Survivor – Breakdown of the Greatest Social Game
Survivor is a reality television show, that prides itself on being one of the greatest social experiments ever. Players, about 20, are put on a remote island and must provide food, shelter, and fire for themselves. Players are initially put into multiple tribes and play in tribal reward challenges, where they can win food or blankets, anything that makes their living situation better. They then face off in tribal immunity challenges where the losing tribe goes to tribal council and votes someone out of the game. Tribal immunity challenges and tribal council occur every 3 days during the 39-day game.
Eventually, enough players get voted out and the tribes get put into one big tribe, this is called the merger. From here on out, the players will now have individual reward challenges and individual immunity challenges. Whoever wins the reward challenge (rewards are usually food or other comforts at this point in the game) typically gets to choose other members of the tribe who lost to tag along to enjoy the reward with them. Whoever wins the individual immunity challenge will be safe from tribal council and cannot be voted off. Since there is only one tribe, after an individual immunity challenge (every 3 days) all members of the tribe go to tribal council all at risk of going home except the winner of the immunity challenge.
The players get voted out until there are about 2 or 3 players left for the finale, then the players who were voted out after the merger will vote who they want to win the cash prize and the title of “Sole Survivor.” Not only does it take a lot of physical skill to play Survivor but also uses a lot of strategy and game theory in order to win.
After season 10 the producers added hidden immunity idols into the game. These idols can be found in their camp, around their camp, at challenges, or even on other islands. With these idols, when a player has a feeling that they are at risk of going home, at tribal council they can play the idol and any votes cast for them will not count and they will be safe from being voted out. Players can play the idol before or after the votes have been cast but must be played before they are read.
There are many aspects to the game and therefore a lot of different factors that go into winning the game. We will be looking into mutable and immutable traits of the participants to see how they affect their position they ended in the game. We will also be using game theory to figure out the players’ incentives to understand their decision-making throughout each step in the game.
The Data
I downloaded data on the first 40 seasons of Survivor (all seasons aired as of 6/21), which included data on every player, from the number of challenges won to their age, to the number of idols found. Data collection credit goes to The True Dork Times.
Initially, I decided to use Days (or the number of days a player stayed in the game of Survivor) as my dependent variable, I used that instead of Finish (which is the position rank the player finished in). The main reason for this choice was an easier interpretation of the regression model (a positive coefficient means it increased the number of days stayed in the game) and another reason is there is more variation in the Y variable. Although there is a downside to using Days which is why I will also look into what factors affect what place you finish. The reason for both is that players don’t just want to stay in the game for more days, their main objective is to win the game.
Independent Variables
I wanted to look at some independent variables which I thought would be the most prevalent with the data that was available, I came up with: Sex of Player (Sex), Age of Player (Age), Individual Reward Challenges Won (InRCW), Individual Immunity Challenges Won (InICW), Tribal Reward Challenges Won (TRCW), Tribal Immunity Challenges Won (TICW), Number of Hidden Immunity Idols Found (Idols), and what Season the play participated in (Season).
Here are some descriptive statistics on the data collected:
Regression Analysis
Running a regression on the data collected I needed to make some changes in order to collect a more accurate analysis. The first ten seasons of the show didn’t have hidden immunity idols, so including those seasons in the regression would give us an inaccurate understanding of how the idol affects a player’s game. I decided to keep the first ten seasons in the regression and included forty dummy variables for each season. This will account for the difference in hidden immunity idols between seasons.
This is the results from the regression:
Immuntable Traits
First looking at the immutable traits, Sex, and Age of the players, we can see that Age has almost no effect on how far you will make it in Survivor. This is because according to the model, for every additional 10 years of age the player is predicted to stay in the game for .3 days longer, holding all other factors fixed. We can confidently say that your age has little impact on how long you stay in the game. Older players could struggle more with the physical challenges of the game for the tribal immunity and reward challenges, thus making them a target to be voted off, you want a strong tribe to win rewards and immunity. But these same players become more valuable to keep around once the players make it to the merge, they compete in individual challenges, and the older players could be easier to beat.
Sex
Sex is the other immutable trait, 1 representing female and 0 representing male. According to the model, a female player is predicted to play in the game for 1.6 days longer, holding other factors fixed. For some reason, female players stay in the game about a day and a half longer than their male counterparts.
This could be explained by the fact that men on average are stronger and more athletic than women (it is important to clarify when talking about men and women that these are averages, meaning not all men are stronger and more athletic than women, there can be women stronger and more athletic than a man but choosing a random man and women there is a greater probability that the man is stronger and more athletic than the women), so you would be more likely to vote out a male over a female with the same resume.
This is because men would be more likely to beat you in future physical challenges, they win about 64% of Individual Reward Challenges and 63% Individual Immunity Challenges. So, rationally once you make it to the merger you would want to vote out the players who are good at winning challenges, which happens to be men a majority of the time.
