Prisoner’s Dilemma explained Eric Cartman’s way

Now, before I get started here, I hope everybody knows Eric Cartman, and may be, some of you might have seen this Southpark episode. In reality, it might not be the most apt way of explaning prisoner’s dilemma, but it sure is a fun way of knowing more about it.

So, what am I talking about? Lets see, first let us define PD: A situation where two or more players are involved in a deal (or a understanding of co-operation), each player has an incentive to defect (or betray his or her partner(s)) after which the other players may select a move which would then result in competition between those players.

The classic example through which PD is explained most easily is as follows:

Two suspects are arrested by the police. The police have insufficient evidence for a conviction, and, having separated both prisoners, visit each of them to offer the same deal. If one testifies (”defects”) for the prosecution against the other and the other remains silent, the betrayer goes free and the silent accomplice receives the full 10-year sentence. If both remain silent, both prisoners are sentenced to only six months in jail for a minor charge. If each betrays the other, each receives a five-year sentence. Each prisoner must choose to betray the other or to remain silent. Each one is assured that the other would not know about the betrayal before the end of the investigation.

In Southpark’s episode 99 (S7E3), the gang is punished by their art teacher for messing around in the art class, and so the kids plan to get back at the teacher by TPing her house. After “decorating” the house that night, Kyle has nightmares about the incident, the art teacher’s house and her crying children, and he can’t sleep anymore.

TP-ed house

Cartman, as the genius he is, comes up with a “perfect alibi”: Last night, all four of us were at the bowling alley until about 7:30, at which time we noticed Ally Sheedy, the Goth chick from The Breakfast Club, was bowling in the lane next to us, and we asked her for her autograph, but she didn’t have a pen, so we followed her out to her car, but on the way we were accosted by five scientologists who wanted to give us all personality tests, which were administered at the Scientology Center in Denver until 10:45, at which time we accidentally boarded the wrong bus home and ended up in Rancho de Fritos Rojos, south of Castle Rock, and finally got a ride home with a man who was missing his left index finger, named Gary Bushwell, arriving home at 11:46.” However, when the counseler calls each of them to the room individually (to see if one or more could mix the story and ride out the others for a better deal), they get nervous and try to tell the exact same story. It seems at the end of that meeting, they manage to stick to story.

Cartman telling the alibi story (Click to listen to the story)

Kyle’s guilt gets better of him, but Cartman senses the situation and plans to kill Kyle. However, since Stan and Kenny refuse to help him, he takes Kyle in a boat-ride to Stark’s pond and tries to kill him by hitting him with a wifflebat, and fails to do so, obviously. So, Kyle, Stan and Kenny go to Officer Barbrady, who has arrested Butters as the prime suspect, for the confession. However, after seeing butters in Jail, Cartman tries to ensure the confession from his friends is never deliver. Stan requests Cartman to confess as well, but Cartman refuses to do so…

The next day  Stan, Kyle and Kenny rush into the Principal’s office, only to find out that Cartman confessed earlier in a bid to secure a better deal for himself. Each of the boys ends up with two weeks’ detention, except for Cartman, who gets only one for “being brave”.

Another example - Dilbert’s Dilemma

Games vs Sports

I’ve always been wondering what is the difference between games and sports, and after several discussion, arguments and a class in strategic decision analysis later I have the answer. So here it is…

The difference between a game and a sport is that in sports there is not interaction between the players, and hence, because of this lack of interaction, one player cannot affect other player’s strategy by the way he or she plays the game. A game is played between two or more players, when they’re consciously (or sub-consciously) aware of the other player’s presence, and when the opponent’s strategies change the way they themselves approach the game.

To make the distinction clear, lets talk about some examples:

Soccer:Game

Why? Because the opponent team’s actions (or passes, kicks and movement) affect the way my team’s going to approach the game.

Chess:Game

Do I really need to explain why chess is a game? I don’t think so.

Swimming:Sport

Now this is interesting. Now matter how the other swimmers swim/float, my game-winning strategy is to swim as fast as you can. And in the most basic of setting, I’m going to win 99% of times I swim faster than others (and of course not using PEDs).

Athletics:Sport

Same as the above unless we’re talking about a marathon or a long distance race where opponents can change lanes and everyone’s looking for the shortest route.

Mental Disintegration & Gamesmanship - My take

For starters, mental integration is a term made famous by Allan Border and Steve Waugh, the Australian cricket captain. Steve use this term to explain what is simple gamesmanship. It comes in various forms, its not invented by the Aussies, however, they’re self-proclaimed practitioners and, now after the India-Australia battles of the recent past, we know that Aussies don’t like it when its dished out at them.

