🕹 Still More Games !!

Which Stranger Am I Talking with Today?

Introduction

Think about the following:

• So, would you wear a veshti/kurta/angavastram, saree/silk paavade/dhaavani to college?
• When you want someone to search the internet, what do you tell them do?
• How do you show someone, a stranger, that you agree with what they are doing at that moment?
• How do you know where the exit is in a public place?
• Where would you stage a protest? How would you get other people to join in?
• If you want a whole bunch of 20-30-something people to raise their arms up and spontaneously rock side to side?
• And, what does “less than three” even mean?!!??

In the previous module on the Prisoners’ Dilemma, we saw how we all are engaged in adversarial and transactional Games with many other people, most of whom are strangers to us. But as remarked before, the Human Species is perhaps unique in that we are able to cooperate with strangers and possess bourgeois virtues!! So we are not always adversaries or enemies, and we are able to obtain unspoken agreement and correspondence with strangers and treat them as our honorary kin for long term benefits.

What use would this be? Would it be a Design Tool? How?

Today, we will study Coordination Games and Schelling Focus Points, and see how these concepts can help create better designs, businesses, and maybe, art.

The Stag Hunt

From Brian Skyrms’ Address at UC.Irvine:

The Stag Hunt is a story that became a game. The game is a prototype of the social contract. The story is briefly told by Jean-Jacques Rousseau, in A Discourse on Inequality:

“…If it was a matter of hunting a deer, everyone well realized that he must remain faithful to his post; but if a hare happened to pass within reach of one of them, we cannot doubt that he would have gone off in pursuit of it without scruple…”

— Rousseau

Rousseau’s story of the hunt leaves many questions open. What are the values of a hare and of an individual’s share of the deer given a successful hunt? What is the probability that the hunt will be successful if all participants remain faithful to the hunt? Might two deer hunters decide to chase the hare?

Here is brief Introduction to the Stag Hunt Game.

What is the Stag Hunt Game?

Coordination Games and Schelling Focus Points

Here is Julia Galef on the idea of Schelling Focus Points:

Coffee, Caramels, and Schelling Points by Julia Galef

And here is another video on the same topic, but with a historical, and spatial, angle to it:

Schelling Focus Points

Focal points can be used in Coordination Games: these are activities where people’s actions tend to organize into Patterns based on specific default options. These actions could be:

1. Conversation, Words, Phrases, Gestures
2. Dress
3. Travel / Meeting / Location
4. Food and Beverage Choices
5. Attention

The Payoff Matrix in SH is:

Stag Hunt Payoff Matrix
Player #2	Player #1
	C	D
C	(R=3, R=3)	(T=1, S=0)
D	(S=0, T=1)	(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

The inequalities relating the payoffs in the Stag Hunt game are:

\[ Reward > Temptation > \pmb{Punishment} > \pmb{Sucker's~ Payoff} \\\ \]

There is in fact no Temptation at all! Rewards for C are always the greatest!

There are two Nash equilibria in the Stag hunt game. The CC corner is representative of both players being pro-risk and cooperating for higher reward. The DD corner is where each Player is risk-averse and prefers to work by themselves and mind their own business, without interference to, or help from, the other Player. This nomenclature, and the insightful analysis that goes with it, is due to Reinhard Selten and John Harsanyi, Nobel Prize winners in 1994, along with John Nash.

The Stag Hunt is a less vindictive than the Prisoners’ Dilemma and may be preferable as a Model in situations where there is not so much of an adversarial engagement as there is a tendency to maximize gains and minimize risks, and a possible high-trust environment.

Is it better to Die than to Kill?

What game is being played here?

The Chicken Game

This is the Chicken Game (CG), where it two Players dare each other to “chicken out” and survive, when put in a very strong adversarial situation.

The Payoff Matrix in CG is:

Chicken Game Payoff Matrix
Player #2	Player #1
	C	D
C	(R=4, R=4)	(T=5, S=2)
D	(S=2, 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

And the inequalities that govern the Chicken game are:

\[ Temptation > Reward > \pmb{Sucker's~ Payoff} > \pmb{Punishment} \]

and as with the PD, we have:

\[ R > (S + T)/2 \]

Where do these Games show up?

