The Clue
At the reunion show of Survivor: Thailand, Jeff Probst openly wondered what that special quality was that made a contestant a winner. Richard Hatch was an over-the-top mastermind leader who took control of the game through politicking and manipulation. Tina Wesson was an under-the-radar, unassuming leader who gained more and more control by voting out Mitchell, Jerri, then Amber, and planting her emotional hooks in deep. Ethan Zohn was an under-the-radar nice guy follower of Lex. Vecepia Towery was a way-under-the-radar follower who always positioned herself under the most powerful alliance and watched as the leaders picked each other off. And now, Brian Heidick was a manipulative leader who gained control by offering people a hint of pseudo-alliances and turning peopleÂ’s weakness against themselves. What quality made these five very different contestants the winners of Survivor? Probst concluded with admitting that after five seasons he still didnÂ’t know.
But he didn’t let us go home empty-handed. During the reunion show, Probst dropped the phrase, “John Nash’s Non-cooperative Game Theory” and acted overly cryptic about it. Obviously, something for the Survivor fanboys to drool over.
Some people are so easily manipulated.
John Nash
John Nash was a young mathematical genius who wrote the 27-page dissertation, “Non-cooperative Games,” when he was only 21 years old. It was for this paper, he was awarded the Nobel Prize in 1994. Nash’s life and struggle with schizophrenia were dramatized in “A Beautiful Mind,” which won an oscar for best picture in 2001.
NashÂ’s Non-cooperative Game Theory
John NashÂ’s Non-cooperative Game Theory is just that- a theory on how competitive games work. Here are the basic concepts behind NashÂ’s theory:
John Nash says that a playerÂ’s unilateral best move is NOT necessarily the best move for either himself or the group. (This flew in the face of John Smith and The Wealth of Nations- modern economic theory.) By constructing several examples, Nash illustrated how oneÂ’s best unilateral move could be detrimental to both the acting individual and the group. Hence, in some games, where everyone is playing their best moves against everyone elseÂ’s best moves, everyone loses.
In Non-cooperative Games, there may exist zero, one, or multiple Nash equilibria. A Nash equilibrium is a sticking point where it benefits none of the players to unilaterally change their moves (their strategy).
This does not represent a complete reiteration with all the proofs and such (as you may have noticed, itÂ’s one paragraph instead of 27 pages).
Example
Imagine you are sitting at a table with three male friends and a gorgeous woman walks into the bar. (Yes, I stole this directly from “A Beautiful Mind.” :P ) You and your three friends all desire to compete for her affection. So, in this game, how do you play optimally for the individual and for the party? Non-cooperative game theory leads us into three scenarios:
Scenario 1 All four players walk up to her and lay down their best moves. The gorgeous woman is scared off and ends up with someone who is sitting down by the end of the night. The four men all lose and are humiliated by the experience. This is the worst case scenario.
Scenario 2 One man, John, walks up to her and lays down his best moves. John is successful while the other three players sit down and do nothing. This is called a Nash equilibrium. If one of the three decided to walk up in the middle of JohnÂ’s conversation, it would only scare the woman off and embarrass them both. Therefore, it is to everyoneÂ’s benefit not to change his strategy. Hence, a balance is reached. One guy ends up with the girl and the other three arenÂ’t humiliated.
Scenario 3 No one approaches the woman! All four men do nothing; they sit and wait. If no one approaches her, the woman has the come to someone. She comes to one lucky man.
Moral The best way to play this game is by doing what others arenÂ’t. If someone has already approached her, stay back and do nothing. You canÂ’t get the girl, but you can save yourself the humiliation. If no one has approached her, approach her! And make sure no other player approaches her by psyching the others out in a game of chicken. YouÂ’ll get the girl and wonÂ’t be approached by the others.
Survivor Example
We can just as easily apply NashÂ’s Non-cooperative Game Theory to the competitive game of Survivor.
Imagine you are a living in a tribe of Survivor contestants. Now, you are a male and on the tribe there are three other males and four females. Collectively, you are a team of eight. The women in the tribe are equivalent to Jan Gentrys- that is, easily led and refusing to take a position of leadership. You are all competing for the million dollar final spot. So, in this game, how do you play optimally for the individual and the party? Non-cooperative game theory leads us into three scenarios:
Scenario 1 All four men play the game with all their best moves. They work hard, they take on a role of leadership, and they work diligently to move and control the female contestants. The four menÂ’s best moves are to vote each other out, resulting in a leader-type doomsday. End result: an unassuming woman, who was afraid to take leadership, is the last remaining in the tribe and winner of Survivor. For the four men, this is a worst case scenario.
Scenario 2 Only one man, John, plays the game of Survivor by laying down all his best moves. He works hard, heÂ’s the only one to take a role of leadership, and he works diligently to move and control the seven other contestants while the other three men follow. This is called a Nash equilibrium. If one of the three decided to assume a leadership position while John had already established one, it would only be a death sentence for them both. Therefore, it is to everyoneÂ’s benefit not to change his strategy. Hence, a balance is reached. John is highly likely to win Survivor while the other three men who follow are likely to get further into the game.
Scenario 3 No man assumes the leadership role! All four men do nothing; they sit and wait. Naturally, someone has to win. Everyone has a one in eight shot of winning. There is a 50% chance a man will be crowned Survivor.
Moral The best way to play this game is by doing what others arenÂ’t. If someone has already assumed the position of tribe leader, stay back and do nothing. You wonÂ’t get the lead role for the time being, but you can save yourself from being voted out. If no one has been crowned leader, seize it! And make sure no other player tries to usurp your power or topple you by voting out the threats and psyching players back beneath your finger. YouÂ’ll have control over the others and net the win.
General Trends
In Survivor, general trends arise in accordance to the dynamics of NashÂ’s Non-cooperative Game Theory. I submit to you the Four Postulates of Non-cooperative Game Theory in Relationship to Survivor, or the Big Four.
