
In some regions it will also cover credit card-renewal fees – though it is still not clear if card data was stolen.
Compensation would only be paid if users suffered damage, Sony said, without providing details.
It has apologised and said it would gradually restart the PlayStation Network with increased security.
However analysts said the company still has some way to go to regain the trust of consumers.
Much of the anger is directed at the fact that Sony took a week to warn its customers after detecting a problem with the network.
The incident has sparked legal action and investigations by authorities in North America and Europe, home to almost 90 percent of the users of the network, which enables gamers to download software and compete with other members.