Quantum Games

We will discuss some examples of two-person games where quantum strategies can give better payoffs than purely classical strategies (even if the latter are probabilistic). The examples are as follows. (i) a coin flipping game where two people, Q and C, play in the order Q, C, Q. It turns out that Q has a quantum strategy which always wins regardless of the classical strategy followed by C. (ii) a game with two questions with yes/no answers and some payoffs for the four possible answers. The best classical strategy has a success rate of 3/4 in the long run, but there is a quantum strategy which has a success rate of about 0.854. (iii) the prisoner's dilemma: this is a famous game in which one strategy is at a Nash equilibrium while the other three strategies are Pareto optimal. A quantum version of this game has a Nash equilibrium which coincides with one of the Pareto optimal strategies and has a better payoff for both players compared to the Nash equilibrium of the classical game. Finally, I will mention some quantum games which have been played using NMR in Prof. Anil Kumar's lab in IISc. I will assume some elementary knowledge of quantum mechanics (two-state systems), but no knowledge of game theory. References: 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