Understanding the Stag Hunt Game: How Deer Hunting Explains Why People are Socially Late

It’s customary for people to arrive “socially late” to parties. In my social circles, this means arriving an hour after the stated invitation time.

But customary does not mean correct. The practice of being socially late creates inefficiency only a government bureaucrat would be proud of. Arriving late means that people spend less time with each other, and punctual people get punished.

Solving this problem is a snap: have everyone show up on time. Everyone would benefit and it’s virtually costless to implement. But change is hard to come by. I’ve discussed this with many people, and no one has a compelling answer.

But I think I’ve come up with one. The reason is that arriving socially late, though sub-optimal, is actually a safer decision than showing up on time. The reasoning comes out of a famous game about hunting for stag (adult deer).

The stag-hunt or assurance game

Image credit: public domain via wikipedia

The stag hunt game is based on a discussion from the philosopher Jean-Jacques Rousseau. It’s a game about social cooperation.

Imagine you and a companion are out hunting. Each of you has the choice of pursuing a rabbit or a stag.

The stag is the bigger prize and tastier, and can be caught for sure if you both choose to pursue it. The rabbit is smaller but still satisfying, and can be captured for sure regardless of what the other person does.

Before you start hunting, you can discuss strategy with your companion, but the game is about individual survival. You can’t be sure your companion will follow through on any agreement.

What choice do you make?

In the next two subsections, I write out the formal version of the game. If that doesn’t interest you, you can skip to the section labeled What’s going to happen?

The diagram

To get the analysis fixed, I’ll write out payoffs that are consistent with the game description.

Let’s assume capturing a rabbit gives a payoff of 3, capturing the stag gives a payoff of 5 to each person, and capturing nothing is a payoff of 0.

By nature of the game, if a player pursues the rabbit, he’s guaranteed a payoff of 3.

On the other hand, if a player pursues the stag, the payoff depends on the other person’s choice. If the other person also chooses stag, then the stag is captured and each gets a payoff of 5. If the other person chooses rabbit instead, then the player captures nothing and gets a payoff of 0.

Here is the matrix for the game:

The solution

The game can be solved by looking for the best responses. For each choice the other person might make, consider what’s best for you. A Nash equilibrium occurs when both players are picking best responses.

What are the best responses? There are two choices to consider.

First, consider if the other person picked stag. In that case, it makes sense to pick stag (5) over rabbit (3).

Second, consider if the other person picked rabbit. Now, it is more sensible to pick rabbit (3) rather than stag (0).

The best responses for each player are:

–Rabbit is a best response to rabbit

–Stag is a best response to stag

This leads us to two Nash equilibriums in pure strategies (no mixing): both picking stag and both picking rabbit.

What’s going to happen?

The above analysis means there are two reasonable outcomes. It is possible both players go for rabbit, or both players go for stag.

This is a comforting solution as it demonstrates selfish incentives can produce social cooperation. Because the stag is a large prize, it’s possible both players will cooperate and achieve it. In fact, this outcome is the best–each player can be made better than the rabbit outcome. Hence, the stag outcome is said to be Pareto optimal.

But is there something wrong with this outcome? On closer inspection, you might realize the stag equilibrium is risky.

If you pick stag, and the other person does not match you, you end up with nothing. If you were a real life hunter a few hundred years ago, you might feel embarrassed. You would have to go home to your family and explain that you had a chance to bring home rabbit and feed everyone, but you instead were going for the big prize and failed. And the reason everyone is starving, you would suggest, is that your partner was stupid. I imagine such answers were the source of many domestic arguments.

The rabbit equilibrium is less risky, and in this particular story, it has no risk. By choosing rabbit, you are guaranteed a tasty meal and a payoff of 3, regardless of what he other person does.

This is why the rabbit equilibrium is called risk dominant. Although it has lower payoffs to each party than stag, picking rabbit might make sense because it is the “safe” option.

The party arrival time game

Should you show up on time or socially late to a party?

If you show up socially late, then you are likely to arrive when other guests will be there for sure. This means you are guaranteed a payoff.

On the other hand, if you show up on time, your payoff depends on what others do. If others show up on time, then you all get to spend lots of time with each other. If others show up late, however, then you might get annoyed and feel like the party is a wash.

Under these considerations, the payoffs to this game are exactly the same as the stag-hunt game, with the strategies having different labels:

So although everyone would prefer to show up on time and have the big payoff, it is a risky equilibrium. Hence, everyone ends up being socially late.

The exact rules and payoffs are up for debate. But the idea is the party arrival game is like the stag-hunt game, and showing up socially late is a safe option.

Some workarounds

As I’ve written about before, if you aren’t winning, then try to change the game.

Not all parties start wastefully, and the reason is people have figured out ways to change the incentives. The solutions are all about creating commitment and incentives for on-time arrivals.

On that note, here are some common ways to induce punctuality:

–Throw a surprise party

No one wants to miss the birthday person’s reaction at the start. And people that do lose out.

–Get a reputation for being short on food/drinks

I don’t like this one, but some people do it on purpose. Scott Adams toys with the idea in one of his Dilbert newsletters.

–Go to a club that charges cover after a certain time

This isn’t a perfect solution, as lots of people are willing to shell out money. I don’t quite understand it, but the people who show up late have to pay, so it’s their choice.

–Buy tickets for a fixed movie time or event in advance

When I’m in a big group, the benefit to committing to a specific time outweighs the small convenience fee, if any. Often, it’s possible to buy tickets at the theater a day or so in advance and avoid the charge.

How do you manage tardy guests? How do you make punctuality the safe and better option?