Pass, Punt, or Fail: Game Theory and Immigration

On the heel of the news that Trump is rescinding DACA over six months it now falls upon congress to make a decision on the future of the program and immigration in general. Also, as I believe that game theory can give us unique and non-intuitive insights into how things will play out, I wanted to explore the options and make a prediction on what I believe will happen.

The Players

In game theory, we need a list of players. In order to be a player, you must have something at stake. This is why voters are not players, but the politicians they vote for are since their job is on the line.

Democrats in the house and senate

Given the lack of moderate democrats due to recent elections, I will bundle them all together since they are likely to mostly vote in a bloc. They represent a minority in both.

Moderate Republicans in the house, and all Senators

These are republicans whos jobs are very highly at stake by democrats if a program to replace DACA isn’t passed and also at stake in primaries if republicans fail to get wall funding passed as well. They represent a majority in the senate, but just barely a minority in the house due to the large presence of conservatives.

Conservatives in the house

These are republicans who are highly unlikely to want to pass any kind of immigration bill, are generally in very red seats and will suffer very few consequences for passing or not passing a DACA like bill, but could be at risk if they pass full immigration reform, or fail to pass funding for the wall. They represent a small bloc in the house, but combined with the moderates make a majority.


Next, in order to evaluate the game, we need a set of consequences for each player. We are going to use a simple system. The preferences are as follows:

  • Keep My Job
  • My party holds majority
  • My party holds minority
  • Lose my Job

Basically the assumption is that each congressman wants to keep his job first and foremost and that party’s overall control is secondary and thus would be willing to maintain a party minority if and only if the he keeps his job.


For a given game, we need to understand the potential choices each player has. In politics, choices can include not making a policy decision. For example, democrats at the state level generally do not favor a minimum wage tied to inflation since they lose the ability to run on that policy during a campaign.

I will attempt to simplify the strategies to 4:

Pass a clean DACA like bill

This means generally taking DACA and passing it almost as is with not attachments.

Pass a DACA bill attached to border security or something else

This means tying the bill to some other priority such as wall funding, tax reform, etc.

Pass a temporary DACA bill

This can be anything from a 3 year authorization (until the next election) or limiting the timeframe to 5 years or something.

Fail to pass a bill

Meaning DACA will expire and nothing to back it up.


Finally, in order to make an accurate model, we need to understand what the choices are and what reward they lead to. I’m going to use slightly older data from 2014 for one reason and that is that I’m only looking at potential midterm outcomes. Data and polling can become skewed during off years when people are not thinking about politics and then are asked a random question. Also, the constituent base that votes in 2018 is more likely to be similar to 2014 than to 2016 due to the lack of a presidential election.

Thus, I’m using this poll with the assumption that it skew slightly democratic


With any game theory model, we now need to set up the game in order to understand it. Thus we will look at each decision and how it would play out.

The matrix here is very complex and I won’t bore you, but it comes down to a few scenarios:

Possible Scenarios

  1. Failure to pass anything. This would be a small win for some democrats a small loss for conservatives and a big loss for moderate republicans.
  2. Pass a temporary measure. This would mostly preserve the existing status quo and thus is neither a win nor loss for anyone.
  3. Pass a a clean bill. This would be a small win for democrats and a small loss for republicans and conservatives.
  4. Pass a bill with attachments. This would be a small loss for democrats, a small win for republicans and a big win for conservatives.

Why would failing to pass anything be a big win for democrats? Because they would not only keep their seats, but would likely win a majority in 2018. Why would passing a clean bill be a small loss for republicans. While conservatives would keep their job, they would potentially lose a majority in the house due to primaries.


In game theory, everything is about minimizing loss. Eliminate the choices that lead to the worst result based on the maximium your opponent would gain. One way to find the optimum solution and ask if anyone can make a decision that would lead to a better outcome. If so, then it’s not optimal.

  1. Failure to pass anything. Republicans would badly lose in this scenario. Them and conservatives would both quickly switch to passing a temporary measure instead, even if democrats opposed it.
  2. Pass a clean bill. This would be done with democrats and republicans supporting and conservatives opposing. If democrats opposed, they would win big, but that would result in conservatives supporting temp solution, so they can’t change. Republicans on the other hand would vote against it in favor of a temp bill if they believed conservatives would join them. Either way, it’s unstable and thus not optimal.
  3. Pass a bill with attachments. Given that there is no big win situation for republicans and that going to a clean bill would have a worse result, this is ideal. Conservatives also win in this situation. The only thing here is democrats. Would enough democrats in the senate support this bill? I believe the answer is no. Democrats can get a significantly better outcome if they oppose this since they would force a temporary bill.
  4. Pass a temporary bill. This is the only situation I see that is optimal. Both parties can rally around the issue in 2018 and keep their current positions. Democrats could threaten to not vote for this bill in the senate, but would be met with huge pushback by voters and likely lose their personal seat.

In the end, the answer comes down to a simple choice for democrats. Vote against a compromise bill and for a temporary bill. A compromise bill would mean they all lose their job, but a temporary bill would only lose them some jobs. Failing to pass anything could mean a majority in 2018, but unless they put party politics first, they are unlikely to do this. Trump also has a trump card up his sleeve, and that is changing his mind on rescinding. Because of this, democrats cannot vote NO on a temporary bill and republicans would suffer too much if no bill got passed.


In short, there is a strong reason why the status quo was the way it was before Obama enacted DACA in 2012. Given the political blowback by supporting amnesty or deportation, the only real solution that is politically viable is to play kick the can once again, until attitudes change from american voters one way or the other.