While it may seem, cynically speaking, that everyone is playing Prisoners’ Dilemma, one can detect situations where the Stag Hunt is more appropriate as a Model:

A. Prisoners’ Dilemma

• Security Check-in at Airports, when travelling in a group together

B. Stag Hunt Game

• Classroom Group Projects https://amyjanzwood.wordpress.com/2018/11/14/game-theory-and-environmental-problems-a-classroom-simulation/
• Communities where tacit social contract that lets people live in peace with each other.
• When people follow queues. This is a high-trust situation, where people reap the benefits of quick service
• When nobody goes to the party / protest because they don’t think anybody else is going to the party, we are getting the risk-dominant outcome in a Stag hunt.
• Hans Christian Andersen.The Emperor’s New Clotheshttps://americanliterature.com/author/hans-christian-andersen/short-story/the-emperors-new-clothes

C. Chicken Game

• Sibling Rivalry, involved in family-home task ( similar to classroom projects)
• Corporate Environments where some people shirk work and others do not. E.g. at Call Centers where the “time-to-answer” is a measured metric
• Driving in the Wrong Direction, or driving a two-wheeler on the footpath
• Chicken Games often occur in politics and of course, in offices and organizations, where co-workers dare each other to shirk from work the longest!!
• Here us a sermon on the Chicken Game. (Listen to the first few minutes for a good description of the Chicken Game.)

Schelling Points and the Lindy Effect

To be written up. You are one lazy bugger. INTJ, but lazy.

The Design of Game Incentives

To be Written Up.

Wait, But Why?

• If we are going to design “public behaviour” ( an Ad, a Brand, a Public Policy, a method for Crowd Management, Signage…) you might want to think of which Game is involved
• What are the Actions and the Payoffs?
• Can you design the Game by changing the Matrix?
• Incentives are both Positive and Negative:
  • Costs/Benefits: Money, Reputation, Physical Danger, or mere Inconvenience?
• Some apocryphal aphorisms to consider: (Trying to imitate Naval Ravikant here 😁)
  
  • The best laws are those that are easiest to follow do not exist on paper
  • Useless laws weaken the necessary laws.
  • Some Products are faulty, some others de-faulty (Schelling Points)
• If you are engaged in Participatory Research with Americans, why would you make passing reference to “motherhood and apple pie”, or “picket fences”?

References

1. William Poundstone. Stag Hunt. https://www.heretical.com/pound/staghunt.html)
2. William Poundstone. Volunteer’s Dilemma. https://www.heretical.com/pound/vdilemma.html A multi-player version of the Chicken Game.

Additional Readings

1. Jim Allen(July 2, 2023). Electro Ecstasy: How Donna Summer’s ‘I Feel Love’ Changed Music. https://www.udiscovermusic.com/stories/donna-summer-i-feel-love-feature/
2. Presh Talwalkar.(2008) How We Naturally Organize. https://mindyourdecisions.com/blog/2008/04/01/focal-points-or-schelling-points-how-we-naturally-organize-in-games-of-coordination/
3. Richard Littauer. (Feb 14, 2017). Using internal Schelling points to plan better. https://medium.com/@richlitt/using-schelling-points-to-perform-better-973243efd989
4. Ron Ashkenas.(July 26, 2011).Why Leaders Play Chicken. https://hbr.org/2011/07/why-leaders-play-chicken
5. Rapoport, A., & Chammah, A. M. (1966). The Game of Chicken. American Behavioral Scientist, 10(3), 10–28. Read here: https://sci-hub.se/https://doi.org/10.1177/000276426601000303
6. Herbert Wulf.(01 March, 2023). Cooperative Security, Arms Control and Disarmament: Chicken-Game. https://toda.org/global-outlook/2023/chicken-game.html
7. https://imotions.com/blog/learning/research-fundamentals/the-stag-hunt-game-theory/
8. An INTJ Professor’s Suicide Note. Sadly. Yes. https://willopines.wordpress.com/2017/04/19/punched-out/
9. Cate Hall.(Jan 11, 2024). How to be More Agentic: On a supposedly difficult thing. https://open.substack.com/pub/usefulfictions/p/how-to-be-more-agentic?utm_campaign=post&utm_medium=web