1. In a tribe heavily saturated with leaders, the followers are more likely to survive.
2. In a tribe heavily saturated with followers, the leader(s) are more likely to survive.
3. In a game heavily saturated with leaders, a follower is most likely to win.
4. In a game heavily saturated with followers, a leader is most likely to win.
Examples:
1. In a tribe with multiple leaders, the leaders will act decisively to vote each other out. This lifts the targets from the followers who live a lot further into the game.
2. In a tribe with seven followers and one controlling leader, the leader chooses who will go. He chooses from his followers which to pick off. By picking off the least valuable followers to his endgame plan, he increases his power of leadership and is safe.
3. In a season with many leaders, you will see many fights, many power shifts, and many leaders going down in flames. And while the leaders kill each other off, the followers survive. The followers make it further into the game and are far more likely to win Survivor.
4. In a season with many followers, you will see the plans of the controlling leader play out. The leader dismisses his biggest threats and pushes the unlikable players more open to suggestion (the one he has ties in) with him to the end of the game. Thus, the leader ensures himself a victory.
What this means, in the broadest sense, is that a follower is best suited surrounded by a great number of leaders. On the other hand, a leader is best suited surrounded by a great number of followers.
In a game with fifteen Lexs and one Ethan, EthanÂ’s chance of winning is extremely good. In a game with fifteen Ethans and one Lex, LexÂ’s chance of winning is extremely good.
The Ideal Tribe
Now, let’s ask, “what makes for an ideal tribe?” Looking at Nash’s Non-cooperative Game Theory, a tribe is ideal if it exemplifies the Nash equilibrium. A tribe has attained equilibrium when all it members are benefited most not to change their positions (from a leader to a follower or vice versa). A Nash equilibrium tribe, or an N-tribe has one leader and seven followers on which to draw from. The followers hurt themselves by becoming or challenging the established leader, and the leader hurts himself by stepping down from power. Thus, the N-tribe has reached a critical balance.
The N-tribe is ideal because itÂ’s stable, thanks to the Nash equilibrium, and has a central guiding strategy, as provided by single leadership. The words that best describe an N-tribe are structured, boring, and free from power shifts. There have been five N-tribes in SurvivorÂ’s history: Tagi, Kucha, Boran, Chuay Gahn, and Sook Jai. The N-tribe is the best-suited post-merge tribe. Also, three Survivor winners hail from N-tribes. N-tribe leaders include Richard, Michael, Lex, Brian, and Penny.
The Flawed Tribes
The further a tribe strays from a one-leader power structure, the further it strays from ideal. LetÂ’s look at different types of less-than-ideal tribes.
A tribe with no leaders, or a leaderless tribe, is okay but far from ideal. This tribe can be seen as unstable and unpredictable. WhatÂ’s worse is its complete lack of a central guiding strategy. Anarchy isnÂ’t as bad as it sounds. This tribe could even be seen as a love tribe. But when merge time comes, there is simply not even structure to combat a rival tribe. The best words to describe leaderless tribes are unstructured, unpredictable, and free from power structures. There has been one leaderless tribe in SurvivorÂ’s history: Pagong. And with contestantsÂ’ increased knowledge of the game, this tribe looks less and less likely. No Survivor winners come from a leaderless tribe.
A tribe with double leaders, or a D-tribe, has a power struggle at its core which makes it inherently weaker than an N-tribe. One leader is ideal. Add a second one, and you create a power struggle, power shift, and elements of instability. The greatest challenge that befalls a D-tribe is unifying as one group during the merge rather than splintering. The best words to describe D-tribes are rivalry-structured, interesting, and open to power shifts. There have been two D-tribes in Survivor history: Ogakor and Rotu. D-tribe leaders include Jerri, Tina, John (S4), and Kathy. Also, one Survivor winner has come from a D-tribe.
A tribe with multiple leaders (more than two), or an M-tribe, is the worst possible tribe and often dies a horrible death. Because M-tribes have too many leaders and too many elements to vote out, the tribe can never create stability for itself. Instead, it self-destructs in a spectacular fashion. The best words to describe M-tribes are volatile, fascinating, and utterly self-destructive. Power shifts are frequent, and the tribe is constantly turning on itself. Ironically, follower-types do well in this atmosphere because leaders are far too busy voting each other off. If both tribes are M-tribes, a follower is greatly benefited and is in the best position to win Survivor. There have been two M-tribes in Survivor history: Samburu and Maraamu. M-tribe leaders include Frank, Carl, Linda, Silas, Brandon, Lindsey, Hunter, Rob, and Sean. One winner has come from an M-tribe (and, of course, she was a gigantic follower).
The Ideal Strategy
More interesting than what makes an ideal tribe is what makes an ideal player. Furthermore, we can ask, “what is the ideal strategy?” And the answer is there isn’t one but two.
Leader: A lot of work is put into this position. Above all else, the leader is charismatic and is able to move people (to control their votes). The leader needs to be savvy of the game dynamics and have incredible foresight. Also, he is extremely aware of the group dynamics and dealing with different personalities. He or she needs to always be looking several steps ahead. By gaining the trust of his fellow members, he ultimately decides whom they will vote out. The leader is all controlling (whether this fact is evident or not). To further his control and position, he votes out the largest threats and the people he needs least. This position takes everything you have and puts it to use. There have been three leader winners in the history of Survivor: Richard, Tina, and Brian. Even though their styles are different, these three could definitely be seen as model leaders.
