The FIA finally introduced a new points system which will result in the driver with most wins crowned world champion.

The interesting aspect of this case from a game theory point of view was how In this class action, U.S. District Judge Lewis Kaplan sought bids from leading law firms on fees they would charge the plaintiffs, looking to tap a qualified firm at the lowest cost to the class. After receiving the bids from about 20 firms, Judge Kaplan appointed Boies, Schiller, which wasn’t involved in the case at the start, as lead counsel in May.” Read this article here.

The anatomy-of-the-rise-and-fall-of-a-pricefixing article illustrates all the events from start to finish in a very compehensive manner.

Following is the description of how the law firm was chosed based on bids from various parties, the following text has been taken from page 515, Microeconomics 7th Ed by Pindyck & Rubinfeld:

Judge Kaplan entertained secret bids from 20 Law Firms. Each firms was told to offer a fee arrangement consisting of a base and a percentage. A settlement or trial award at or below the base would be given entirely to the plaintiffs, with the law firm receiving nothing. If the settlement or award was higher than the base, the law firm would receive the stated percentage of the amount over the base. Many attorneys operate under a contingent fee system in which they offer a base of zero and expect to receive one-third of the award.

The winning bid was the law firm of Boies, Schiller & Flexner, which bid a base of $405 million and a percentage of 25% to be earned on any award above $405 million. Some of the losing bidders were outraged that BSF had bid so high to get the business. Indeed, some suggested that the firm might not work hard in the plaintiff’s interest because the minimum might be unachievable. Prior to the bidding, observers expected the case to generate a settlement of $130 million. In the end, it appears that Judge Kaplan, the plaintiff’s class, and BSF were all winners. Months after taking on the case, BSF settled with defendants for $512 million, earning the attorney’s a $26.75 million fee (25% of excess of base) and generating just over $475 million for the class members.

Vamsi Duvvuri

MBA Class of 2009

Goizueta Business School

On 26 November 2008, FIA boss Bernie Eccelstone told in a news conference (click here to watch the video) that he intends to introduce a new points system in F1 racing to ensure the driver with most wins is crowned the champion. Gold, silver and bronze medals would be given to the top three finishers. The driver with most gold medals won will be crowned, and in case of similar tally, the decision will be made on the bases of count of the next medal in line.The system still requires approval from F1′s governing body, the FIA, Its world council – the body that would decide whether to introduce the system – meets next month.

The current system awards points (10, 8, 6, 5, 4, 3, 2, 1) to the top 8 finishers in a race, and its difficult to see how Bernie would convince the FIA and the minnows in the F1 world to agree on the new system, one which ensures the teams finishing outside the top 3 would remain empty handed. The FIA also awards money for each point earned, and hence how the classification (standings) will decide the prize money will also have to be confirmed.

The points system has been criticised not just this year, but even in 2003, the world title went down to the last race between Ferrari’s Michael Schumacher and McLaren’s Kimi Raikkonen even though the German had won six races to the Finn’s one.

The game plan

Starting with an expectation of a good potential fit, let us see how Tata and Corus have together won out. Visualise a two-dimensional (X-Y) space with Tata’s objective function along the horizontal axis (X) and Corus’s along a vertical axis (Y). The essential requirement for this analysis is that there is an objective function, i.e. a line that measures increasing overall benefit, which can be defined separately for each party along one of these axes. We may surmise that Tata’s primary concern was to pay no more than reasonable compensation for Corus in order to result in a profitable combination, shown as a percentage cut from a notional asking price on the horizontal axis. Corus’s objective function could be the retention of maximum sustainable benefits with employment participation (assuming that the management and union are in sync). This is shown as a percentage on the vertical axis. Mapping Tata’s and Corus’s responses in terms of the percentage cut in price and percentage benefits retained, we get one set of points for Tata and another set for Corus. A line through the first set represents Tata’s response function or strategy, and a line through the other set represents Corus’s response function. For a given cut in price, Tata favours fewer benefits than Corus expects, and for a given benefit level, Corus wants less of a price cut than Tata.

[vduvvur: And hence when the deal was being made, there would've been a negotiation going on between the parties about the mix of price vs. employee benefits. It is similar to the Riverside DEC case we did in SDA where DEC could help Riverside with certain financial incentives to adapt a new technology, and Riverside could choose certain particular forms of help and mix them to ensure they receive max benefits]

The Hamada diagram

The Hamada diagram enables a graphic depiction of game theory, and this analysis is an adaptation.* Tata’s ideal solution, referred to as its “bliss point”, is on its strategy line corresponding to a high price cut. This is where it has its highest economic welfare. Corus’s bliss point [vduvvur: the bliss point could be seen as the BATNA, where each party maximize their payoffs], likewise, is on its strategy line where retained benefits are high. Each party’s economic welfare decreases as it moves away from its bliss point; each party’s indifference curves are therefore concentric around its bliss point. [vduvvur: this indifference curve can be seen as the Pareto frontier, along which lies the maximum value created from the transaction]

# For Tata Steel, as the cost of acquisition reduces moving right along the horizontal axis, Tata can concede more benefits to Corus’s employees.
# For Corus, the management and employees seek a sustainable long-term solution that yields benefits with participation. Despite their premium product line, image, and access to markets for these products, their high-cost structure militates against easy solutions. This realisation impelled Chairman James Leng of Corus to initiate discussions with potential alliance candidates.
# Tata’s and Corus’s responses intersect (coincide) at N, the non-cooperative or Nash equilibrium (Figure 2).

