The chess championships in Geneva pit seasoned communist “Akiva” (Michel Piccoli) against former Soviet player “Pavius” (Alexander Arbatt), and the animosity between them is palpable; he declines to even acknowledge his opponent with a handshake. It becomes apparent that Akiva is struggling with health concerns, but Pavius also has personal difficulties—his wife, who didn’t join him in defecting, is initiating divorc…