Follower/Lamb: This position takes considerably less work, but there are five steadfast rules. 1.)Follow: This goes without saying but the biggest rule is to follow the person who is or soon-will-be in power (a leader). You want to gain the leaderÂ’s trust and closely align with him or her. You should definitely be his number one or two guy. DonÂ’t be independent! Be obedient. This may sound easy but it would definitely challenge someone with an ego. 2.)Jump Ship When You Need To: If the former leader is in the process of losing power or is being toppled, jump ship. Yes, you are going back on the trust you cultivated, but screw it. Immediately latch on to the man or woman who has the most power (the new leader in power) and follow him. Act just as obedient and trustworthy to the new leader as you did the last. Vecepia did this a total of six times! In this respect, she truly is a master. From kissing HunterÂ’s bottom in episode one to banishing Kathy when she couldnÂ’t hold onto the immunity idol, she proved to be an expert in make-and-break following. 3.)Be weak but not too weak: If youÂ’re a muscle man, this strategy isnÂ’t for you (look at leader). To be a lamb, you need to be perceived as weak but not too weak whereas you would be voted out pre-merge. Your stature shouldnÂ’t be threatening to others (especially the leader). It generally helps to be a woman. And for godÂ’s sake, donÂ’t win unnecessary challenges. 4.)Win the last couple immunity challenges at the end. These are often vital. This rule is somewhat contradictory to three, but youÂ’d be surprised at what a seemingly weak lamb could pull off. Examples: Kim J, Vecepia, Neleh. 5.)Play for Yourself: Remember that youÂ’re playing for the benefit of yourself, not your leader. If this requires you to cut the throat of your leader-best-friend to get closer to the million dollars, then DO IT! In the final four, lie and backstab when you need to. There have been two follower winners in the history of Survivor: Ethan and Vecepia. These two could definitely be seen as model lambs.
Which of the two strategies is better? It depends. In a game with many leaders, it is far better to be a follower. In a game with many followers, it is far better to be a leader.
For example, Richard Hatch was on an island with fifteen lambs from which to pick off one by one. Could you imagine how much more difficult it would be for him if he were competing against the cast of Survivor Marquesas? How would he win if every other contestant aspired to be a leader and power shifts were an everyday thing? The answer is he wouldnÂ’t. Richard Hatch could easily win in such political climates as S1, S2, or S5, but he wouldnÂ’t last two days as a member of Samburu or Maraamu.
Conversely, Vecepia Towery was placed in a backdrop where power shifts and political upheaval were common. She followed six different leaders. Six! Hunter, Sean, John, Sean again, Kathy, and then Neleh. Vecepia originated in Maraamu, a tribe with four people aspiring for leadership. She quietly supported whoever was in power and never entered the fray of egomaniacs. At merge, Rotu was in a similar state. It was splitting in two like the titanic. Vecepia quietly followed the power, and with the help of one or two key immunity wins, she was crowned Survivor. If, however, Vecepia was dropped in S1, S2, or S5, she would have been picked off like all the other followers. The same goes for Ethan.
The political environment goes a long, long way in selecting a Survivor winner. And before I press on, I want to mention two special cases: Tina and Brian. They both won on their leadership roles, but they seem to be the only winners that also possess a chameleon-like quality that would allow them to play both roles ideally. Tina entered the game as a lamb and was immediately fitted into JerriÂ’s powerful hierarchy. She became a leader when she was instrumental in voting Mitchell out. She became THE leader when she voted Jerri out. And she became the all-powerful-leader when she went behind ColbyÂ’s back to vote out Amber. But she was sweet (and manipulative) enough as to make it appear as if she had an alliance with everyone. Brian could also play the follower (although he never really did). He had a special ability to gain peopleÂ’s trust and give them exactly what they wanted. In the S2 and S5 climates, it definitely paid off to be a leader. And thatÂ’s what Tina and Brian adapted to.
Half-breeds
People who arenÂ’t quite leaders and arenÂ’t quite followers are half-breeds. Half-breeds donÂ’t have the charisma or social skills to attain a leadership position. Plus, they are too independent to be considered lambs. Playing the game as a half-breed is the WORST possible strategy one can have. You CANÂ’T win this game both ways.
LetÂ’s focus on the most recent Survivor, S5, identify the five half-breeds, and see how far they made it into the game. 1.) Pastor John: a man who had aspirations to be a leader but was grossly unqualified in the charisma department, a leader without charisma is just bossy (he was booted first and JohnÂ’s competition included a weak, old woman); 2.) Jed: right in the middle, he made a retarded sort-of leader and a fiercely independent lamb, therefore, no one needed him; 3.) Ghandia: leader without the charisma to support two followers, and far too hostile to be a lamb; 4.) Stephanie: a fiercely-independent lambÂ… UGH; 5.) Shii-Ann: too independent to be a lamb - powerless to assume a leadership position.
These five members were among the first seven to be booted off of Thailand. Among the other two, Tanya was an ideal lamb if it wasnÂ’t for her unfortunate illness. And Robb would also have made an ideal lamb. He was the far better choice to bring into merge rather than the less-gullible Shii-Ann. The final nine had Penny, PennyÂ’s lambs (Jake, Erin, Ken), Brian, and BrianÂ’s lambs (Clay, Helen, Ted, Jan). No half-breeds.
History of the Seasons
S1: Borneo: A leaderless tribe versus an N-tribe. At Pagong, no one was intelligent enough (Gretchen) or charismatic enough (Joel) to assume leadership. Thus, their tribe remained unstructured- a happy anarchy. At Tagi, Richard quickly grew into a position of power and was able to vote out elements he foresaw as least likely to help him (Stacey). He structured a four-person alliance around him and became TagiÂ’s leader. At merge, PagongÂ’s unstructured tribe could not compete against TagiÂ’s (an N-tribe) four unified votes. Pagong fell by the wayside as Richard took his lambs to the finals. Now, I donÂ’t want to detract from RichardÂ’s impressive accomplishments, but a game with one leader and fifteen followers, heavily favors the leader. Through manipulating his followers (turning Kelly against Susan, turning Kelly and Rudy against each other), Richard made his way into the final two and won.
