



01359nas a2200157   4500008004100000245003200041210003200073260001400105520093200119100002001051700002001071700002701091700002201118700002401140856003701164       2021                        eng d00aSynchronous Values of Games0 aSynchronous Values of Games  c9/29/20213 a<p>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.</p>1 aHelton, William1 aMousavi, Hamoon1 aNezhadi, Seyed, Sajjad1 aPaulsen, Vern, I.1 aRussell, Travis, B.  uhttps://arxiv.org/abs/2109.14741