Shares of Sony rose on Monday, a day after the firm said it would resume some services on its PlayStation Network this week and offer customer incentives following the theft of personal information belonging to 78 million users.

Many PlayStation users around the world have been angered after the first warning of one of the largest Internet security break-ins ever came a week after Sony detected a problem with the network on April 19.

Shares in Sony were 2 percent higher at 2,306 yen in early trade on Monday, after tumbling 4.5 percent Thursday. Tokyo markets were closed Friday.

Sony said on Sunday it would offer some free content, including 30 days of free membership to a premium service to existing users and in some regions pay credit card-renewal fees, but added compensation would only be paid if users suffered damage.

The news sparked thousands of comments on the official PlayStation fan page on Facebook, some of them from users who said they would switch to Microsoft's Xbox Live games 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.

Sony is the latest Japanese company to come under fire for how it has disclosed bad news.

Tokyo Electric Power Co was criticized for how it handled the nuclear crisis after the March 11 earthquake. Last year, Toyota Motor Corp was slammed for being less than forthright about problems over a massive vehicle recall.

(Reporting by James Topham; Editing by Chris Gallagher and Edwina Gibbs)