Bridgestone Corp. said Tuesday it will not increase its offer price for the acquisition of U.S. auto parts retailer Pep Boys-Manny, Moe & Jack, after U.S. activist investor Carl Icahn sweetened his proposal.

While Bridgestone awaits a final decision from the Pep Boys board of directors, the announcement indicates that the Japanese tire maker has effectively backed out of the bidding war with Icahn Enterprises LP.

On Monday, Icahn raised his offer to $18.50 per share, topping Bridgestone's bid of $17.00 a share offered last Thursday.

In October, Bridgestone, one of the world's largest automobile tire makers, said it will buy Pep Boys for $835 million through a takeover bid to bolster its U.S. sales network.

The bidding war between Icahn and the tire company began after the investor, who has a 12 percent stake in Pep Boys, jumped in this month, ultimately raising share prices more than $3.00 from Bridgestone's initial offer of $15.00 per share.

Based in Philadelphia, Pep Boys has more than 800 shops — mainly in the United States.