S2: Australia: An N-tribe versus a D-tribe. At Kucha, Michael assumed the role of leader and provider. Jeff Varner also had leadership ambitions but knew it was best to lay low as a follower for the time being (an example of the Nash equilibrium). After MichaelÂ’s disastrous accident, Varner became president pro tempore (very tempore). Things were different at Ogakor. Jerri must have been incredibly charismatic because she had the tribe wrapped around her fingers in just a few days. At the bottom of her heirarchy: Kel, Maralyn, Keith, Tina. Tina wooed Colby over to her side and led a rebellion against Jerri (thus voting out Mitchell). At merge time, Kucha(N-tribe) was better prepared to go up against the fractured Ogakor(D-tribe). But Ogakor miraculously saw past its rivalry, and united to knock down Kucha. The two-leader rivalry flared during the pagonging of Kucha members. Tina broke the pagonging (once they had the numbers) to vote out Jerri. Now, Tina was the only leader in the tribe. Later, she went behind ColbyÂ’s back to vote out Amber. This took a lot of power away from Colby and was equivalent to cutting his balls off. Tina was a leader that structured the group around favoritism, in many ways transcending political boundaries. Everyone thought they had an alliance with her. Everyone was competing for her love. Convincing Colby that she was his mother was probably the greatest act of manipulation and leadership in the entire history of Survivor. This game only had three leaders, therefore it was likely that a leader would win. This is especially the case when the game reached the final seven with one leader (Tina) and six followers. Tina wins Survivor.
S3: Africa: An N-tribe versus an M-tribe. Matching an N-tribe versus an M-tribe is like matching the best possible tribe to the worst possible tribe. At Boran, Lex was free to build alliances and assume leadership in the face of seven very docile followers. At Samburu, I counted six leaders. So, it didn’t take long before the tribe self-destructed and became irreparably fractured. A fracture impossible to fix because there were simply too many leaders on both sides to vote out. Boran went into the merge solid while Samburu entered as the amazing self-destructing tribe. In the final nine, there were three leaders, making it seem as if a follower would likely to win. However, Lex quickly overcame the competition and entered the final five with four complete lambs. Now it seems likely that a leader would win. In the final four, the game was prepared almost perfectly for a Lex win. Tom and Ethan wanted to go to the finals with Lex (where he’d win) and Kim J was a complete weakling. Lex’s leadership was paying off in a big way and his chances of winning were extremely high. However, a freak occurrence transpired: Kim J won two immunities and took the younger Ethan with her to the finals. Ethan, a follower of Lex, won in a game that the big four would probably have favored Lex. The big four is not absolute. Freak variables seem to enter every situation. And that’s why the language is “more likely” and “most likely” (which were absolutely true).
S4: Marquesas: A D-tribe versus an M-tribe. Look at all those leaders. Our first season without an N-tribe (which are boring). Maraamu immediately exploded under the weight of its sheer amount of leaders (just like Samburu). Leaders included Hunter, Sean, and Rob. The left-over pieces of Maraamu were then thrust into a larger power struggle that was Rotu. Rotu had two leaders: John and Kathy. John was always in the good graces of his tribe and was able to build-up a Hatchian foursome. Kathy, on the other hand, found little support in her tribe despite her fervent work and episodes where she pleaded for emotional support. Unfortunately for John, Rotu didnÂ’t have the opportunity to vote Kathy out. At the merge, Survivor quickly became a struggle between John and Kathy rather than Rotu and Maraamu. Kathy came back with a vengeance. She felt her way around the game and quickly grew aware of JohnÂ’s pecking order. In retaliation, she picked up outside pieces of Rotu (Paschal, Neleh) and pieces of Maraamu (Sean, Vecepia) to combat JohnÂ’s Four. The power-shift was massive as Kathy toppled John and became a leader of Soliantu. The problem was that she wasnÂ’t the only one. S4Â’s final five saw two leaders (something that has never been duplicated). And neither had as much control over the three followers (Neleh, Paschal, Vecepia) as they would have liked. Therefore, the two leaders became colossal targets to each other and the three followers. Sean and Kathy were the next two voted out (not using a rock). In the end, Vecepia, a tribe-hopping follower of massive proportion won Survivor 4. This Survivor season heavily favored a follower. There were too many leaders in Maraamu, too many leaders in Rotu, and too many leaders in the final five. Obviously a follower (Vecepia, Neleh, Paschal) stood most to benefit from all this leader-toppling and social upheaval.
S5: Thailand: An N-tribe versus an N-tribe.
Two N-tribes! How boring and predictable. At Chuay Gahn, Brian assumed leadership through a masterful style of giving people what they wanted and making it appear as if they were politically linked. Through his control, Brian voted out the people who were of least use to him (Pastor John, sick Tanya, Ghandia). At Sook Jai, tribemates fell in love with Penny as an alliance was built simultaneously with a shelter. Penny quickly erected a power structure around herself using emotional dependencies. She had Erin and Jake wrapped around her finger. And Penny knew Ken was wrapped around JakeÂ’s finger. This became PennyÂ’s Final Four (a group she could easily manipulate into a Penny-Erin final two and a Penny win). Shii-Ann, a member of the shelter alliance but not PennyÂ’s final four, was in an odd position. She diligently tried to make lasting bonds with Jake and Ken but was stopped by Penny. To finalize her final four, Penny erected an emotional barrier around her final four and kept Shii-Ann at a distance. An astute Shii-Ann foresaw the giant fifth place looming over her head but still played the role of the team player (for the time being). Penny and the shelter alliance picked-off the independent lambs one by one. During day 18, Penny makes the catastrophic mistake of voting out gullible Robb instead of an all-too-knowing Shii-Ann. WeÂ’re looking at a Penny five versus a Brian five at fake merge. At this time, Shii-Ann wows the group by jumping ship (or jumping plank). Sook Jai loses two immunities and gets rid of PennyÂ’s biggest threats (Shii-Ann and long-run threat Erin). Chuay Gahn pagongs the other tribe (because thatÂ’s what N-tribes do), and weÂ’re left with Brian and his pack of lambs. Brian manipulates himself into the final two and wins. This Survivor had only two leaders (the least of any season aside from the original). It was extremely likely that a leader would win. And due to a better understanding of personal dynamics and more IC wins, that leader was Brian.
