Competitive effect of cross-shareholdings in all-pay auctions with complete information

► This paper explores the competitive effects of cross-shareholdings in all-pay-auctions. ► A complete account of bidding behaviors in all-pay-auctions with cross-shareholdings is provided. ► Cross-shareholdings may intensify competition and improve effort supply. ► The conditions under which cross-shareholdings lead to higher (lower) effort are identified. ► The pro-competitive effect of cross-shareholding comes at a loss of efficiency.