This is the norm for non-zero-sum games when players adopt conflicting, mistrustful strategies, so competitive responses force the solution to a point where neither can benefit by acting unilaterally. Coordinated solutions, however, can make both better-off, i.e. deliver a bigger price cut together with more benefits. This is because efficiency occurs where the respective indifference curves are tangential to each other, whereas they intersect at the point of Nash equilibrium. These tangential points are on the “contract curve” joining the two bliss points. A coordinated solution on this line is efficient, and at the midpoint C, is Pareto optimal (most efficient).

While perfectly logical, that analysis misses the point. New Year’s resolutions help people cope with some of the most difficult conflicts human beings face.

So argues one of the economics profession’s greatest experts on conflict, the Noble Prize Winner Thomas C. Schelling, in the words of the citation, “having enhanced our understanding of conflict and cooperation through game-theory analysis.”

One of his best-known ideas is “precommitment.” One party in a conflict, he demonstrated, can often strengthen its strategic position by cutting off some of its options to make its threats more credible. An army that burns its bridges, making retreat impossible, is a classic military example.

Others involve strong diplomatic commitments. By passing a law saying the United States will defend Taiwan if it is attacked, for example, Congress gives future administrations less flexibility in dealing with a crisis, but the threat makes an attack less likely.

“What I have in mind is an act or decision that a person takes decisively at some particular point in time, about which the person’s preferences differ from what they were earlier, when the prospect was contemplated but the decision was still in the future,” he wrote in “Ethics, Law and the Exercise of Self-Command. If the person could make the final decision about that action at the earlier time, precluding a later change in mind, he would make a different choice from what he knows will be his choice on that later occasion.”

New Year’s resolutions help the earlier self overrule the later one by raising the cost of straying. “More is threatened by failure than just the substance of the resolution: one’s personal constitution is violated, confidence demoralized, and the whole year spoiled. At least one can try to make it so,” wrote Professor Schelling in “The Intimate Contest for Self-Command,” a 1980 essay in his book “Choice and Consequence: Perspectives of an Errant Economist” (Harvard University Press, 1984).

As many a broken resolution demonstrates, those consequences often are not a big enough deterrent. To make success more likely, Professor Schelling’s work suggests a few additional strategies.

One is a mild precommitment: not keeping sweets or tobacco in the house, for instance. At the very least, this step forces you to delay indulgence until you can go to the store – and allows time to recover your resolve.

Another approach is to use bright-line rules, which make it harder to cheat through clever reinterpretation. That may explain why many people find it easier to eliminate whole categories of food, like carbohydrates, rather than simply to cut back on calories.

“Just as it may be easier to ban nuclear weapons from the battlefield in toto than through carefully graduated specifications on their use, zero is a more enforceable limit on cigarettes or chewing gum than some flexible quantitative ration,” Professor Schelling wrote.

Here’s one. The following is an excerpt from the famous article on Newsweek

Just about everyone who has an iPod has wondered how random the iPod shuffle function really is. From the day I loaded up my first Pod, it was as if the little devil liked to play favorites. It had a particular fondness for Steely Dan, whose songs always seemed to pop up two or three times in the first hour of play. Other songs seemed to be exiled to a forgotten corner of the disk drive. Months after I bought “Wild Thing” from the iTunes store, I’m still waiting for my iPod to cue it up.

More specifically, when an iPod does a shuffle, it reorders the songs much the way a Vegas dealer shuffles a deck of cards, then plays them back in the new order. So if you keep listening for the week or so it takes to complete the list, you will hear everything, just once. But people generally listen only to the first few dozen songs. In theory, that sample should be evenly distributed among all the artists and albums in their collections. So why do you typically get three Wilco songs in an hour while Aretha Franklin waits in the wings forever?

I explained this phenomenon to Temple University prof John Allen Paulos, an expert in applying mathematical theory to everyday life. His conclusion: it’s entirely possible that nothing at all is amiss with the shuffle function. It’s quite common for random processes (like coin tosses) to get unlikely results here and there, like runs of six heads in a row. Over a very long time, it evens out, but it’s hard for us to envision that. “We often interpret and impose patterns on random processes,” he says, adding that this might be expected in the case of music, which evokes strong emotions. Paul Kocher, president of Cryptography Research, puts it another way: “Our brains aren’t wired to understand randomness.”

“A pursuit-evasion game is an intuitive notion indicating that one of the players of the game, called the pursuer, is chasing and wants to capture the other, called the evader. It is a game of two players only. Since the gain of one player is the loss of the other, the game is called a zero-sum game,” explains Shinar.

“This notion is well suited to an interception scenario, where the pay-off is the probability of destruction of the ballistic missile,” he adds. The interceptor missile (pursuer) wants to maximize this pay-off and the TBM (evader) wants to minimize it.

