"The only thing known to go faster than ordinary light is monarchy, according to the philosopher Ly Tin Wheedle. He reasoned like this: you can't have more than one king, and tradition demands that there is no gap between kings, so when a king dies the succession must therefore pass to the heir instantaneously. Presumably, he said, there must be some elementary particles -- kingons, or possibly queons -- that do this job, but of course succession sometimes fails if, in mid-flight, they strike an anti-particle, or republicon. His ambitious plans to use his discovery to send messages, involving the careful torturing of a small king in order to modulate the signal, were never fully expanded because, at that point, the bar closed."
The fundamental particles, kingon, queons and republicons, all travel at the speed of light, and are presumably massless. In the timeframe of the photons, and other politicons, they travel instantly from point A to B; so they communicate the King swap instantly.
The solution of the paradox is that each object has a unique inertial frame. Therefore, the King is not dead until the light cones of the dying King and his subject intersect. If the Queen of England dies in London, she's still alive to her subjects in Auckland for 4 hundredths of a second until the news reaches them through the center of the earth.
That's 40ms for light to travel through the Earth. Lag in New Zealand must suck.
Luckily a lot of really big games have servers in Australia now though. I miss the days where player hosted dedicated servers were the norm and you didn't have to rely on the publisher deeming you important enough to have one close to you.
Analytically solvable problems are rare, simple unicorns that have even more rare practical application.
Almost no practical system is analytically solvable.