The Schelling Game (or Coordination Game) is a simple but fun party game that seems to have been independently invented several times. (One might even say it represents a Schelling point in game-space...) I have played it both with LessWrong meetups and with other groups; good times were had by all. This article describes the rules of the game as I've seen it.
The purpose of the game is to discern Schelling points among the group. You should have at least 4 players; there may be an upper limit at which the game becomes unwieldy, but I've never seen it get that large. (The most I've seen was about 15 players, and that seemed to work fine.) No materials are required, although paper-and-pencil are helpful.
On each turn, play proceeds as follows:
Someone (the "prompter") names a category (e.g. "Living people").
Everyone (including the prompter) precommits to some answer in response.
Everyone reveals their answer, and each player gets as many points as there are other players giving the same answer.
A round is completed when every player has given one prompt. The number of rounds should be set in advance, usually such that there are 10–20 prompts in total. (The game tends to get boring if it goes on much longer.) At the end, whoever has the most points wins.
The unanimous answer rule
If all players give the same answer for a prompt, then under the basic rules everyone would get the same number of points, so the turn is effectively a wash. To discourage this, and encourage more interesting prompts, you can say: If everyone gives the same answer, then everyone gets 0 points, except for the prompter, who loses 1 point.
If, at the end of the pre-set number of rounds, multiple players are tied for first place, you can enter a "sudden-death round" to determine the winner. Take turns giving prompts in the same order as before, but skip any player involved in the tie. All players should answer the prompt, but only the first-place contenders are eligible to earn points. The game ends as soon as the tie is broken, regardless of whether the turn order has completed.
Talking during turns
Under the most strict rules, all players must be silent after the prompt is given and before the answers are revealed (since anything said aloud might create a new Schelling point). You may find that this makes the game less fun, so you can relax this restriction; but in any case, players should not blurt out answers while others are still thinking. If this happens, you can declare that answer to be excluded.
It's the prompter's job to determine when everyone has come up with an answer, and to tell everyone when to reveal them.
It may be tempting to say "Just mentally commit to an answer; we trust you not to change it after hearing other answers." I would strongly discourage this: even if everyone's being honest, it's easy to subconsciously rewrite one's own memory of what one's answer is. Rather, there should be some tangible evidence of the precommitment. You can write it down on paper; or, if paper is lacking, the prompter can count down and have everyone say their answer at once, and then go around the circle to repeat the answers one at a time. Even if the simultaneous shouting is indiscernable, the act of physically speaking the answer will prevent any subconscious memory-rewriting.
The game is also suitable for playing in online chats. You can set up an editable-by-all Google spreadsheet like this:
Name a living person
(The next prompt...)
On each turn, each player should enter their answer in the corresponding cell, without pressing Enter. This will make the cell turn gray for everyone else, indicating that some text has been written into the cell but not yet revealed. When it looks like everyone has written something, the prompter should confirm that everyone has settled on their final answer, and then count down "3, 2, 1, go!" whereupon everyone presses Enter to reveal their answer.
Disputes over matches
Determining whether two answers are "the same" may be subjective, but you can usually resolve this by consensus (unless, I suppose, you're playing for a cash prize, but I've never done this myself). You don't really have to read this section before playing, but you can refer to these heuristics if questions arise:
Supercategory/subcategory (e.g. "dog" vs. "poodle") is not a match.
Two different names for the same thing are a match, as long as at least one party to the match knew about the synonymy beforehand. (And you can't give answers whose meaning is unknown at the time the prompt is given, e.g. "Whatever Alice's answer is.")
The answer should at least attempt to match the prompt; i.e. it has to be plausible that someone might believe that the answer matches the prompt. For example, if the prompt is "What is the 123,456,789th digit of π?" then any decimal digit may be accepted. Generally, however, you should avoid giving prompts with a single correct answer. If the prompt specifically excludes one or more answers, then those answers (or any synonyms thereof) should not be accepted.
Heh, I also know a road trip game called contact which, though similar in style, is quite different.
One player picks a word, and tells the other players the first letter of that word.
The other players need to say together words that start with the letters they have been given. They can use clues, and when one of the players thinks they have they're both thinking of the same word he'll say "1, 2, 3 contact" and then the two players will say it together.
If any player says a word alone (including the player who picked the first word) that word is burned and cannot be used again in the round, if two players say a word together that starts with the letters they've been given, the first player reveals the next letter of the word they picked.
The round continues until that word is guessed, and then another round starts.
I also know a word game called Contact, different from both of those (but very similar to Yoav's) and not very suitable for road trips.
One player picks a word and tells everyone the first letter. (Call this player the defender and the others the attackers.)
Attackers make clues (a clue can be anything at all) for words (a word can be anything at all provided it begins with the same initial letters as are known for the target word). Many clues can be "active" at once.
If another attacker thinks they know what word a clue is pointing at, they can declare "contact" on it, but at this point they don't yet say what they think the word is.
The defender can respond to a clue by saying "My word is not X" (which must actually be true); if their X is the same as the attackers' intended one (players trust one another to be honest) then that clue is retired.
Or the defender can (and after a reasonable interval must; players trust one another to be reasonable) pass on a clue that has been contacted, at which point each "contacting" attacker says what word they had in mind. If any of them matches the clue-setter's intended word (again, players trust one another to be honest) then the defender reveals a new letter. At this point, existing clues that no longer match all known letters are retired; attackers need not reveal what words they had in mind.
A successful contact on a word that turns out to be the defender's is a win for the attacker who made the clue. In principle, the defender wins if the attackers get completely stuck, but that probably actually means that the defender chose a word too obscure to be fun for the particular set of defenders.
There's too much state to keep track of easily on a road trip. It works better in online chat.
There's some scope for varying how exactly words need to match when another attacker declares contact (and the defender passes), or when the defender says "my word is not X"; the main thing is to be consistent between these.
I've played a variant like this before, except that only one clue would be active at once - if the clue is neither defeated nor contacted within some amount of time, then we'd move on to another clue, but the first clue can be re-asked later. The amount of state seemed manageable for roadtrips/hikes/etc.
What counts as "fitting" the clue? ("My" version permits clues to be literally anything and in actual play they may be very obscure or indirect; in particular, they are very often not straightforward definitions.)
Fair enough. In "my" version, a contacting attacker, or a defending defender, has to figure out the specific word the clue-making attacker has in mind (or "essentially" the same word; e.g., if what's known is that the defender's word begins GA and a clue is "Eppur si muove", clearly GALILEO and GALILEI and GALILEO GALILEI are all equally good answers).
Again, I think the game works about equally well with any convention for how close you have to be, so long as you apply the same convention to attackers and defender.
In Listorama's Threefold mode, everyone lists out 3 entries for a particular category (e.g. "Movies"), and earn points based on how many others put down the same word. If you enjoy the Schelling game, give this one a try too!
(There are two other modes, too: Forgotten Four, where you earn points for putting entries that nobody else put; and One on One, where the goal is to match exactly one other person)
I don't think there's a generalized skill of being good at this game as such, but you can get good at it when playing with a particular group, as you become more familiar with their thought processes. Playing the game might not develop any individual's skills, but it can help the group as a whole develop camaraderie by encouraging people to make mental models of each other.