There are some two-person games where quantum strategies can outperform classical strategies. One example is a coin-flipping game, alternating between players Q and C. Q possesses a quantum strategy which always ensures victory, irrespective of C's classical strategy. This provides the simplest example of a quantum error correction code.
Another instance involves a yes/no question game which is related to the Clauser-Horne-Shimony-Holt and Bell inequalities. The best classical strategy attains a 3/4 success rate, but a quantum strategy surpasses it with a 0.854 success rate.
In the well-known prisoner's dilemma, the best classical strategy aligns with a Nash equilibrium but it is not Pareto optimal. In contrast, there is a quantum strategy which is both Pareto optimal and is at a Nash equilibrium.
This talk will be at an elementary level. I will assume only a basic knowledge of two-state systems in quantum mechanics, and no knowledge of game theory.
1. Meyer, Phys. Rev. Lett. 82, 1052 (1999)
2. Eisert, Wilkens, and Lewenstein, Phys. Rev. Lett. 83, 3077 (1999)
3. Cleve, Hoyer, Toner, and Watrous, arXiv:quant-ph/0404076
4. Landsburg, Notices of the AMS 51, 394 (2004); available at
http://www.ams.org/notices/200404/fea-landsburg.pdf (this is a simple introduction to quantum game theory written by an economist)
Zoom link: https://icts-res-in.zoom.us/j/99445250208?pwd=N1N4Z2JvWlBqNFQyY2R2QkpBY0g2UT09
Meeting ID: 994 4525 0208
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