Prime example, look at any team that visits Australia for a series, the media starts digging into the main player’s past and call them such absurd and humiliating names that visitors focus more in defending themselves rather than concentrating on the game. So, Australia already have an upper hand in the contest without even stepping onto the pitch.

Sledging, another form of mental disintegration (adopted by many of the top cricketing nations). Players around the batsman keep talking to the him and poke him with sometime innocuous, sometime venomous banter and try to push him to a limit where he’s defending the arguments and not the deliveries. Here are some examples:

A cricket tour in Australia would be the most delightful period in one’s life, if one was deaf.
-Harold Larwood

Merv is a funny guy, though he would sledge his own mother if he thought it would help the cause.
-Gladstone Small

Ian Botham had just taken guard in the Ashes match when Iron Gloves (Rod Marsh) greeted him saying: “So how’s your wife and my kids?”

This article talks about the history of mental integration, and it enlightens us about the fact that teams use this technique to further demoralise opponents and take the game away from the classic definition “a gentleman’s game”. But Aussies are responsible not only for MI, but also for some of the most infamous incidents, that they can’t be trusted with the spirit of sportsmanship and they’ve proven time and again that they’re sour losers.

Example 1 - Australians love to win, even if it requires winning ugly. This is the prime example.

This incident is listed on 8th position in the top 10 sporting cheats ever. That’s a disgrace in a game that is revered by millions and millions of fans for its sportsman’s spirit.

Example 2 - One of the most controversial test matches of all time. Indians got the short end of the stick, and turned out to be one of the most tense cricket series of our times. The issue was not that umpiring decisions went one way and not the other, it was the way the game was conducted. Australian captain Ricky Ponting was questioned for his integrity when in the first incident he told an umpire that a batsman was out, but then in another incident, he appealed when in fact the ball he himself caught was clearly grounded. The match contained many ugly spat between the players and the captains, and it turned out to be one of the worst examples of how to conduct on the field in a cricket match.

F1 Points System - The True Story

So, how does one select a winner? If you’re a formula 1 fan, you think the guy who wins most races in a season wins it. Well, not quite so.

F1 racing works on a controversial points system which seems to be biased on making the sport more competitive, more interesting and hence more appealing to the viewers and fans. Now, don’t get me wrong, I’m not saying making a sport more competitive is bad. In fact as a viewer its great. You’re making races closer than ever, the balance of championship goes till the last race and its good for the sport (with more sponsers, ticket sales, etc).

However, I think the new system is not as fair as it should be. Because the drivers in the second and third places are not too far away from the race winner in terms of points, its not necessary that the guy who won the most number of races in an year would win the title, as the 2008 season showed us.

So, here are the facts. I took the standings from all of the 18 races, recorded the standings of the first 8 drivers and teams (for constructor’s standings), and calculated the final points tally with the old and the new system. So first, here is the results table (click on the image to view the spreadsheet on Google docs):

2008 Race Results

So, here is the calculation of points based on the current points system (click on the image to view the spreadsheet on Google docs):

2008 Standings - Current Points System

As you can see, Hamilton won this championship by one point. But here is the problem, Hamilton has won less number of races that Massa in 2008. The points difference is 10, which he made up by finishing higher in other places more number of times. Now, I’m not saying the FIA conceived a devious plan at the end of 2002 to ensure Hamilton wins the 2008 season and becomes “the first black driver to win a championship in Formula One” (wikipedia, not me) and the youngest ever champion.

How does the points tally look if we use the system in existence prior to 2003, here it is:

2008 Standings - Old Points System Prior to 2002

As you can see, Massa wins this one by three points. Now, how does the points tally looks if we use an older system which was in existance during 1985-1990. Here is it:

2008 Old Points 1985-1990

So, what do intend to prove? Not that Hamilton is not a deserved winner, not that F1 is unfair. I conclude that no system is perfect, and FIA instated this system to ensure the sport is more competitive but not not not perfect.

Application Portfolio - What is it?

So, the SDA class that I took with so much of excitement has been a wonderful experience. It makes you think about the situations when we make decisions, and we think we’ve made an “informed decision”, when in fact we didn’t even think about 1/10th of the options, choices, results and pay-offs.

The class is highly interactive where we’ve made to think on our feet, but dig deep into the problem; look at every angle and make as informed a decision, as we can. The application portfolio is a collection of real-life (or even fiction from movies and television) events that have game theory, prisoner’s dilemma, or other concepts of SDA involved in it. So the next few posts will be dedicated to my application portfolio.