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Quantum Information Processing

A quantum approach to play asymmetric coordination games

Haozhen Situ

Published Nov 11, 2013• 28 citations
Publisher
DOI
10.1007/s11128-013-0675-9

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arXiv:2606.00190•May 29, 2026•0 citations
A simulation scheme of quantum version of Cournot's duopoly is proposed, in which there is a new Nash equilibrium that may also be Pareto optimal without any entanglement involved. The unique property of this simulation scheme is decoherence-free against the symmetric photon loss. Furthermore, we analyze the effects of the asymmetric information on this simulation scheme and investigate the case of asymmetric game caused by asymmetric photon loss. A second-order phase transition-like behavior of the average profits of firms 1 and 2 in a Nash equilibrium can be observed with the change of the degree of asymmetry of the information or the degree of ‘virtual cooperation’. It is also found that asymmetric photon loss in this simulation scheme plays a similar role as that with the asymmetric entangled states in the quantum game.
Social deduction games, or hidden-role games, are multiplayer games in which players are assigned private roles and act under asymmetric information about other players' roles and actions. In the canonical example Werewolf, werewolves conceal their roles and mislead the other players, while the seer can obtain role information about a chosen player. Thus, a central functionality of such games is controlling which players can access which information. In typical play, this control is implemented by a trusted human moderator, who assigns roles, mediates secret actions, and reveals outcomes. This reliance raises the barrier to participation and introduces a trusted third party as a single point of failure. In this work, we show that Werewolf can be played without a moderator or any digital device, using only ordinary playing cards. Our construction maintains a shared pool of cards that is observable to all players and manipulated according to a common public procedure, while its interpretation depends on each player's private role. This induces role-dependent views from a single public sequence of card operations. Consequently, even without private messages, werewolves can identify one another and coordinate, and the seer can test whether a chosen player is a werewolf in each round. The proposed implementation is built from card-based physical cryptographic primitives, such as face-down commitments and verifiable shuffles, and higher-level subprotocols for intra-role information sharing, secret action designation, and attribute testing. These subprotocols implement the moderator's core functions while keeping all card operations public and auditable under standard assumptions on physical card operations. We show that the resulting complete moderatorless implementation of Werewolf scales to an arbitrary number n of players using O(n^3) cards.