Author: Devanshi Parekh

The holiday season is just around the corner. Everyone loves spending time with their friends and families doing fun activities like cooking and watching movies. Gift exchanging games is a fun activity that many do during the holiday. With any gift exchange, the real goal is to win the best gift.

The payoff matrix below represents a normal gift exchange between 2 people. E represents the enjoyment the player feels when they get a gift. C represents the cost of the gift the player gives. As we learned in class, we can apply nash equilibrium to see that both players will choose to receive, as it’s the dominant strategy for both players. Assuming the enjoyment is greater than the cost, the payoff is like the prisoner’s dilemma. So there is no winning here.

White Elephant gift exchange, also known as Yankee swaps is a variation on Secret Santa. Everyone brings a wrapped gift to the party and leaves them in the middle. Then everyone is given a random number which is the order in which everyone picks a gift. The first person picks a gift and opens it. The player after then makes a choice to either pick another gift and open it or steal a gift that has already been opened. If the player decides to steal the gift from someone, then the player whose gift got stolen will have a chance to steal another gift or choose a wrapped gift. A player can’t steal a gift that just got stolen from them and a gift can only be stolen a certain number of times. This gift exchange finish after all players have played and all gifts are opened.

The best scenario would be to go last, so if you want to steal you have the most variety of gifts to choose from. However, you don’t get to choose the order you play, but you can always pick the best strategy. Ben Casselman used basic game theory questions (such as Should you always steal? Never steal? Steal only under certain circumstances?) to come with steps to get the best gift. He tested the following 8 strategies:

1. Player steals with probability p = (number of gifts taken) / N (naive).
2. Player always steals most valuable gift available.
3. Player always steals second-most-valuable gift available (if only one gift is available, player steals that one).
4. Player never steals.
5. Player steals if any stealable gift has value (to them) greater than the mean value of all opened gifts.
6. Player steals about-to-be unstealable gift (steals == max.steal – 1) if one is available with a value greater than the mean value of all opened gifts.
7. Same as #5 but factor in knowledge of the gift the player brought.
8. Player steals if best available gift has value > expected value

Running the model resulting in the follwoing:

Using that result, Ben came up with the following step for the best strategy: 

1. As each gift is opened, mentally assign it a value (perhaps a dollar value or a 1-to-5 ranking);
2. When it’s your turn, average the value of all the opened gifts (whether or not they’re available for stealing);
3. If there is a stealable gift “worth” at least as much as the average, steal it! Otherwise, open a gift. (Depending on the rules you’re playing by, not every gift might be available for stealing.)

Happy swapping! Hope you get the best gift!

Sources:

https://theconversation.com/how-to-apply-game-theory-to-buying-your-christmas-presents-52233

https://github.com/BenCasselman/YankeeSwap

https://fivethirtyeight.com/videos/white-elephant-yankee-swap-game-theory/

Over recent years the term “fake news” is getting used more frequently. Fake news defined by the Cambridge dictionary is “false stories that appear to be news, spread on the internet or using other media, usually created to influence political views or as a joke”. The recent increase in fake news has negative effects, one being that people believe the lies told as truth and another effect is that it changes the way people view legitimate news. It can be very harmful in certain scenarios such as spreading fake cures for coronavirus that is actually dangerous or spreading lies that can have a big impact on an election. 

The paper, “Studying Fake News via Network Analysis: Detection and Mitigation” by Kai Shu, H. Russell Bernard, and Huan Liu examines the spread of fake news through network analysis. They talk about various network properties that helped them do analysis on fake news; Echo Chambers, Individual Users, Filter Bubbles, and Malicious Accounts.

Echo chambers refer to the idea that beliefs are amplified because the person is in a closed system. It is based on 2 factors; social credibility and frequency heuristic. Social credibility is a factor because people usually surround themselves with like-minded people, hence most people in a person X’s circle will have similar beliefs as them. Because everyone around X thinks that news, which could be fake,  is correct, X will also believe it cause of social credibility. The other factor frequency heuristic points out that people are likely to believe something they hear more often. Therefore if a person is in a closed system and everyone in it believes the same info then they will not hear any other opinions. So if the fake news is what they are hearing the most then they will likely believe it.

Filter bubbles are similar to echo chambers but it’s isolation on social media. Almost all social media sites use algorithms to figure out what type of content you like. They then proceed to continue feed you content on that topic and things similar to it. Due to this users would get to see one perspective on their social media like they are in a closed system. Therefore if they are only fed fake news then they will believe it.

Both echo chambers and filter bubbles relate to strong triadic closure, a topic we learned in class. Looking at the figure above, Y is close to and agrees with what both X and Z say. So even if initially X and Z aren’t friends, because Y has a strong connection with both of them, X and Z will become friends and trust each other’s opinions. Therefore if Z is talking about some fake news to X, because Y believes and trusts Z, X will also believe that fake news.

It’s interesting to see that rise of fake news has been at the same time as the rise of social media. The echo chambers and flitters bubble help understand why this is the case through network analysis. We usually surround over selves if with people who have similar views and believes and only view content from one side perspective. Therefore it is important to educate ourselves with different perspectives, rather than believing something from the first and maybe only perspective you see.

Works Cited 

1. https://arxiv.org/pdf/1804.10233.pdf
2. https://dictionary.cambridge.org/dictionary/english/fake-news