Game Theory etc

Wanted to copy this over from the other board, with the specific suggestion of using Volunteer's Dilemma and Chicken this time around in place of Prisoner's Dilemma and The Box as the final pre-merge and first post-merge challenges.

I realize that most of the ones I've penned out so far (and most of the challenges I've used in the past as a whole, for that matter) tend to be more cerebral, preparation-heavy, and dense whereas Stranded offerings tend to be simpler and faster with more of a "fun" factor. Prisoner's Dilemma and The Box from this year inspired me to try to shift gears and look to game theory for inspiration for some other ideas.

So, all of these are inspired by some famous game, intending to pose to players some basic strategic or sociological test. Just to group them all together, I'll list out Jeff's two existing original challenges that fit this bill (and feel free to add others in the same vain that I simply haven't seen in these three seasons).

Tribal Prisoner's Dilemma
Tribal Stage, Twist
Description: All players on both tribes are given the chance to earn individual immunity by simply asking for it. The first player to ask for it gets it, but forces their tribe to go to Tribal Council while the other tribe gets tribal immunity. If no player takes it, both players go to Tribal Council.

The Box
Individual Stage, Twist
Description: Players are are restricted from private messaging while competing in the challenge. Players can opt to leave the challenge to regain private communications. The last person standing wins immunity. Challenge generally takes place over a long period of time so as to pressure players to leave, for missing out on secret discussions outside.

Now, some new proposals.

Pairwise Prisoner's Dilemma
Individual Stage, Twist
Game Theory: Two players are given the opportunity to comply or defect. If both comply, they are both rewarded. If both defect, they are both punished. If one complies and the other defects, the defector is rewarded more than in any other case, and the player who complies is punished.
Challenge: Have the tribe split themselves into pairs (or groups). Each pair runs their own Prisoner's Dilemma, casting a private ballot for their decision. If both players (or all within the group) comply, we flip a coin to give one of them immunity for this round. If both players defect, neither gets immunity for Tribal Council. If one player complies and the other defects, the defector gets a Guatemala Hidden Immunity idol for play only on themselves at any of the next (some small number, say three) rounds, while the other player gets nothing. The benefit would be avoiding random draw to get it yourself, and being able to choose when best to use it.

Chicken (or Hawk-Dove)
Individual Stage, Twist
Game Theory: Imagine two people driving full-speed ahead in opposite directions approaching a one-lane bridge from opposite sides. The first player to stop thier car loses, while the other player speeds past on the bridge forcing the stopping player to wait. However, if neither player stops, the cars collide, and both players lose with even worse consequences than if either had stopped.
Challenge: This game is much in the vain of The Box, but slightly different. Remove the time component (where it comes at a merge, and lasts for days), and let this game elapse over the course of fifteen or so minutes, restricting their communication to only this thread. All players are "driving full-speed ahead" (which we'll represent by staying in The Box). If, at the predetermined and announced end time of the challenge, only two (or some number X) or less players remain, they all win immunity. Everyone who left is vulnerable at Tribal Council. However, if more than X players remain in The Box at the time the challenge is over, everyone who LEFT wins immunity, and the players who stayed in The Box are the only ones vulnerable at Tribal Council--an arguably worse outcome for them than just being normally vulnerable, because chances are, most people left The Box leaving less than a handful of them who stayed in danger of being eliminated.

Braess' Paradox
Individual Stage, Challenge
Game Theory: Imagine we have two roads of equal distance that go from point A to point B, and ten people trying to get from point A to point B. For optimal efficiency, we can expect the ten people to split five and five between the two roads, minimizing congestion. Now, let's say we shorten road #1 by a mile, and leave road #2 at the same length (they both still go from A to B). Now, when people are to decide which road to take, more of them are going to take road #1, leading to more congestion, and in some cases, actually taking LONGER to traverse the shorted road than it would have taken had they driven the longer one.
Challenge: Setup three different threads. Assign 1/3 of the tribe to each of them. Your assigned thread is the one in which you "reside" (the road you are choosing to take). You can change by simply posting in another thread. You reside in whichever thread you most recently posted in. At the predetermined and announced end time of the challenge, whichever thread has the least number of people residing in it (whichever thread includes the least number of last-posts that people made before the deadline) will reward immunity to all of its inhabitants.

