Abstract
We have investigated the quantization of the multi-player Stackelberg game by proposing an asymmetric quantum entanglement operation. Due to the informational asymmetry between the leaders and followers in the Stackelberg model, it is more natural to have differential quantum entanglement in a multi-player quantum Stackelberg game. It is found that the profit functions considered in the multi-player Stackelberg model display interesting and intriguing patterns as functions of quantum entanglement parameters. In particular, differential quantum entanglement could cause the leaders to lose the first-mover advantage inherent in the classical Stackelberg model. This surprising feature raises an important question: “To move first or not to move first?”
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The two approaches of course should give the same profit result if in the first one sets all the entanglement parameters to be the same, and in the second one sets \(N=3\). However, the two in their paper did not agree. The result they obtained by setting all the parameters equal in the first approach actually became independent of the entanglement parameter. This can be corrected if the limit of the three parameters approaching to the same value is taken properly.
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Lo, C.F., Kiang, D. To move first or not to move first?. Quantum Inf Process 18, 335 (2019). https://doi.org/10.1007/s11128-019-2452-x
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DOI: https://doi.org/10.1007/s11128-019-2452-x