Another possibility is that women are more trustworthy. Women on average rank higher for levels of agreeableness, one of the big five personality traits (Leonora). Once again, we are talking about averages, not all women are more agreeable than men, but a choosing a random man and woman there is a greater probability that the women would be more agreeable than the man. People who exhibit high levels of agreeableness tend to show altruism, kindness, trust, and affection. They also are more likely to show prosocial behaviors, which is an indicator for sharing and helping others.
In Survivor, this trait is useful for creating and keeping alliances. Meaning that female contestants would be more likely to create trustworthy alliances, unlike males who on average would be less trustworthy and more likely to break the alliance. Being able to fully trust your alliance is rare, as at any time your alliance can flip on you and betray you. So, if female players are more trustworthy than male players, contestants will likely keep them around longer because of that valuable quality of trustworthiness.
Mutable Traits
Looking into the mutable traits, this includes the different challenges that the players compete in throughout the game, as well as other in-game elements like finding hidden immunity idols. According to the model, for each Tribal Reward Challenge Win is predicted to increase the amount of time you are in the game by 2.7 days, holding other factors fixed. And for each Tribal Immunity Challenge Win is predicted to increase the amount of time you are in the game by 2.6 days, holding other factors fixed. Both independent variables are quite significant and clearly are beneficial in increasing your stay in the game.
Similarly, according to the model for each Individual Reward Challenge won the play is predicted to stay in the game 3.1 days longer holding everything else constant. And for each Individual Immunity Challenge won, the model predicts a player will stay in the game 3.1 days longer, holding everything else constant. The most interesting aspect of these results is that the immunity challenges, both tribal and individual, protects you from leaving the game for that night’s tribal council, thus leaving you vulnerable again in three days when the tribal council is. So, it is expected that the immunity challenges increase your stay in the game by about 3 days, which is approximately what we see.
What’s weird though is that the reward challenges, don’t give you any direct benefits in staying in the game longer like the immunity challenges do. Instead, they give you rewards to increase the quality of life on the show, whether that be food, shelter, or cooking equipment. Yet, the amount of extra days you stay in the game according to the model is very similar to that if you won an immunity challenge. Meaning that reward challenges may be just as important to win as immunity challenges. Or that immunity challenges aren’t as important as we may have previously thought.
Immunity Idols
The introduction of hidden immunity idols was a huge game-changer in Survivor. This allowed players who were almost destined to be voted out a glimmer of hope to stay in the game just a little bit longer. According to the model, finding a hidden immunity idol is predicted to increase the number of days you stay in the game for about 2.7 days, holding everything else fixed. This makes sense as the idol protects the player from being voted out for one tribal council, and they have tribal council approximately every three days on the show. The reason finding an idol doesn’t increase your stay by exactly 3 days is because this variable is only finding an idol, not playing the idol. That means a player could find an idol and never play it or play the idol incorrectly and get voted out at the next tribal council.
Dummy Variable: Season
The independent dummy variable Season (left out of reporting) was initially used to be able to accurately look at the Idols variable since the first ten seasons of the show didn’t have any immunity idols. But in Seasons 22, 38, and 40 the model predicts the players to stay in the game for much longer compared to the other seasons (other seasons estimators were roughly between -2 and 2). The model predicted that players playing in these seasons would stay in the game for 7, 9, and 11 days longer, holding everything else constant, meaning because they are playing in this specific season that is the reason their stay was longer.
Looking a bit more into these seasons the reason for this is because Season 22 was called Survivor: Redemption Island, which means that a player voted out wasn’t actually voted completely out of the game but instead taken to a secluded island for a chance to get back into the main game. Season 38 and Season 40 had very similar premises that allowed players who were voted out to be allowed to fight their way back into the game through challenges. This change in the rules of the game changed how long a player would stay in the game when compared to other Seasons.
Prisoners Dilemma
Looking at the model as a whole, 59% of the variation in the number of days a player stays in the game can be explained by the variation in the independent variables. So, if all immutable traits and in-game elements of the game survivor can explain about 59% of the variation in the number of days you will stay in the game, then what explains the other 40%? This can be partly explained by game theory. The game show Survivor is a repeated prisoners dilemma game.
The game above depicts two players in Survivor who are allied together. Every three days when tribal council comes around a variation of this game is played between the two players. I say a variation because the values of the outcomes change each week depending on the circumstances that happened in the game (the numbers above are just placeholders to easily interpret how the players play the game and what their best decision should be based on game theory).
The players can either choose to be loyal to one another and each gain 3 utility, this is because theoretically if you both stay loyal you should be safe from being voted off. If one player decides to flip while the other remains loyal the player who flipped will receive more utility than the player who remained loyal, 5 compared to 0. This is because a player who “makes moves” to vote people out is seen as aggressive and strategic, this builds up their resumes for the end game of the show.
