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Episode 10 of Alien Nation depicts the Tenctonese slaves being subjected to a game of life-or-death Russian roulette in the form of the Game. Two slaves are strapped to a machine and water is fired at the competitors until one of them is blasted with salt water (which is fatal for Tenctonese).This game took place aboard their transport ship.

The slaves were seemingly employed in mining camps. They were presumably a valuable human resource and wouldn't have been seen as expendable. After all, the fewer slaves you have the less work you can get done.

Given this, wasn't the Game a huge waste of resources for the Overseers? A finite stock of slaves were frittered away on temporary entertainment. Surely there was an economic incentive to keep all the slaves alive.

Why was the Game permitted when it involved the unnecessary depletion in numbers of valuable slaves?

Alien Nation very deliberately drew parallels to real-world racism, bigotry and discrimination in a variety of ways. The Overseers in this case are acting as a stand-in for groups such as slave owners, who did in fact engage in vicious acts of cruelty in order to dehumanize their victims, punish real or perceived insubordination, indulge their own sadism, reassert their own supposed dominance and superiority, etc. Bigotry and racism are not logical, rational processes, and there are countless examples of people acting in these ways despite it being a waste of resources. As a direct parallel, Japanese POW camps during World War 2 regularly used prisoners for labor, but still inflicted vicious, often fatal punishments on prisoners for little or no reason.