At the reunion show of Survivor: Thailand, Jeff Probst openly wondered what that special quality was that made a contestant a winner. Richard Hatch was an over-the-top mastermind leader who took control of the game through politicking and manipulation. Tina Wesson was an under-the-radar, unassuming leader who gained more and more control by voting out Mitchell, Jerri, then Amber, and planting her emotional hooks in deep. Ethan Zohn was an under-the-radar nice guy follower of Lex. Vecepia Towery was a way-under-the-radar follower who always positioned herself under the most powerful alliance and watched as the leaders picked each other off. And now, Brian Heidick was a manipulative leader who gained control by offering people a hint of pseudo-alliances and turning peopleÂ’s weakness against themselves. What quality made these five very different contestants the winners of Survivor? Probst concluded with admitting that after five seasons he still didnÂ’t know.
But he didn’t let us go home empty-handed. During the reunion show, Probst dropped the phrase, “John Nash’s Non-cooperative Game Theory” and acted overly cryptic about it. Obviously, something for the Survivor fanboys to drool over.
Some people are so easily manipulated.John Nash
John Nash was a young mathematical genius who wrote the 27-page dissertation, “Non-cooperative Games,” when he was only 21 years old. It was for this paper, he was awarded the Nobel Prize in 1994. Nash’s life and struggle with schizophrenia were dramatized in “A Beautiful Mind,” which won an oscar for best picture in 2001.
NashÂ’s Non-cooperative Game Theory
John NashÂ’s Non-cooperative Game Theory is just that- a theory on how competitive games work. Here are the basic concepts behind NashÂ’s theory:
John Nash says that a playerÂ’s unilateral best move is NOT necessarily the best move for either himself or the group. (This flew in the face of John Smith and The Wealth of Nations- modern economic theory.) By constructing several examples, Nash illustrated how oneÂ’s best unilateral move could be detrimental to both the acting individual and the group. Hence, in some games, where everyone is playing their best moves against everyone elseÂ’s best moves, everyone loses.
In Non-cooperative Games, there may exist zero, one, or multiple Nash equilibria. A Nash equilibrium is a sticking point where it benefits none of the players to unilaterally change their moves (their strategy).
This does not represent a complete reiteration with all the proofs and such (as you may have noticed, itÂ’s one paragraph instead of 27 pages).
Example
Imagine you are sitting at a table with three male friends and a gorgeous woman walks into the bar. (Yes, I stole this directly from “A Beautiful Mind.” :P ) You and your three friends all desire to compete for her affection. So, in this game, how do you play optimally for the individual and for the party? Non-cooperative game theory leads us into three scenarios:
Scenario 1 All four players walk up to her and lay down their best moves. The gorgeous woman is scared off and ends up with someone who is sitting down by the end of the night. The four men all lose and are humiliated by the experience. This is the worst case scenario.
Scenario 2 One man, John, walks up to her and lays down his best moves. John is successful while the other three players sit down and do nothing. This is called a Nash equilibrium. If one of the three decided to walk up in the middle of JohnÂ’s conversation, it would only scare the woman off and embarrass them both. Therefore, it is to everyoneÂ’s benefit not to change his strategy. Hence, a balance is reached. One guy ends up with the girl and the other three arenÂ’t humiliated.
Scenario 3 No one approaches the woman! All four men do nothing; they sit and wait. If no one approaches her, the woman has the come to someone. She comes to one lucky man.
Moral The best way to play this game is by doing what others arenÂ’t. If someone has already approached her, stay back and do nothing. You canÂ’t get the girl, but you can save yourself the humiliation. If no one has approached her, approach her! And make sure no other player approaches her by psyching the others out in a game of chicken. YouÂ’ll get the girl and wonÂ’t be approached by the others.
Survivor Example
We can just as easily apply NashÂ’s Non-cooperative Game Theory to the competitive game of Survivor.
Imagine you are a living in a tribe of Survivor contestants. Now, you are a male and on the tribe there are three other males and four females. Collectively, you are a team of eight. The women in the tribe are equivalent to Jan Gentrys- that is, easily led and refusing to take a position of leadership. You are all competing for the million dollar final spot. So, in this game, how do you play optimally for the individual and the party? Non-cooperative game theory leads us into three scenarios:
Scenario 1 All four men play the game with all their best moves. They work hard, they take on a role of leadership, and they work diligently to move and control the female contestants. The four menÂ’s best moves are to vote each other out, resulting in a leader-type doomsday. End result: an unassuming woman, who was afraid to take leadership, is the last remaining in the tribe and winner of Survivor. For the four men, this is a worst case scenario.
Scenario 2 Only one man, John, plays the game of Survivor by laying down all his best moves. He works hard, heÂ’s the only one to take a role of leadership, and he works diligently to move and control the seven other contestants while the other three men follow. This is called a Nash equilibrium. If one of the three decided to assume a leadership position while John had already established one, it would only be a death sentence for them both. Therefore, it is to everyoneÂ’s benefit not to change his strategy. Hence, a balance is reached. John is highly likely to win Survivor while the other three men who follow are likely to get further into the game.
Scenario 3 No man assumes the leadership role! All four men do nothing; they sit and wait. Naturally, someone has to win. Everyone has a one in eight shot of winning. There is a 50% chance a man will be crowned Survivor.
Moral The best way to play this game is by doing what others arenÂ’t. If someone has already assumed the position of tribe leader, stay back and do nothing. You wonÂ’t get the lead role for the time being, but you can save yourself from being voted out. If no one has been crowned leader, seize it! And make sure no other player tries to usurp your power or topple you by voting out the threats and psyching players back beneath your finger. YouÂ’ll have control over the others and net the win.
General Trends
In Survivor, general trends arise in accordance to the dynamics of NashÂ’s Non-cooperative Game Theory. I submit to you the Four Postulates of Non-cooperative Game Theory in Relationship to Survivor, or the Big Four.
