US video games retailer GameStop has offered to buy eBay for $55.5bn (£41bn) in an unsolicited bid that its boss warned could turn hostile if the proposal is rebuffed by eBay’s board. GameStop, which has quietly accumulated a 5% stake in eBay , said it was willing to pay $125 a share, split 50-50 between cash and stock. It is an ambitious move by the games company, which catapulted to fame during the meme-stock craze of 2021 but is worth far less than its takeover target. GameStop had a market valuation of roughly $12bn on Friday before its bid, while eBay – originally launched as a side hobby by its founder Pierre Omidyar in 1995 – is worth about $46bn. But Ryan Cohen, who has run GameStop since 2020, claims eBay could be worth much more under his leadership, saying in a letter to eBay chair, Paul Pressler, that he would immediately launch a cost-cutting programme that would slash $2bn worth of spending a year.…