Giveaway Part 1

The Facebooker’s Dilemma.  
Here are the rules:
  • Each player selects a card from a standard 52 card deck to support.  (This is done in comments on The Loaded Die’s Facebook post)
  • The number of votes for all 52 cards will be tallied and made known to all players.  
  •  Each player then has 2 options; to continue to support their original card (show true support), or defect, and show new support to a different card. 
 
Scoring:
  • True support earns a player 5 points for all supporters (true and new) of their original card.
  • Defecting earns a player 6 points for each true supporters of their original card, and 1 point for all supporters (true and new) of their new card.

 Incentive of play, and examples:
This game is founded on the principles of game theory.  A player’s actions should be highly dependent on what their expectations are for other player’s actions.  
  • Players are incentivized to band together – a player can earn points 5-at-a-time for each player that ends on the card he originally chose. 
  • But, although each true supporter of a card earns 5 points per true supporter, defectors earn 6.  If a player expects all original supporters of a card to remain in true support, then they have incentive to defect.   

Ex 1:  3 player game – all 3 initially support the 5 of clubs (5c).
Outcome A) All three remain in true support of 5c: 
  • They tie the game with 3 supporters * 5 points = 15 points each.
Outcome B)  2 of the players remain in true support, and 1 defects to the 8 of hearts (8h).  
  • The true supporters of 5c earn 2 * 5 = 10 points.  
  • The defector earns [6 points * 2 true supporters of 5c ] + [1 * 1 supporter (true or new) of8h] = 13 points and the solo victory.

 Ex 2:  30 player game - Initial support looks like this: 
Card - Original Support
  • 5c - 10
  • 9c - 8
  • Jd - 7
  • 8h - 3
  • Ah - 1
  • Qs - 1

 Outcome Discussion.  There are now millions of possible outcomes, and the social element of the game comes into play.  Let’s focus on only the 5c and 9c.   
Set A) of possible assumptions
  1. Of the 10 supporters of the 5c, 7 are trusted friends, and the other 3 are perfect strangers who supported a popular card with intent to defect.
  2. The 8 supporters of 9c has are all trusted friends.  
  3. The 3 perfect strangers are unaware of each other.

Set A.1) possible outcome
All 3 perfect strangers defect from 5c to 9c, thinking that they might not be the only defectors, and that in order to break a tie they’ll need the extra 1 point from those loyal to 9c.

Card - TRUE - NEW - TOTAL
5c - 7 - 0 - 7
9c - 8 - 3 - 11
  • True supporters of 5c get 5*7 = 35 points
  • The 3 defectors get 6*7 + 1*11 = 53 points
  • True supporters of 9c get 5*11 = 55 points, and the win.  

Set A.2) possible outcome
2 perfect strangers defect from 5c to 9c due to the reasoning above, and 1 defected to Jd, worried that 2 or more members of 9c would defect. Similar to above:
  • True supporters of 5c get 5*7 = 35 points
  • The 2 defectors to 9c get 6*7 + 1*10 = 52 points, and the win
  • True supporters of 9c get 5*10 = 50 points 
  • The 1 defector to Jd gets 6*7 + 1*8 = 50 points

It can be gleaned that true supporters will have a lot to gain from defectors from other well supported cards, so there is no clear strategy for victory.


This puzzle is from 07/08/2015. You can find our current puzzle here.
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