1. In a tribe heavily saturated with leaders, the followers are more likely to survive.
2. In a tribe heavily saturated with followers, the leader(s) are more likely to survive.
3. In a game heavily saturated with leaders, a follower is most likely to win.
4. In a game heavily saturated with followers, a leader is most likely to win.
Examples:
1. In a tribe with multiple leaders, the leaders will act decisively to vote each other out. This lifts the targets from the followers who live a lot further into the game.
2. In a tribe with seven followers and one controlling leader, the leader chooses who will go. He chooses from his followers which to pick off. By picking off the least valuable followers to his endgame plan, he increases his power of leadership and is safe.
3. In a season with many leaders, you will see many fights, many power shifts, and many leaders going down in flames. And while the leaders kill each other off, the followers survive. The followers make it further into the game and are far more likely to win Survivor.
4. In a season with many followers, you will see the plans of the controlling leader play out. The leader dismisses his biggest threats and pushes the unlikable players more open to suggestion (the one he has ties in) with him to the end of the game. Thus, the leader ensures himself a victory.
What this means, in the broadest sense, is that a follower is best suited surrounded by a great number of leaders. On the other hand, a leader is best suited surrounded by a great number of followers.
In a game with fifteen Lexs and one Ethan, EthanÂ’s chance of winning is extremely good. In a game with fifteen Ethans and one Lex, LexÂ’s chance of winning is extremely good.
The Ideal Tribe
Now, let’s ask, “what makes for an ideal tribe?” Looking at Nash’s Non-cooperative Game Theory, a tribe is ideal if it exemplifies the Nash equilibrium. A tribe has attained equilibrium when all it members are benefited most not to change their positions (from a leader to a follower or vice versa). A Nash equilibrium tribe, or an N-tribe has one leader and seven followers on which to draw from. The followers hurt themselves by becoming or challenging the established leader, and the leader hurts himself by stepping down from power. Thus, the N-tribe has reached a critical balance.
The N-tribe is ideal because itÂ’s stable, thanks to the Nash equilibrium, and has a central guiding strategy, as provided by single leadership. The words that best describe an N-tribe are structured, boring, and free from power shifts. There have been five N-tribes in SurvivorÂ’s history: Tagi, Kucha, Boran, Chuay Gahn, and Sook Jai. The N-tribe is the best-suited post-merge tribe. Also, three Survivor winners hail from N-tribes. N-tribe leaders include Richard, Michael, Lex, Brian, and Penny.
The Flawed Tribes
The further a tribe strays from a one-leader power structure, the further it strays from ideal. LetÂ’s look at different types of less-than-ideal tribes.
A tribe with no leaders, or a leaderless tribe, is okay but far from ideal. This tribe can be seen as unstable and unpredictable. WhatÂ’s worse is its complete lack of a central guiding strategy. Anarchy isnÂ’t as bad as it sounds. This tribe could even be seen as a love tribe. But when merge time comes, there is simply not even structure to combat a rival tribe. The best words to describe leaderless tribes are unstructured, unpredictable, and free from power structures. There has been one leaderless tribe in SurvivorÂ’s history: Pagong. And with contestantsÂ’ increased knowledge of the game, this tribe looks less and less likely. No Survivor winners come from a leaderless tribe.
A tribe with double leaders, or a D-tribe, has a power struggle at its core which makes it inherently weaker than an N-tribe. One leader is ideal. Add a second one, and you create a power struggle, power shift, and elements of instability. The greatest challenge that befalls a D-tribe is unifying as one group during the merge rather than splintering. The best words to describe D-tribes are rivalry-structured, interesting, and open to power shifts. There have been two D-tribes in Survivor history: Ogakor and Rotu. D-tribe leaders include Jerri, Tina, John (S4), and Kathy. Also, one Survivor winner has come from a D-tribe.
A tribe with multiple leaders (more than two), or an M-tribe, is the worst possible tribe and often dies a horrible death. Because M-tribes have too many leaders and too many elements to vote out, the tribe can never create stability for itself. Instead, it self-destructs in a spectacular fashion. The best words to describe M-tribes are volatile, fascinating, and utterly self-destructive. Power shifts are frequent, and the tribe is constantly turning on itself. Ironically, follower-types do well in this atmosphere because leaders are far too busy voting each other off. If both tribes are M-tribes, a follower is greatly benefited and is in the best position to win Survivor. There have been two M-tribes in Survivor history: Samburu and Maraamu. M-tribe leaders include Frank, Carl, Linda, Silas, Brandon, Lindsey, Hunter, Rob, and Sean. One winner has come from an M-tribe (and, of course, she was a gigantic follower).
The Ideal Strategy
More interesting than what makes an ideal tribe is what makes an ideal player. Furthermore, we can ask, “what is the ideal strategy?” And the answer is there isn’t one but two.
Leader: A lot of work is put into this position. Above all else, the leader is charismatic and is able to move people (to control their votes). The leader needs to be savvy of the game dynamics and have incredible foresight. Also, he is extremely aware of the group dynamics and dealing with different personalities. He or she needs to always be looking several steps ahead. By gaining the trust of his fellow members, he ultimately decides whom they will vote out. The leader is all controlling (whether this fact is evident or not). To further his control and position, he votes out the largest threats and the people he needs least. This position takes everything you have and puts it to use. There have been three leader winners in the history of Survivor: Richard, Tina, and Brian. Even though their styles are different, these three could definitely be seen as model leaders.
