Solving diner’s dilemma game, circuit implementation and verification on the IBM quantum simulator

Abstract

Diner's dilemma is a problem of interest to both economics and game theory. Here, we solve this problem for n = 4 (where n is the number of players)with quantum rules. We are able to remove the dilemma of diners between the Pareto optimal and Nash equilibrium points of the game. We find the quantum strategy that gives maximum payoff for each diner without affecting the payoff and strategy of others. Quantum superposition and entanglement is used as a resource which gave the supremacy over any classical strategies. We present the circuit implementation for the game, design it on the IBM quantum simulator and verify the strategies in the quantum model.

A Quantum Adaptation for the Morra Game and Some of Its Variants

“…Diner's Dilemma is a classical problem related to game theory and economics. In the quantum world, it has been faced and solved in the 4-player variant [22] by implementing and testing a circuit built using IBM ® Quantum Simulator. It has also been shown that players can reach both the Nash equilibrium point and the Pareto optimum point.…”

Experimental Realization of Quantum Darwinism State on Quantum Computers

“…A python module named QISKit [13] is also introduced to write programs, for running the quantum circuits on real devices and to collect the results. A larger number of tasks have already been performed such as quantum simulation [14][15][16], quantum machine learning [17][18][19], quantum algorithms [20][21][22], quantum communication [23][24][25], quantum cryptography [26,27], quantum circuit architecture [28][29][30], quantum game [31,32] to name a few.…”

Quantum Multiplayer Colonel Blotto Game

“…Since 1999 several classical games was brought to the quantum realm due to the intrinsic probabilistic nature of quantum theory and game theory (for mixed strategies), such as Prisoners' Dilemma [2], Hawk-Dove [3,4], Quantum duel [5,6] and recently Colonel Blotto [7]. The quantum games are investigated in order to find new properties [8,9,10,11,12] or deep connections with game theory [13]. Our purpose is to present a quantum version of multiplayer Colonel Blotto game.…”