On the “prisoner’s dilemma” of order timing in a cross-border and co-opetitive supply chain

•We investigate the order timing decision in a cross-border and co-opetitive supply chain.•Our key trade-off is among first-mover advantages, second-mover disadvantages, and information value.•The order timing equilibrium if (B,B) when demand fluctuation and transfer price (downstream relative tax rate) are small.•We find that the affiliated and non-affiliated retailers might be trapped in the “prisoner’s dilemma”.•The “prisoner’s dilemma” leads to a “lose-lose-lose” situation. In this paper, we consider a cross-border and co-opetitive supply chain consisting of a non-affiliated retailer and a multinational firm (MNF) that owns an affiliated retailer and a manufacturing division. We concentrate on the order timing decisions of retailers. If a retailer opts to delay the order, he/she may suffer from second-mover disadvantages, but he/she can obtain demand information. If not, he/she may gain first-mover advantages. We study the impact of downstream relative tax rate on transfer price and analyze the trade-off among first-mover advantages, second-mover disadvantages, and information value, to obtain the equilibrium results about the order timing of both retailers. We find that both the affiliated and non-affiliated retailers do not delay the order, when demand fluctuation and transfer price (downstream relative tax rate) are small under exogenous (endogenous) transfer price. This implies that they might be trapped in the “prisoner’s dilemma”. Also, the MNF is not able to maximize the profit in that region. Hence, the “prisoner’s dilemma” leads to a “lose-lose-lose” situation. To deal with that, we suggest that the governments should adjust the corporate income tax rates to assist MNFs in avoiding the “prisoner’s dilemma”.