In game theory, you model a real-world situation by simplifying it to depict a finite group of “players” who are defined by preferences and choices. You predict outcomes based on how these players will choose. The structure of the choice matters, e.g., Will they decide simultaneously or in turn? Once, or several times? (Here’s my argument that game theory is useful.)

In the case of the current shutdown, it seems that at least the following six players are relevant:

• Donald Trump: He can choose at any time between the status quo (threatening to veto a continuing resolution, or CR, unless it includes money for a wall) or folding (saying that he would sign such a resolution). His decision-making process is simple: he does what he wants to do. He could, however, renege on a promise to sign a “clean” CR. He presumably wants: 1) the wall, 2) the ability to claim a victory, 3) higher instead of lower popularity, 4) strong support among Republican voters, to head off a primary, 5) economic growth, and 6) an outcome that will satisfy the actual opponents of immigration (who know that a wall won’t really help their cause). NB: these are not in order, because I am not sure how to rank them.
• Chuck and Nancy: They can choose at any time between the status quo (supporting only a “clean” CR) or else folding (agreeing to fund the wall). Their decision-making process is complex since they are elected by caucuses full of diverse interests and values. They presumably want: 1) no wall, 2) a victory over Trump that is popular on the center-left, 3) Trump’s popularity to fall, 4) the Republican congressional caucuses to fracture, 5) federal workers to be paid, and 6) other policies, such as DACA, to pass. Again, these are not in order–maybe they want 6) most of all.
• Mitch McConnell: He can choose at any time to propose a “clean” CR or some kind of win/win agreement, such as the wall plus DACA. He presumably wants: 1) this whole thing to go away, 2) conservatives in Kentucky to like him, 3) Republican Senators in diverse circumstances all to be reelected in 2020, and 4) his caucus to hang together.
• Federal workers: They can choose at any time between the status quo (showing up to work without being paid) or some kind of civil resistance: massive absenteeism, a wildcat strike. Their decision-making is very complex. For instance, the National Border Patrol Council (a union) is right behind Trump, but perhaps its members aren’t. In general, federal workers presumably want: 1) to get paid. Their other interests–such as harming or else supporting Trump–vary.
• Right-wing personalities and organizations: They can choose to put pressure on Trump or back off. They like the wall but differ in how much they like it. Many know that it wouldn’t actually reduce immigration and are dead-set against giving up a punitive immigration law in return for a wall that doesn’t work. But their opinions on that matter vary. They need not speak in unison, and perhaps it’s necessary to model them as several players. They presumably want: 1) less immigration, 2) symbolic manifestations of white nationalism, 3) Democrats and liberals to look bad, 4) their own audiences to stay loyal.
• The people who are sampled in opinion polls: They can each say whether they blame Trump or the Democrats. Their decision-making process is individual choice followed by a pollster’s statistical aggregation. They want lots of things, but current polls suggest that the largest group wants: 1) no wall, 2) the government to reopen, and 3) the politicians to move onto other things. This is what they say, but the partisan heuristics with which they’d assess any specific outcome cannot be discounted.

I tend to think that Tyler Cowan is right that the federal workers will end this. Of course, their ability to act is much constrained by labor law, but they still have a range of tactics available to them. Mitch McConnell is the other player with a lot of clout–but bad options, which is why he isn’t playing so far.

The time dimension is crucial, since the status quo could be interrupted unpredictably by a disaster that needs a federal response, an economic crisis, a serious decline in Trump’s popularity, an erosion of public support for the Democrats, or a major distraction, such as a certain Special Council’s final report. Smart players must decide how to choose based on deep uncertainty about what happens next.