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

Evolutionarily Stable Strategies in Quantum Hawk-Dove Game

We quantized the Hawk-Dove game by using the most general form of a pure initial state to investigate the existence of pure and mixed Evolutionarily Stable Strategies (ESS). An example is considered to draw a comparison between classical and quantum version of the game. Our choice of most general initial quantum state enables us to make the game symmetric or asymmetric. We show that for a particular set of game parameters where there exist only mixed ESS in the classical version of the game, however, quantization allows even a pure strategy to be an ESS for symmetric game in addition to ixed ESS. On the other hand only pure strategy ESS can exist for asymmetric quantum version of the Hawk-Dove game.Comment: Revised version. LaTex, 11 pages, no figure. Corresponding author's email: [email protected]

Entanlement-Assisted Classical Capacity of Quantum Channels with Correlated Noise

We calculate the entanglement-assisted classical capacity of symmetric and asymmetric Pauli channels where two consecutive uses of the channels are correlated. It is evident from our study that in the presence of memory, a higher amount of classical information is transmitted over quantum channels if there exists prior entanglement as compared to product and entangled state coding.Comment: 8 Pages, 2 Figure

Channel Capacities of an Exactly Solvable Spin-Star System

We calculate the entanglement-assisted and unassisted channel capacities of an exactly solvable spin star system, which models the quantum dephasing channel. The capacities for this non-Markovian model exhibit a strong dependence on the coupling strengths of the bath spins with the system, the bath temperature, and the number of bath spins. For equal couplings and bath frequencies, the channel becomes periodically noiseless.Comment: 8 pages, 5 figure

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