Now if both players decide to flip and not remain loyal then they both receive 1 utility, this is because it is clear that the alliance is broken and now the other players can choose out of these two players who they want to side with since they both wanted to flip. Basically, the game is out of control for both players if they both decide to flip, and having control in the game is beneficial to winning.
Repeated Prisoners Dilemma
When the players are aware that the prisoner’s dilemma game will be played multiple times, they will tend to go towards loyalty. This is especially true for repeated games in which the players do not know when the game will end (Axelrod). The reason being is players want the max amount of utility and Player 1 choosing flip while Player 2 chooses loyalty will gain Player 1 max amount of utility. But Player 2 has a memory of the previous game and the next game will choose to flip as well, this is because Player 1 chose to flip the last game, and if they choose that again Player 2 gains more utility this time by choosing flip over loyalty, 1 utils versus 0 utils.
Repeating the game, the players will choose to flip each time as they both have a memory of the other players’ choice last game. This ends up being less utility for both players if they both choose flip instead of both choosing loyalty. This is typically why in repeating games where the players don’t know when the game ends both players choose to remain loyal in order to maximize utility.
Backwards Induction
In Survivor though, we know when the game ends, it ends when either the player is voted out or announced the Sole Survivor. Therefore, in order for a player in Survivor to maximize their utility in the game, players will remain loyal to their alliance until there is a threat of their game coming to an end and that’s when they flip. This creates a really interesting dynamic to the game because if you know that players will flip once they feel they are in danger of going home then your best strategy would be to flip on them right before they flip on you. This is known as the backwards induction argument.
In the last iteration of the game, the players best move is to flip, since the players know this then in the second to last iteration of the game the players best move is to flip, thus flipping on the other player before them (Benoit). This gets repeated until the players first iteration of the game is to flip on each other. That is the Nash Equilibrium of a repeated prisoners dilemma game where we know when the game ends. Every player’s best move is to never be loyal but instead always flip.
Since we know through observation of the game, not everyone flips in the first iteration of the game; therefore, there must be some extra benefit to cooperation and staying loyal, whether that’s added trustworthiness or genuine care for the other player you are allying with. The equilibrium of this game seems to be that players will stay loyal and cooperate until they are suspect of their alliance will flip on them, then they decide to flip. It is clear that other elements go into a players decision-making of when to stay loyal and when to flip with an alliance since the equilibrium in the game is not the same as the Nash Equilibrium that game theory predicts.
Adding Layers to the Game
The other elements that players take into account are quite difficult to find, and more than likely different for each player. But the basic rule of thumb seems to be that if you find out when someone is in danger of going home, where the chance of them flipping on you is greater because they receive more utility than if they stayed loyal, your best bet is to flip on them first. But the game is a lot more complicated than that.
For one you aren’t just playing the prisoner’s dilemma game with just one person, you are playing with every single player, and every other player is playing it with every other player as well. Second, we also do not know what the utility of each player is for flipping or remaining loyal, we could get a rough estimate on what we think might give them more utility but in no way would it be accurate. Lastly, even if you are able to correctly predict when someone in your alliance is going to flip, there may be reasons why you might not want to flip on them first.
Flipping on them first makes you look like the ‘bad guy’, the traitor, and untrustworthy. Survivor is built on relationships and trustworthiness; this is the social aspect of the game. So even though flipping on someone before they flip on you would maximize your present utility, flipping on your alliance shows that you can not be trusted and are not the best at cooperation, therefore many people would not want to work with you in the future.
That’s the tricky part of playing Survivor is when and who do you create alliances with and when is the best time to break them off, because your ability in challenges and other physical parts of the game can only take you so far. Finding Idols and winning challenges can help you get further in the game, but without the social aspect of the game and understanding how to use game theory to your advantage, you will most likely fall short of the goal of Sole Survivor.
Another Regression
One of the big assumptions we make about Survivor is that all players come on the show with the goal of winning the million dollars and the title of Sole Survivor. Instead of looking at how these estimators affect the number of days you are in the game let’s look at how they predict winning. Winning the game show is the ultimate goal. So, I have changed the dependent variable from Days to Finish (or what place you finished at in the game, the lower the number the better, 1 is winning the game).
These are the results from the new regression:
One thing that stood out to me in this model is that for every Individual Immunity Challenge won the place you finish in, according to the model, is predicted to decrease by 1.8 holding all other variables fixed. So, you decrease the position you finish in by nearly two whole spots, that’s quite a significant boost for just winning one individual immunity challenge.
Similarly, according to the model for every hidden immunity idol a player finds, the model predicts it will decrease the place you finish by 1.7 holding everything else constant. So, both of these elements of the game are made to help you survive one tribal council, as the individual immunity only lasts one tribal council and the idol can only be used once, decreasing your position by one spot. Yet, the model predicts that when you win an individual immunity challenge or find an idol you will decrease your position finished by almost two spots. Nearly double the expected outcome of these elements of the game.
