The idea is simple enough: two players each have two options; cooperate or defect. If both cooperate, both do well (gain utility). But if either one defects, they do better (gain more utility), at the others' expense. And if both defect both do very poorly (lose utility). But game theory can also elegantly explains why third-party candidates, and especially moderate third-party candidates, perform so poorly.
Consider the setup: two players, although each "player" is actually a block of voters, those who prefer one of the two major parties, but would be willing to vote for the compromise candidate. Each bloc has two options; vote for their party-line candidate, or vote for the compromise (third-party, moderate) candidate (voting for the opposing party-line candidate isn't really an option.)
If both blocks choose to compromise, the compromise candidate will win, and this will usually result in the greatest net-gain for the electorate (no one gets everything they want, but most people get most of what they want). Eventually, one bloc will notice that the compromise choice isn't polling well enough to win, and neither is their preferred major-party candidate, and so they will drift back towards their party-line favorite; the opposition will then see that the compromise candidate has lost some support, but even worse, their preferred major-party candidate is now no-longer winning either, and so they will also fall back toward their own party-line candidate. As voters abandon the compromise, the balance shifts back and forth, inspiring even more voters to abandon the compromise, and so on. Rapidly, the entire compromise collapses, and one of the two major-party candidates is, once again, elected.
This is what happened to Chris Daggett in the New Jersey gubernatorial race last month, and has happened to thousands of third-party and moderate candidates in the past. Daggett polled as high as 20% just two weeks before the election, but as election day drew closer, voters began to abandon him in droves; on election day itself, he got less than 6% of the vote. If a moderate/third-party candidate isn't leading in the polls—which would only have to be around 33%—this is bound to happen. In fact, Daggett's polling plus undecideds never exceeded that critical one-third benchmark.
When a third-party candidate results in a spoiled election, that's a tragedy; but this, where the fear of a spoiled election drives out the compromise choice, is the true tyranny of the electoral system. Actually, fear isn't the right word: each voter who abandons the compromise doesn't do so out of fear, but because it is the only rational choice they have to maximize their own utility from the election. Each one comes to the rational realization that, while the compromise would be best for everyone overall, it looks like the other guy is going to win, and so they have no choice but to run to the support of their guy.
These elections are, mathematically, precisely identical to the prisoner's dilemma, and the only rational result to the prisoner's dilemma results in everyone losing.
The only solution to avoid this problem is to play a different game. That's what score voting and approval voting do. They change the rules of the game so that the strategic choice which is best for each individual player's utility more often matches the strategic choice that is best for the utility of the population as a whole. No other proposed fix—not anti-gerrymandering laws, not fairer ballot-access laws, not instant runoff voting—changes the game. Change the game. Vote with score voting.