J. William Helton, Hamoon Mousavi, Seyed Sajjad Nezhadi, Vern I. Paulsen, Travis B. Russell
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引用次数: 0
Abstract
We study synchronous values of games, especially synchronous games. It is known that a synchronous game has a perfect strategy if and only if it has a perfect synchronous strategy. However, we give examples of synchronous games, in particular graph colouring games, with synchronous value that is strictly smaller than their ordinary value. Thus, the optimal strategy for a synchronous game need not be synchronous. We derive a formula for the synchronous value of an XOR game as an optimization problem over a spectrahedron involving a matrix related to the cost matrix. We give an example of a game such that the synchronous value of repeated products of the game is strictly increasing. We show that the synchronous quantum bias of the XOR of two XOR games is not multiplicative. Finally, we derive geometric and algebraic conditions that a set of projections that yields the synchronous value of a game must satisfy.
期刊介绍：
The two journals Annales de l''Institut Henri Poincaré, physique théorique and Helvetica Physical Acta merged into a single new journal under the name Annales Henri Poincaré - A Journal of Theoretical and Mathematical Physics edited jointly by the Institut Henri Poincaré and by the Swiss Physical Society.
The goal of the journal is to serve the international scientific community in theoretical and mathematical physics by collecting and publishing original research papers meeting the highest professional standards in the field. The emphasis will be on analytical theoretical and mathematical physics in a broad sense.
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