Archive for October 2009

The Ethicist and the Gamer III: Snakes and Ladders   1 comment

It has been….

Which way will your soul go?

a while since last time and for that I apologize.  I have had several things occur one of which is completely related to our discussion on the rule of reciprocity and gaming.

Number 1: My transmission tanked on my car.

Number 2: I had the flu.

This is not a combination I would recommend for anyone. Yet, I had an opportunity to experience the ethic of reciprocity.  It was with my mechanic. Limping in with my car to a man I had only spoken with a few times before –I cringed as I handed over the keys, while I watched the transmission fluid drip from under the car.  Bill said he would call me. I just sighed.  Still living on a graduate student budget made me fear his future words.

The phone call came.  It was happy news at first.  The gasket was gone on the transmission pan.  But my left CV boot and axle needed replacing, but happily all under $300.00.  I breathed a sigh of relief.

Then the second phone call came.  No, the seals were blown and repairing the seals would cost as much as putting in a rebuilt transmission.  My heart sank.

I said okay, and that I would scrabble the funds together.  It took a week.  Long enough for me to contract and live through the flu.  Horrors.

I went to pick up my car and noticed that he didn’t charge me for the CV boot and left axle.

I asked: “Did you repair them?”

He looked at me shyly and said: “Yeah, but don’t worry about it.”

I paid the bill and walked out.  I came back the next day because of a noise which turned out to be a misplaced sway bar on the axle and the new transmission pan gasket wasn’t working.  He repaired both for free, even paying for a better gasket out of his own pocket.

I asked for a few of his business cards to spread out to friends. Well, it turns out he just had one left.  I smiled and said, I’ll make up a new one for you. Surprised, Bill smiled back.  “Sure”, he said.

One person set up the rules of the game, and I followed. The rule of  reciprocity, or the Golden Rule, or whatever you call it, changed things. You see that’s what we keep forgetting we can set up the rules. We can change the rules of the game.  People lose when we’re working with mismatched game rules.  One person chooses rules of honesty and the other person chooses less than honest rules. The person who is honest inevitably loses with those mismatched rules, or they withdraw from the game ( I will discuss this further in the next installment).

One of the oldest games in existence is Snakes and Ladders.  It originated in India as a morality board game for children.  It is interesting because of the manner in which the game is designed is representative of a Markov chain. A Markov chain, named after Andrey Markov, is a random process where all information about the future is contained in the present state and independent of past states.

Well, what does that mean in real life? A mathematician by the name of Claude Shannon, 1948, came up with a mathematical theory of communication, in fact he and Warren Weaver, published a book by the title in 1963.  Basically the idea goes like this:

1. An informational source produces a message.

2. A transmitter which operates on the message creates a signal to carry the message through a channel.

3. The channel is the medium that the signal is sent, carrying the information that composes the message.

4. A receiver transforms the signal back into the message for delivery.

5. A destination, whether it is a machine, a person receives the message.

So the message depends on the present state which the message is sent (More on this next installment.  I know, I know be patient).

This leads us to something mathematicians and computer programmers call Reinforcement Learning. So, a reinforcement learning mathematical equation for a computer will try to find a “policy” that maps the state of the world to the actions the computer agent should take in that state to maximize reward.

Stay with me a moment here. Let’s go back to Snakes and Ladders. In Snakes and Ladders, the player starts in one state, one given square.  From that one square are fixed odds to moving to another square or other states.  Snakes and Ladders, or it’s current variation Chutes and Ladders, is played on a 10X10 board with die or a spinner.  At the top of the ladder there are usually images of a child doing a good deed and receiving a reward, at the top of the Chutes or the Snake, is an image of a child engaging in bad behavior, and the images on the bottom show the consequences.

To play, you place your token on the “1” square. Then a die is rolled or a spinner is spun and the token is moved along the winding path where you either land at a ladder or a snake/chute.  If you land at the ladder you can move your token up to a higher numbered square. If you land on a higher numbered square of a snake or chute, you must move your token down to the lower numbered square. Interestingly, if the player rolls three 6’s in a roll they must go back to square “1” and wait until they roll another “6”.  The game is won when a token reaches the last square of the track.

In it’s origin the game was created to teach Hindu values.  About obtaining salvation through good deeds, while evil deeds has one reborn into a lower life form.  The number of ladders is less than the number of snakes representing the idea that walking the path of good is difficult compared to the path of sin. Or long term rewards versus short term rewards.

Let’s look at my interaction with Bill my mechanic.  Bill could have tried to cheat me.  He could of took me for the $250.00 then when that didn’t work, I would have to come back and have the transmission replaced anyway.  He would have made more money.  But he took his state, went with the good rule and rolled the die that by helping me out and being honest, I would treat him the same in return. Long term reward.  As it is, I heartily recommend him to anyone, and I will be designing his business cards and I will continue to do business with him.  We both chose the ladders and not the snakes.

Next time: How rules build people and people build rules.

Thank you and have a good state of a week.

Posted October 26, 2009 by prosperospen in Culture, Game Theory, Games, Relationships, Society