Blotto Game
Tribal Stage, Challenge
Game Theory: Two competing players have the same number of soldiers to spread between a number of battlefields. At each battlefield, the player who places the most soldiers there wins; however, players do not know how many soldiers their opponent has put anywhere. So they have to predict their actions, and make the assignment blind.
Challenge: Play it in rounds. Say, each tribe has ten soldiers to put amongst three battlefields. After each round, we announce which tribe won the battle at each battlefield. Whichever tribe won the majority of battles wins a point. Repeat until one tribe gets four points. The catch is that while tribes know which battlefields they lost, they don't know how many soldiers they'd need to put to beat the other tribe there next time.

Traveler's Dilemma
Tribal Stage, Challenge
Game Theory: Two travelers have identical bags of identical value. The airline loses them both. Now, the airline separates the travelers, and asks each how much the bag was worth. The traveler can respond with any value between $0 and $100. If both say the same number, the airline sees that they are telling the truth, and awards them both that value. However, if they say different numbers, the airline assumes the traveler who said the lowest value is telling the truth. So, while the airline gives both travelers the lower value, the traveler who SAID the lower value gets awarded $5 for being honest while the traveler who listed the higher number is penalized $5 in their prize for being deceitful.
Challenge: Play it in rounds. Each tribe submits a number 1-100. The tribe giving the lower number wins. However, based on the reward/penalty system above +$5/-$5, if the tribes both guessed within $10 then the tribe that guessed higher actually wins. Repeat until one tribe gets four points.

Volunteer's Dilemma
Tribal Stage, Twist
Game Theory: The power goes out in a neighborhood. Everyone is without power. To get the power turned on, at least one neighbor has to call the electric company, and then everyone gets power. But calling the electric company costs money. So, ideally, you want someone else to call, and you reap the same reward anyways. But if no one calls, everyone suffers.
Challenge: Each player has to make an individual and private decision on their own to make a sacrifice for the tribe. For example, forfeit your vote at the next Tribal Council. Players PM the hosts if they are willing. All other communication must cease for the time the challenge is running. Whichever tribe had more people be willing to forfeit their votes at the next Tribal Council wins the challenge, and doesn't have to go to Tribal Council or actually forfeit their votes. The tribe with less volunteers does have to go to Tribal Council, and everyone on that tribe who did volunteer won't even get a say as to who goes home.

Dictator Game
Tribal Stage, Twist
Game Theory: This really isn't a game at all, since it's only one player making a decision and everyone else has to deal with it. Thus, the dictator has no reason to pick anything other than the option which is best for them personally, but will be threatened by social blowback for the others for their decisions (assuming they are offered a decision round after round).
Challenge: This would essentially be like reviving the Khaan twist from Stranded in India. Some other thing where they must sabotage the tribe to get individual immunity. Or perhaps the Khaan can award an individual immunity to any player on their tribe each round (including themselves), but giving it to no player more than once consecutively. Thus, if the Khaan hogs it, the plebians may revolt.

So, to summarize:

Tribal Twist (run it immediately before a merge): Tribal Prisoner's Dilemma, Volunteer's Dilemma, Dictator Game*
Tribal Challenge (run it anytime): Blotto Game, Traveler's Dilemma
Individual Twist (run it immediately following a merge): The Box, Chicken, Pairwise Prisoner's Dilemma
Individual Challenge (run it anytime): Braess' Paradox
* has installments each round

tl;dr
My personal suggestion, for potentially next season, would be (using this season's challenge schedule as a template):
- Instead of Mastermind, run Blotto Game
- Instead of Tribal Prisoner's Dilemma (right before merge), run Volunteer's Dilemma
- Instead of The Box (right after merge), run Chicken

I'm going to cry if you guys don't do Hot Tamale. Jolanda has to protect her legacy, obviously.

Chicken sounds awesome. I would say to make it list a little longer, like half an hour or so. Volunteer's Dilemma is cool, too, but not quite as good as Chicken sounds.

I had an idea for a challenge. Not sure if something like this has ever been done before. Probably a post merge challenge, with maybe 6, 7, or 8 people left.

Every player has 10 points, and the objective is to be the last player still standing with points. But the catch is that you can ONLY give away your points. Every round, a player gives one of their points away to another player until only 1 remains. If would have to be done in rounds, with the order maybe being based on check in order.

Here's how it might work: Let's say it's Chad, Ami, Mia, and Kim playing.

Mia: gives a point to Chad
Kim: gives a point to Chad
Ami: gives a point to Chad
Chad: Gives a point to Kim.

After that, Ami, Mia, and Kim all have 9 points, while Chad has 12. It keeps going until someone runs out of points. It would probably be a little dull and predictable when it's down to only 2 players, but I think it would be interesting until that point.