QBOS {QGameTheory}

Quantum Battle of the Sexes game

Description

This function returns the expected payoffs to Alice and Bob with respect to the probabilities p and q. p+q should equal 1 and moves is a list of two possible strategies for each of the players and alpha, beta, gamma are the payoffs for the players corresponding to the choices available to them with the chain of inequalities, alpha>beta>gamma.

Usage

QBOS(p, q, moves, alpha, beta, gamma)

Arguments

p

a real number between 0 and 1 including the end points

q

a real number between 0 and 1 including the end points

moves

alist of matrices

alpha

a number

beta

a number

gamma

a number

Value

A vector consisting of the Payoffs to Alice and Bob as its two elements depending on the inputs.

References

https://arxiv.org/pdf/quant-ph/0506219.pdf
https://arxiv.org/pdf/quant-ph/0208069.pdf
https://arxiv.org/abs/quant-ph/0110096

Examples

init()
moves <- list(Q$I2, sigmaX(Q$I2))
QBOS(0, 1, moves, 5, 3, 1)
QBOS(1, 1, moves, 5, 3, 1)
QBOS(0.5, 0.5, moves, 5, 3, 1)