Though Shinar’s guidance law was conceived against TBMs (with a range of about 600 to 1,200 miles), there is no theoretical reason why his law could not eventually be applied to longer-range incoming Intercontinental Ballistic Missiles (ICBMs). And while still at the theoretical investigation level, computer simulations of his law have offered “very impressive results.” He says the law, could be easily incorporated into any already developed missile defense system.

Original Source – http://www.scienceagogo.com/news/20000612224419data_trunc_sys.shtml

Mario Monti, the European Union’s competition commissioner, said the cartel could be dubbed Vitamins Inc, and was the most damaging and serious it had ever investigated and had cheated European consumers of billions of pounds since vitamins were used in and affected the price of a whole range of products.

He described how senior executives in 13 companies had cynically collaborated to ensure that consumers paid over the odds for vitamins used on their own and in products such as cereals, biscuits, drinks, pharmaceuticals and cosmetics.

“It is particularly unacceptable that this illegal behavior concerned substances which are vital elements for nutrition and essential for normal growth and maintenance of life,” Mr Monti said.

“The companies’ collusive behavior enabled them to charge higher prices than if the full forces of competition had been at play, damaging consumers and allowing the companies to pocket illicit profits.”

Roche, the Swiss pharmaceuticals company, received particular criticism and was given the biggest fine of all – £288m – while German firm BASF was deemed to be the second worst offender and made to pay a fine of £185m.

When Mr Monti was asked whether the 13 firms were in effect just one big global monopoly which could be dubbed Vitamins Inc, he agreed. Others fined included Aventis (£3m), Solvay (£5.7m) and Merck (£5.7m), together with three Japanese firms which were fined a total of £46m.

The commission described how the companies had operated a highly organised cartel holding regular meetings to collude on prices, exchange sales figures and coordinate price increases.

The cartels were run, Brussels said, “at the most senior levels of the undertakings concerned”.

The commission concluded after its two-year investigation: “The prime mover and main beneficiary of these schemes was Hoffman La Roche, the largest vitamin producer in the world, with some 50% of the overall market.

“The involvement of some of its most senior executives tends to confirm that the arrangements were part of a strategic plan conceived at the highest levels to control the world market in vitamins by illegal means.”

The investigation was helped by one of the offenders – French company Aventis – which agreed to “defect” and furnished the commission with what Mr Monti called “decisive information”. As a reward, Aventis was fined just £3m instead of a figure nearer to £70m.

A similar story enlightens us with another price fixing by European Glass makers. And here.

Original Article Source

Vamsi Krishna Duvvuri

MBA Class of 2009

Goizueta Business School

Well, after reading this article, I’ve realised that it’s not that simple. There is a game that goes on between different producers, studios and media. There is a sense of “sensibleness” among the various media houses and a continual game of who blinks first, or who’s the chicken is played between them.

The unspoken pact is that no two similar movies should get released on one date, because otherwise the profits are split between the two, and both ending up with little to cheer about. And hence there is always a race to pick a release date for one’s movie and ensure no one else is releasing a similar movie, on the same day.

E.g December 2002 featured one of the most dramatic games of chicken in recent memory, when two films starring Leonardo DiCaprio were both slated to open on Christmas weekend. Ultimately, Miramax blinked first, moving the release of Martin Scorsese’s ”Gangs of New York” five days earlier and ceding the holiday to the other DiCaprio film, DreamWorks’ ”Catch Me if You Can.” ”We didn’t think about moving,” says Terry Press, the head of marketing for DreamWorks. ”We had been there first, and ‘Catch Me if You Can’ was perfect for that date.” This year, DreamWorks chose to schedule a somber psychological drama, ”House of Sand and Fog,” for the day after Christmas, deferring a bit to Miramax. ”I don’t want our reviews to run on the same day as ‘Cold Mountain,”’ Press says.

And sometimes when studios do have to move a film’s release, the size does matter. Bigger the star-cast, the budget and marketing matter, more effort is required to move the release dates. However, the party to move its date (or the chicken) doesn’t always loses, on occasions, a studio may see that test audiences are going berserk for a film and move it into a more competitive time period. Universal initially had only modest expectations for the 1999 teenage sex comedy ”American Pie,” but when the test screenings did so well, it pushed the film from the spring — historically something of a dumping ground — into the summer, where it became a smash hit and established a franchise. ”We did the same thing with ‘The Fast and the Furious,”’ says Nikki Rocco, Universal’s head of distribution.

Of course you don’t want to just keep playing with the release dates, which might irk the audience and media, and they could end up dumping the movie altogether. And sometimes when a movie release schedule is postponed to give space to a bigger more obvious hit, the producers of the movie whose schedule has been changed wish that the bigger movie gets a great start and that more and more people flock in the first weeks to watch it, because the people watch it in the first few weeks, the lesser will watch it later, when the postponed movie is released.

But at the end, it all comes down to this – ” ”There is never a bad time to release a good film — and there is never a good time to release a bad film.”

Vamsi Krishna Duvvuri

MBA Class of 2009

Goizueta Business School

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

Vamsi Krishna Duvvuri

MBA Class of 2009

Goizueta Business School