Donald Trump is now the only president to have been impeached twice and will soon be the only president to be tried by the Senate after his term expired.

That poses a quandary for Republican senators such as Josh Hawley (Mo.) and Ted Cruz (Tex.) who want to win the GOP’s nomination for president in 2024. On the one hand, they need to court Trump’s most loyal voters if they’re going to realize (or even have a chance of realizing) their executive aspirations. On the other hand, they need Trump — who has suggested he’ll make another go at it in 2024 — out of the way to make all that effort worth their while. Although Trump’s lead in the polls for the 2024 nomination may have slipped since the Jan. 6 insurrection at the Capitol, he remains the Republican front-runner. Ambitious Republican senators’ path to the White House would be a lot easier if Trump were barred from office, something that is now in their power.

This is where the coming impeachment trial puts them in an improbable bind. Removal from office is the most prominent penalty of impeachment but not the only one. The Constitution also states that an impeachment conviction can result in “disqualification to hold and enjoy any office of honor, trust, or profit under the United States.” Conviction and removal requires a two-thirds vote of the Senate, but disqualification requires only a subsequent majority vote.

The prospect of barring Trump from federal office permanently provides the most concrete reason House Democrats chose to move forward with impeachment proceedings. It would also stand to benefit — perhaps still more directly — Republicans across the spectrum, even those with less alpine ambitions than Hawley and Cruz who simply want to reclaim their party from its once and hopefully-not-future king. And yet there’s a simple and rational reason they likely won’t do it.

To explain why … well, it’s time for some game theory.

Game theory is a branch of the social sciences and biology that studies how the strategies of different agents — players, to normal people — create outcomes in interactive situations. It’s widely used — and, let’s be clear, sometimes controversial — in economics, political science and other disciplines to study phenomena as different as bargaining during nuclear crises, how Congress oversees federal agencies and why it’s so hard for the international community to fight global warming.

The basic method of game theory is simple: specify the players, the rules that constitute the game and what the players know about each other and themselves, then model their interactions in ways that let you understand under what circumstances they’ll choose a strategy to maximize their gains from that interaction.

The game that Republican members of the Senate are playing right now is surprisingly straightforward. Any successful impeachment conviction would require about 17 Republican senators to cross party lines. Once that happens, disqualification would be all but certain. That would be unprecedented, and the likeliest outcome is that most or all Republican senators, especially those worried about a primary challenge, will vote to acquit.

But there is a remote chance that enough Republican senators are interested enough in punishing Trump for the Jan. 6 riot that conviction might be a possibility. It’s unlikely that would happen without the participation of at least some combination of senators like Hawley, Cruz or Marco Rubio (Fla.) — and the more of those presidential hopefuls join, the easier it would be for other Republicans to vote to convict as well.

In that unlikely case, for an ambitious Republican senator, the prospect of removing your top rival from the 2024 field would seem to practically constitute a conflict of interest, given that senators are functionally, if not technically, jurors in an impeachment trial and yet they would stand to directly benefit from the outcome. But if you break it apart, the situation starts to look a lot like a variant of the elementary game theory scenario known as the “Stag Hunt” — and that means the prospects for conviction and disqualification look even more remote than ever.

In Stag Hunt, hunters face a choice between collaborating to bring down game that can only be bagged by a group acting in concert or breaking away from the hunting party to go after a smaller prize one hunter can get by themself, even though doing so will mean that the hunting party can’t get the big game. The outcome of the classic Stag Hunt model depends on trust. If everyone trusts that everyone else will work together, the group can feast — but if anyone suspects that someone else will break away, they’ll be better off breaking away, too.

In this game, the difficulties of getting everyone to cooperate in the first place are compounded by the fact that anyone who defects would still stand to gain if all of the others voted to ban Trump. That one loyalist would suddenly not only benefit from having Trump removed from the race but would also be in line to scoop up Trump’s supporters in the primaries — and maybe even pick up a Trump endorsement. By breaking away, he (and, yeah, it would be a “he”) would receive all of the benefits of barring Trump from office plus all of the benefits of an endorsement. If the primary field is as crowded as it looks likely to be, the Trump lane could be the one that leads to victory — just like 2016.

Knowing that breaking away would carry such benefits, an ambitious Republican senator would expect that none of the other ambitious Republican senators would vote to convict. Even though they would all be better off as a group by disqualifying Trump, each of them is best off voting to acquit and letting the others bear the costs of voting to convict.

There’s a similar calculation for less-ambitious Republican senators as well. Trump may be unpopular generally, but impeachment and removal are overwhelmingly unpopular among Republican voters. A principled vote to convict might lead to a challenge from the right in their next primary election (maybe even from a Trump offspring). Only the most principled and the most electorally secure Republican senators would want to risk that. (The current Republican vogue of arguing that impeachments after leaving office are unconstitutional may reflect a desire to find a principled defense of a strategic vote to acquit.)

This calculation broadly resonates with one of the many dynamics that produced a Trump victory in the 2016 Republican primaries. If anti-Trump Republicans had consolidated their support behind a single candidate — perhaps Cruz, Rubio or even Jeb Bush — they might well have stopped the then-reality TV star’s ascent. But for any individual candidate the downsides of giving up were worse than remaining in the race in the hopes of being the eventual winner.

The logic of the situation points to an almost inevitable acquittal. And in some sense it isn’t any one player’s fault, because the structure of the interaction between Republican voters and officeholders so plainly favors one course of action. But if you can’t hate the player, you can still hate the game.