  We demonstrate a Bayesian quantum game on an ion trap quantum computer with
five qubits. The players share an entangled pair of qubits and perform
rotations on their qubit as the strategy choice. Two five-qubit circuits are
sufficient to run all 16 possible strategy choice sets in a game with four
possible strategies. The data are then parsed into player types randomly in
order to combine them classically into a Bayesian framework. We exhaustively
compute the possible strategies of the game so that the experimental data can
be used to solve for the Nash equilibria of the game directly. Then we compare
the payoff at the Nash equilibria and location of phase-change-like transitions
obtained from the experimental data to the theory, and study how it changes as
a function of the amount of entanglement.
