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arXiv:1503.00903 · International Journal of Theoretical Physics

A Quantum-Like View to a Generalized Two Players Game

Fabio Bagarello

Published Mar 19, 2015• 34 citations
arXivHTMLPDF
DOI
10.1007/s10773-015-2599-x

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INFORMATION GAMES

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In a game each player holds a strategy based upon the actions that he can actually take. The quality and the quantity of the feasible actions are determined by his ability or power in the game. Generally every player has no information on the others' powers, so it is one of the most important problems for them to know the powers. We treat such unknown games, played periodically, from the view point of information theory. We discuss both non-cooperative and cooperative games and prove some sufficient conditions under which a player can get the full information on the other players' powers from sequential observations on the states. In two person games we show also optimal strategies with respect to the information.

Bulletin of informatics and cybernetics•Mar 1, 1982•0 citations
In a recent work, Moshkovitz [FOCS '14] presented a transformation on two-player games called "fortification", and gave an elementary proof of an (exponential decay) parallel repetition theorem for fortified two-player projection games. In this paper, we give an analytic reformulation of Moshkovitz's fortification framework, which was originally cast in combinatorial terms. This reformulation allows us to expand the scope of the fortification method to new settings. First, we show any game (not just projection games) can be fortified, and give a simple proof of parallel repetition for general fortified games. Then, we prove parallel repetition and fortification theorems for games with players sharing quantum entanglement, as well as games with more than two players. This gives a new gap amplification method for general games in the quantum and multiplayer settings, which has recently received much interest. An important component of our work is a variant of the fortification transformation, called "ordered fortification", that preserves the entangled value of a game. The original fortification of Moshkovitz does not in general preserve the entangled value of a game, and this was a barrier to extending the fortification framework to the quantum setting.
In a recent work, Moshkovitz [FOCS'14] presented a transformation n two-player games called "fortification", and gave an elementary proof of an (exponential decay) parallel repetition theorem for fortified two-player projection games. In this paper, we give an analytic reformulation of Moshkovitz's fortification framework, which was originally cast in combinatorial terms. This reformulation allows us to expand the scope of the fortification method to new settings. First, we show any game (not just projection games) can be fortified, and give a simple proof of parallel repetition for general fortified games. Then, we prove parallel repetition and fortification theorems for games with players sharing quantum entanglement, as well as games with more than two players. This gives a new gap amplification method for general games in the quantum and multiplayer settings, which has recently received much interest. An important component of our work is a variant of the fortification transformation, called "ordered fortification", that preserves the entangled value of a game. The original fortification of Moshkovitz does not in general preserve the entangled value of a game, and this was a barrier to extending the fortification framework to the quantum setting.
In a game each player holds a strategy based upon the actions that he can actually take. The quality and the quantity of the feasible actions are determined by his ability or power in the game. Generally every player has no information on the others' powers, so it is one of the most important problems for them to know the powers. We treat such unknown games, played periodically, from the view point of information theory. We discuss both non-cooperative and cooperative games and prove some sufficient conditions under which a player can get the full information on the other players' powers from sequential observations on the states. In two person games we show also optimal strategies with respect to the information.