đź•ą How Must I Play?
The Rules of My Game
Introduction
We read The Three Musketeers, and also saw a brief video from Squid Game. Let us further contemplate the actions of the characters.
Discussion-1: Structure
The Game consists of:
- Rational Players
- Numerical Payoffs
- Arranged in a Game Payoff Matrix
- Player Strategies to navigate the Matrix
What strategies are possible as a bowler in Cricket? As a batsman? What strategies are permitted? By whom?
The Game of Trust
So, let us play a Game, on the Game of Trust Website ! Please pair up on one laptop to play this.
Discussion-2: Nature
- Strategies in PD define what actions you will take in response to actions others might take.
- We saw quite a few strategies here
- The best strategy is one that survives!
- Survival is everything. That is what D’Artagnan and the Three Musketeers were also basing their actions on!
- Read more about this idea in this (possibly illegal) copy of Nassim Nicholas Taleb’s Book, “Skin in the Game”.
- Or you can watch Taleb speak
- We will encounter Survival again soon!
Reading: Robert Axelrod’s Study on Cooperation
This is a famous study of the Iterated Prisoners’ Dilemma by Robert Axelrod, The Evolution of Cooperation (PDF). We will read just a wee bit of it in class.
And here is Robert Axelrod on the RadioLab Podcast:
Spotify:
Transcript: https://www.wnycstudios.org/podcasts/radiolab/segments/104010-one-good-deed-deserves-another
Nash Equilibrium and Dominant Strategy in PD
Are there COSTs to ACTIONs? Who decides?
How does one ACT to minimize costs and maximize rewards? Remember, we are all Agents, with our own vocabulary of Actions which we might use Again and again, and experience an Aggregate outcome in society.
The Payoff Matrix in PD is:
| Prisoners’ Dilemma Payoff Matrix | ||
| Player #2 | Player #1 | |
|---|---|---|
| C | D | |
| C | (R=3, R=3) | (T=5, S=0) |
| D | (S=0, T=5) | (P=1, P=1) |
| Payoffs are (Player#1, Player#2) | ||
| R = Reward; S = Sucker’s Payoff; T = Temptation; P = Punishment | ||
| Shaded Cells are Nash Equilibria | ||
Note that, in order for this to be a true Prisoners’ Dilemma, we need:
\[ Temptation > Reward > Punishment > Sucker's~ Payoff\\\ \] \[ R > (S + T)/2 \] The first condition ensures that Temptation (to D) is always stronger than the Reward(for C); and the second ensures that the two Players cannot mutually agree to alternate between C and D and have a higher net reward !! Can you Game Game-Theory ? That’s a Cabal !!
Wherever you “are” on the matrix, you can always improve your situation by defecting!! “D” is your best move, your “Dominant Strategy”, because that is how the matrix is (numerically) stacked. And if both players do that, then we end up at the bottom-right cell, which says “(D,D)”, where the game stays forever, in state called the “Nash Equilibrium”.
While just a little thought, even hesitation, could have led us “(C, C)”…An altruistic decision to “C” first could tip the scales in favour of “(C,C)”.
Sigh.
SouthWest Airlines: A Case Study
OK, so how does PD show up in a real-world context? Here is a business story: The story of Southwest Airlines’ Early Bird Check-In.
What could be the passengers’ strategy?
Hotelling’s Phenomenon: A Case Study
Why are Hotels and Petrol Pumps located next to each other? Here is the Hotelling’s Phenomenon, explained.
What are the Assumptions in Prisoners’ Dilemma?
- That gains and pains can be quantified
- Rationality
- Players have identical and opposed aims i.e. Adverserial Symmetry.
- In most cases, the game is zero-sum
- Some form of spoke/unspoken agreement as to what may and may not be done ( i.e Rules of the Game )
Wait, But Why?
- So, the PD matrix is loaded towards “D”. ;-(
- “Defect” is the Dominant Strategy
- Societal Outcomes will then be ….horrible. This is the Nash Equilibrium in PD.
- OK, so public behaviour can be influenced by individual decisions to first C, and then respond?
- But is it always zero sum? Can it be non-adverserial?
- Are there other Strategies? Other Games even?
We’ll see.
Fun Stuff With Game Theory
- Olivia Jack , Dirk Brockmann. “The Prisoner’s Kaleidoscope”: The prisoner’s dilemma game on a lattice Pattern Formation, Beauty and Chaos in a Game Theoretic Model. https://www.complexity-explorables.org/explorables/prisoners-kaleidoscope/
References
Jeff Desjardins (2014). The Silver Rule, Taleb, and the Slippery Slope to Interventionism. https://medium.com/@jeffdesjardins/the-silver-rule-taleb-and-the-slippery-slope-to-interventionism-ef6baef17c23
Carl Sagan’s “A New Way To Think About Rules To Live By”. https://tetrahedral.blogspot.com/2011/12/carl-sagans-new-way-to-think-about.html
Here is a good Summary of modern thinking about Human Cooperation: The Evolution of Human Cooperation, PDF
John D. Williams, The Compleat Strategyst: Being a Primer on the Theory of Games of Strategy, RAND Corporation, ISBN:9780833042224. This is a very humourous and fun book on Game Theory ! It is available for free online at the RAND Corporation Website.
Ken Binmore,Playing for Real: A Text on Game Theory, ISBN:9780195300574, Oxford University Press, March 2007. Available here.
Avinash Dixit, Susan Skeath, David Reiley, Games of strategy, ISBN: 9780393124446, New York :W.W. Norton & Company, 2015.
Brams Steven J., 1994. “Game Theory and Literature,” Games and Economic Behavior, Elsevier, vol. 6(1), pages 32-54, January. Available here.
Alexander Mehlmann,The game’s afoot! Game theory in myth and paradox, American Mathematical Society 2000. AMS Bookstore
The Tragedy of the Commons. https://en.wikipedia.org/wiki/Tragedy_of_the_commons
Game Theory Pop Music, Movie Clip, and TV ad Playlist !!
The Alan Parsons Project: Eye in the Sky. https://youtu.be/fRMf3wKBCPo
Chris de Burgh: Don’t Pay the Ferryman! https://www.youtube.com/watch?v=Q-a5TAL-IXs
Abba: The Name of the Game https://www.youtube.com/watch?v=T5Qf_7HM1cM
Bachchan vs Warsi: Want a Pepsi - Tit for Tat https://www.youtube.com/watch?v=gc6QZcxbMZE
The Princess Bride - Battle of Wits - Which Strategy to Use here? (Asymmetric Information) https://www.youtube.com/watch?v=rMz7JBRbmNo
The Gods Must be Crazy (Brinkmanship) https://www.youtube.com/watch?v=9LvViKftRnA
L.A. Confidential https://criticalcommons.org/embed?m=pBXsAUvh9
Activity-2
Take a walk in the nearest urban area this weekend. Unobtrusively, observe what people are doing. Note these down when they seem to be visible examples of “Cooperate” or “Defect”. For or Against whom?
No pictures.