Quantum Cooperative Games

We study two forms of a symmetric cooperative game played by three players, one classical and other quantum. In its classical form making a coalition gives advantage to players and they are motivated to do so. However in its quantum form the advantage is lost and players are left with no motivation to make a coalition.Comment: Revised in the light of referee's comments. Submitted to Physics Letters A. LaTex, 9 pages, 1 figure. Parts of this paper are rewritte

Stability of mixed Nash equilibria in symmetric quantum games

In bi-matrix games the Bishop-Cannings theorem of the classical evolutionary game theory does not permit pure evolutionarily stable strategies (ESSs) when a mixed ESS exists. We find the necessary form of two-qubit initial quantum states when a switch-over to a quantum version of the game also changes the evolutionary stability of a mixed symmetric Nash equilibrium.Comment: 8 pages, no figure, to appear in Communications in Theoretical Physic

Backwards-induction outcome in a quantum game

In economics duopoly is a market dominated by two firms large enough to influence the market price. Stackelberg presented a dynamic form of duopoly that is also called `leader-follower' model. We give a quantum perspective on Stackelberg duopoly that gives a backwards-induction outcome same as the Nash equilibrium in static form of duopoly also known as Cournot's duopoly. We find two qubit quantum pure states required for this purpose.Comment: Revised in the light of referee's comments. Latex, 16 pages, 2 figures, To appear in Phy. Rev.

Topological spin liquids: Robustness under perturbations

We study the robustness of the paradigmatic kagome Resonating Valence Bond (RVB) spin liquid and its orthogonal version, the quantum dimer model. The non-orthogonality of singlets in the RVB model and the induced finite length scale not only makes it difficult to analyze, but can also significantly affect its physics, such as how much noise resilience it exhibits. Surprisingly, we find that this is not the case: The amount of perturbations which the RVB spin liquid can tolerate is not affected by the finite correlation length, making the dimer model a viable model for studying RVB physics under perturbations. Remarkably, we find that this is a universal phenomenon protected by symmetries: First, the dominant correlations in the RVB are spinon correlations, making the state robust against doping with visons. Second, reflection symmetry stabilizes the spin liquid against doping with spinons, by forbidding mixing of the initially dominant correlations with those which lead to the breakdown of topological order.Comment: v2: accepted versio