Follower/Lamb: This position takes considerably less work, but there are five steadfast rules. 1.)Follow: This goes without saying but the biggest rule is to follow the person who is or soon-will-be in power (a leader). You want to gain the leaderÂ’s trust and closely align with him or her. You should definitely be his number one or two guy. DonÂ’t be independent! Be obedient. This may sound easy but it would definitely challenge someone with an ego. 2.)Jump Ship When You Need To: If the former leader is in the process of losing power or is being toppled, jump ship. Yes, you are going back on the trust you cultivated, but screw it. Immediately latch on to the man or woman who has the most power (the new leader in power) and follow him. Act just as obedient and trustworthy to the new leader as you did the last. Vecepia did this a total of six times! In this respect, she truly is a master. From kissing HunterÂ’s bottom in episode one to banishing Kathy when she couldnÂ’t hold onto the immunity idol, she proved to be an expert in make-and-break following. 3.)Be weak but not too weak: If youÂ’re a muscle man, this strategy isnÂ’t for you (look at leader). To be a lamb, you need to be perceived as weak but not too weak whereas you would be voted out pre-merge. Your stature shouldnÂ’t be threatening to others (especially the leader). It generally helps to be a woman. And for godÂ’s sake, donÂ’t win unnecessary challenges. 4.)Win the last couple immunity challenges at the end. These are often vital. This rule is somewhat contradictory to three, but youÂ’d be surprised at what a seemingly weak lamb could pull off. Examples: Kim J, Vecepia, Neleh. 5.)Play for Yourself: Remember that youÂ’re playing for the benefit of yourself, not your leader. If this requires you to cut the throat of your leader-best-friend to get closer to the million dollars, then DO IT! In the final four, lie and backstab when you need to. There have been two follower winners in the history of Survivor: Ethan and Vecepia. These two could definitely be seen as model lambs.
Which of the two strategies is better? It depends. In a game with many leaders, it is far better to be a follower. In a game with many followers, it is far better to be a leader.
For example, Richard Hatch was on an island with fifteen lambs from which to pick off one by one. Could you imagine how much more difficult it would be for him if he were competing against the cast of Survivor Marquesas? How would he win if every other contestant aspired to be a leader and power shifts were an everyday thing? The answer is he wouldnÂ’t. Richard Hatch could easily win in such political climates as S1, S2, or S5, but he wouldnÂ’t last two days as a member of Samburu or Maraamu.
Conversely, Vecepia Towery was placed in a backdrop where power shifts and political upheaval were common. She followed six different leaders. Six! Hunter, Sean, John, Sean again, Kathy, and then Neleh. Vecepia originated in Maraamu, a tribe with four people aspiring for leadership. She quietly supported whoever was in power and never entered the fray of egomaniacs. At merge, Rotu was in a similar state. It was splitting in two like the titanic. Vecepia quietly followed the power, and with the help of one or two key immunity wins, she was crowned Survivor. If, however, Vecepia was dropped in S1, S2, or S5, she would have been picked off like all the other followers. The same goes for Ethan.
The political environment goes a long, long way in selecting a Survivor winner. And before I press on, I want to mention two special cases: Tina and Brian. They both won on their leadership roles, but they seem to be the only winners that also possess a chameleon-like quality that would allow them to play both roles ideally. Tina entered the game as a lamb and was immediately fitted into JerriÂ’s powerful hierarchy. She became a leader when she was instrumental in voting Mitchell out. She became THE leader when she voted Jerri out. And she became the all-powerful-leader when she went behind ColbyÂ’s back to vote out Amber. But she was sweet (and manipulative) enough as to make it appear as if she had an alliance with everyone. Brian could also play the follower (although he never really did). He had a special ability to gain peopleÂ’s trust and give them exactly what they wanted. In the S2 and S5 climates, it definitely paid off to be a leader. And thatÂ’s what Tina and Brian adapted to.
Half-breeds
People who arenÂ’t quite leaders and arenÂ’t quite followers are half-breeds. Half-breeds donÂ’t have the charisma or social skills to attain a leadership position. Plus, they are too independent to be considered lambs. Playing the game as a half-breed is the WORST possible strategy one can have. You CANÂ’T win this game both ways.
LetÂ’s focus on the most recent Survivor, S5, identify the five half-breeds, and see how far they made it into the game. 1.) Pastor John: a man who had aspirations to be a leader but was grossly unqualified in the charisma department, a leader without charisma is just bossy (he was booted first and JohnÂ’s competition included a weak, old woman); 2.) Jed: right in the middle, he made a retarded sort-of leader and a fiercely independent lamb, therefore, no one needed him; 3.) Ghandia: leader without the charisma to support two followers, and far too hostile to be a lamb; 4.) Stephanie: a fiercely-independent lambÂ… UGH; 5.) Shii-Ann: too independent to be a lamb - powerless to assume a leadership position.
These five members were among the first seven to be booted off of Thailand. Among the other two, Tanya was an ideal lamb if it wasnÂ’t for her unfortunate illness. And Robb would also have made an ideal lamb. He was the far better choice to bring into merge rather than the less-gullible Shii-Ann. The final nine had Penny, PennyÂ’s lambs (Jake, Erin, Ken), Brian, and BrianÂ’s lambs (Clay, Helen, Ted, Jan). No half-breeds.
History of the Seasons
S1: Borneo: A leaderless tribe versus an N-tribe. At Pagong, no one was intelligent enough (Gretchen) or charismatic enough (Joel) to assume leadership. Thus, their tribe remained unstructured- a happy anarchy. At Tagi, Richard quickly grew into a position of power and was able to vote out elements he foresaw as least likely to help him (Stacey). He structured a four-person alliance around him and became TagiÂ’s leader. At merge, PagongÂ’s unstructured tribe could not compete against TagiÂ’s (an N-tribe) four unified votes. Pagong fell by the wayside as Richard took his lambs to the finals. Now, I donÂ’t want to detract from RichardÂ’s impressive accomplishments, but a game with one leader and fifteen followers, heavily favors the leader. Through manipulating his followers (turning Kelly against Susan, turning Kelly and Rudy against each other), Richard made his way into the final two and won.
