🤝 The Quantum Prisoner's Dilemma
Entanglement makes cooperation pay — for a restricted set of moves. Then comes the catch.
Opens a free Jupyter session on mybinder.org (via QuBins) — starting it can take a few minutes
git clone the repository, create the conda environment from environment.yml, and open Prisoners-Dilemma.ipynb.Two players each choose to cooperate or defect. Defecting pays more whatever the other does, so rational players both defect and get 1 point each — although cooperating would give both 3.
In the quantum version of Eisert, Wilkens and Lewenstein (1999), a referee entangles the players’ qubits, and a new quantum move Q turns (Q, Q) into an equilibrium worth 3 each: the dilemma disappears. The notebook builds the game in Qiskit, maps the payoffs and searches for equilibria — and then shows the catch found by Benjamin and Hayden (2001): with every one-qubit move allowed, each move has a counter, so equilibria exist only with random (mixed) strategies — for example both players picking a completely random one-qubit move, worth 2.25 points each.