Something else to point out is that according to this model females are predicted to finish .9 spots lower than their male counterparts, holding everything else constant. This model seems to indicate that being female actually does increase the position you finish by one spot, unlike the first model in which it only predicted to increase the length of your game by about one and half days. This made me question the assumptions I made at the beginning of this regression analysis.
Changing the Assumptions
The assumption that all players play to win the title of sole survivor is fundamentally flawed. Initially, when signing up for the show it is safe to say that all players main goal is to win, but once they are put into the game and can see their competition and compare strengths and weaknesses their goals change. Players know themselves the best, so if a player knows they can not compete with the other players in physical challenges then their strategy might change. Instead of trying to make big moves or win a bunch of challenges, this player could instead be very loyal and reserved. Other big playmaker contestants would want to bring this player to the finale because they have no resume so no chance of actually winning sole survivor.
These types of players are called ‘sheep’, at first, it seems like no one would want that label and are not likely to win Sole Survivor. But there is a big incentive to make it to the finale, second place gets $100,000 and third gets $85,000 (first-place win $1 Mil). So, the player in a position with no resume and has little to no chance to win first place would change their incentive to strictly making it to the finale, under any conditions, regardless of what their resume looks like.
Who would not want to be Sole Survivor?
The ones who would change their focus from winning sole survivor to just making it to the finale are the players who know they don’t have a big resume and struggle to win in challenges. As explained before, females are on average more agreeable and physically weaker than men, therefore on average, they are less likely to make big moves for their resume and struggle to win some of the challenges (some challenges are puzzles and others are physical, I am clearly referencing the physical challenges here). So, females are more likely to switch their focus from winning the whole game to just making it to the finale.
This can be seen in the players who make it to the finale versus who wins. For players who make it to the finale (top 3), the distribution is 51% male and 49% female. Yet, when you look at the distribution of winners, 63% male, and 37% female. Showing that female players are just as likely to make it to the finale as male players, but their resume is not as extensive enough on average compared to males to win.
This could be because males are more likely to win challenges and find hidden immunity idols, males found 68% of all idols. These elements are quantifiable, you can say how many wins you got, how many idols you found, how many big plays you made. There is an easy way to compare these elements, whoever has more, played a better game.
But when it comes to the female resume on average it is not as quantifiable. They would have trustworthiness and loyalty within their alliance but there is no real way to quantify or compare these traits. Or females on average are more sociable and care about the other players they are playing against, again not a quantifiable element. These traits are good for making it to the finale just like winning challenges and finding idols but are much harder to compare to see who played a better game. Maybe that is the big reason for the larger share of wins for the male players, their resumes are more quantifiable than their female counterparts.
The Social Media Effect
Another reason the assumption of playing the game to win is incorrect is that like other reality TV shows some join for fame or popularity. Players in Survivor now all have social media accounts. Having a large number of followers is a good way to be an influencer and generate money and fame. Some may not join the show survivor for the goal of winning but instead the goal of stirring up the pot, creating drama and chaos. This will lead to people wanting to follow what they are doing in real life; thus, they gain followers, popularity, and fame. Although I think the survivor cast does a good job at vetting contestants that do this out of the game, it is definitely prevalent in other popular reality TV shows like the bachelor, so it is worth considering and it may have an effect here too.
Conclusion
It is clear that it is difficult, if not impossible, to find a definitive answer to find out what are the most important factors to win Sole Survivor. Some of it can be attributed to the quantifiable elements of the game, winning challenges, rewards, and finding idols. But a lot of it is still unknown, some can because of our personality and our play style of the game. Some are determined by the timing of when we create our alliances and when we betray them. Some are because of our goals of the game; do we want to go big or go home and attempt to win Sole Survivor or play it safer and sneak into the top three. All these factors create this social masterpiece of a game, as even with lots of data and understanding game theory the outcome will still always be unknown.
Sources:
https://www.truedorktimes.com/survivor/boxscores/data.htm
Axelrod, Robert, and Robert O. Keohane. “Achieving Cooperation under Anarchy: Strategies and Institutions.” World Politics 38, no. 1 (1985): 226–54. https://doi.org/10.2307/2010357.
Leonora Risse, Lisa Farrell, Tim R L Fry, Personality and pay: do gender gaps in confidence explain gender gaps in wages?, Oxford Economic Papers, Volume 70, Issue 4, October 2018, Pages 919–949, https://doi.org/10.1093/oep/gpy021
Benoit, Jean-Pierre, and Vijay Krishna. “Finitely Repeated Games.” Econometrica, vol. 53, no. 4, [Wiley, Econometric Society], 1985, pp. 905–22, https://doi.org/10.2307/1912660.
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