S2: Australia: An N-tribe versus a D-tribe. At Kucha, Michael assumed the role of leader and provider. Jeff Varner also had leadership ambitions but knew it was best to lay low as a follower for the time being (an example of the Nash equilibrium). After MichaelÂ’s disastrous accident, Varner became president pro tempore (very tempore). Things were different at Ogakor. Jerri must have been incredibly charismatic because she had the tribe wrapped around her fingers in just a few days. At the bottom of her heirarchy: Kel, Maralyn, Keith, Tina. Tina wooed Colby over to her side and led a rebellion against Jerri (thus voting out Mitchell). At merge time, Kucha(N-tribe) was better prepared to go up against the fractured Ogakor(D-tribe). But Ogakor miraculously saw past its rivalry, and united to knock down Kucha. The two-leader rivalry flared during the pagonging of Kucha members. Tina broke the pagonging (once they had the numbers) to vote out Jerri. Now, Tina was the only leader in the tribe. Later, she went behind ColbyÂ’s back to vote out Amber. This took a lot of power away from Colby and was equivalent to cutting his balls off. Tina was a leader that structured the group around favoritism, in many ways transcending political boundaries. Everyone thought they had an alliance with her. Everyone was competing for her love. Convincing Colby that she was his mother was probably the greatest act of manipulation and leadership in the entire history of Survivor. This game only had three leaders, therefore it was likely that a leader would win. This is especially the case when the game reached the final seven with one leader (Tina) and six followers. Tina wins Survivor.
S3: Africa: An N-tribe versus an M-tribe. Matching an N-tribe versus an M-tribe is like matching the best possible tribe to the worst possible tribe. At Boran, Lex was free to build alliances and assume leadership in the face of seven very docile followers. At Samburu, I counted six leaders. So, it didn’t take long before the tribe self-destructed and became irreparably fractured. A fracture impossible to fix because there were simply too many leaders on both sides to vote out. Boran went into the merge solid while Samburu entered as the amazing self-destructing tribe. In the final nine, there were three leaders, making it seem as if a follower would likely to win. However, Lex quickly overcame the competition and entered the final five with four complete lambs. Now it seems likely that a leader would win. In the final four, the game was prepared almost perfectly for a Lex win. Tom and Ethan wanted to go to the finals with Lex (where he’d win) and Kim J was a complete weakling. Lex’s leadership was paying off in a big way and his chances of winning were extremely high. However, a freak occurrence transpired: Kim J won two immunities and took the younger Ethan with her to the finals. Ethan, a follower of Lex, won in a game that the big four would probably have favored Lex. The big four is not absolute. Freak variables seem to enter every situation. And that’s why the language is “more likely” and “most likely” (which were absolutely true).
S4: Marquesas: A D-tribe versus an M-tribe. Look at all those leaders. Our first season without an N-tribe (which are boring). Maraamu immediately exploded under the weight of its sheer amount of leaders (just like Samburu). Leaders included Hunter, Sean, and Rob. The left-over pieces of Maraamu were then thrust into a larger power struggle that was Rotu. Rotu had two leaders: John and Kathy. John was always in the good graces of his tribe and was able to build-up a Hatchian foursome. Kathy, on the other hand, found little support in her tribe despite her fervent work and episodes where she pleaded for emotional support. Unfortunately for John, Rotu didnÂ’t have the opportunity to vote Kathy out. At the merge, Survivor quickly became a struggle between John and Kathy rather than Rotu and Maraamu. Kathy came back with a vengeance. She felt her way around the game and quickly grew aware of JohnÂ’s pecking order. In retaliation, she picked up outside pieces of Rotu (Paschal, Neleh) and pieces of Maraamu (Sean, Vecepia) to combat JohnÂ’s Four. The power-shift was massive as Kathy toppled John and became a leader of Soliantu. The problem was that she wasnÂ’t the only one. S4Â’s final five saw two leaders (something that has never been duplicated). And neither had as much control over the three followers (Neleh, Paschal, Vecepia) as they would have liked. Therefore, the two leaders became colossal targets to each other and the three followers. Sean and Kathy were the next two voted out (not using a rock). In the end, Vecepia, a tribe-hopping follower of massive proportion won Survivor 4. This Survivor season heavily favored a follower. There were too many leaders in Maraamu, too many leaders in Rotu, and too many leaders in the final five. Obviously a follower (Vecepia, Neleh, Paschal) stood most to benefit from all this leader-toppling and social upheaval.
S5: Thailand: An N-tribe versus an N-tribe.
Two N-tribes! How boring and predictable. At Chuay Gahn, Brian assumed leadership through a masterful style of giving people what they wanted and making it appear as if they were politically linked. Through his control, Brian voted out the people who were of least use to him (Pastor John, sick Tanya, Ghandia). At Sook Jai, tribemates fell in love with Penny as an alliance was built simultaneously with a shelter. Penny quickly erected a power structure around herself using emotional dependencies. She had Erin and Jake wrapped around her finger. And Penny knew Ken was wrapped around JakeÂ’s finger. This became PennyÂ’s Final Four (a group she could easily manipulate into a Penny-Erin final two and a Penny win). Shii-Ann, a member of the shelter alliance but not PennyÂ’s final four, was in an odd position. She diligently tried to make lasting bonds with Jake and Ken but was stopped by Penny. To finalize her final four, Penny erected an emotional barrier around her final four and kept Shii-Ann at a distance. An astute Shii-Ann foresaw the giant fifth place looming over her head but still played the role of the team player (for the time being). Penny and the shelter alliance picked-off the independent lambs one by one. During day 18, Penny makes the catastrophic mistake of voting out gullible Robb instead of an all-too-knowing Shii-Ann. WeÂ’re looking at a Penny five versus a Brian five at fake merge. At this time, Shii-Ann wows the group by jumping ship (or jumping plank). Sook Jai loses two immunities and gets rid of PennyÂ’s biggest threats (Shii-Ann and long-run threat Erin). Chuay Gahn pagongs the other tribe (because thatÂ’s what N-tribes do), and weÂ’re left with Brian and his pack of lambs. Brian manipulates himself into the final two and wins. This Survivor had only two leaders (the least of any season aside from the original). It was extremely likely that a leader would win. And due to a better understanding of personal dynamics and more IC wins, that leader was Brian.
BITCH IS DEAD
