Game Theory, Game of Chicken and Traffic Rules

In game of chicken, two cars are coming in opposite direction on a very narrow road. One car can pass only if driver of other car swerves, if one who swerves faces humiliation of being called “Chicken”, so both drivers will not swerve and will keep driving straight expecting that other driver will swerve. This often results in accidents.

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To prevent this France has a rule called as La priorite a droite (priority to right). France has rule of right hand traffic, so if two cars are coming from opposite direction at intersection, then onus is on the car on the left to slow down and allow car coming from right to pass. In event of accident, the car from left is blamed.

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I doubt if similar laws will work in India. Since we have left hand traffic in India and if similar rule were to be implemented it will be – priority to left. Indians are known for breaking traffic rules, so chances of such rule being followed are nil.

 

 

 

Thomas Schelling, Focal Point and Grand Station

Thomas Schelling is an American Economist, who was awarded the 2005 Nobel Memorial Prize in Economic Sciences, which he shared with Robert Aumann.

“He is a producer of game theory and I am a user of game theory, … I use game theory to help myself understand conflict situations and opportunities.”

-Thomas Schelling, Nobel Prize winner in Economics

Thomas Schelling wrote book “The Strategy of Conflict” in 1960, in which he introduced concept of focal point.

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To explain the concept, Schelling used to give interesting example. Suppose you are asked to meet a stranger in New York tomorrow, where and when will you meet him? You not only don’t know this person, but you also cannot communicate with him. In most of the cases answer was 12 noon, near clock at Grand Station.

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There is nothing special about Grand Station. From Game Theory point of view any place in city is Nash equilibrium i.e. be it bar, restaurant, café etc., Grand Station is also one of the them and it does not offer any higher payoff. But our mind focuses more prominently on certain places or things and hence we prefer it over others. These are generally the places about which we have knowledge and are familiar with. Schelling called it as focal point. It is called as Schelling point.

He gives one more example in his book. A map is given to two paratroopers and both have to land on same spot, both cannot communicate with each other. In theory any point in map has same probability, but most of the participants opted for a bridge on river (there is only one bridge shown in map) instead of roads, houses etc.

Had we asked Mumbaikar where he would meet stranger, my guess is it will be at noon, below indicator at bridge joining Central and Western railways at Dadar Station.

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Forensic Anthropology and Story of Two Anthropologists- Dr. Clyde Snow & Dr. Josef Mengele

“Bones make good witnesses. Although they speak softly, they never lie and they never forget”

-Dr.Clyde Snow

Josef Mengele  was physician in German army during Second World War. Mengele received doctorates in anthropology and medicine from Munich University.

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When Mengele was posted at Auschwitz concentration camp, he used it as an opportunity to continue his anthropological studies and research on heredity using Jewish prisoners for his experiments.

One of the objectives of experiments was to prove supremacy of heredity over environment and to prove superiority of Aryan race. The experiments had no regard for the health or safety of the victims. Many died during these experiments. To study heredity he performed lot of experiments of twins.

Experiments performed by Mengele on twins included unnecessary amputation of limbs, intentionally infecting one twin with typhus or other diseases, and transfusing the blood of one twin into the other, sewing twins together back to back, injecting chemicals into eyes of subjects etc. after an experiment was over, the twins were sometimes killed and their bodies dissected.

Post war, Josef was declared war criminal, but he managed to escape to Argentina with the help of Nazi sympathisers. Israeli and German authorities were unable to have him arrested. With help of money send by his wife and son from Germany he managed to lead a comfortable life in South America.

Sometime in 1985 after receiving tip from German police, a skeleton was dug from cemetery in Sao Paulo and Brazilian police claimed that it was of Josef. But records showed that man buried in 1979 was Wolfgang Gerhard.

Was Wolfgand Gerhard actually Josef Mengele? Was name change just to avoid identification?

A team of experts was send to Brazil from US, consisting of Dr. Snow. Clyde Snow was a well-known U.S. forensic anthropologist, who obtained Ph.D. in Anthropology from Arizona University.

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“There are 206 bones and 32 teeth in the human body…and each has a story to tell.”

-Dr.Clyde Snow

Dr. Snow studied the skull, bones, teeth, hair etc. He then did skull photo super imposition and finally reached conclusion that skull belonged to Josef Mengele. Dr. Snow and his team conducted exhaustive studies consisting of matching hair samples; study of bones, study of teeth based on dental records etc. and confirmed that skeleton was of Josef.

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Later in 1992 Professor Jeffreys used reverse paternity testing: he used blood specimens from Mengele’s wife and son to reconstitute Mengele’s DNA pattern. The remains were confirmed to be those of Mengele.

Mengele’s health had been steadily deteriorating since 1972, and he had a stroke in 1976. He had high blood pressure and an ear infection that had an impact on his balance. In 1979 he suffered another stroke while swimming and drowned.

Mengele was buried in Embu das Artes cemetery at Sao Paluo under the name “Wolfgang Gerhard”, whose identification card he had been using since 1971.

 

FTII, Tit for Tat and Grim Trigger Strategy

Film and Television Institute of India ( FTII) is in news for wrong reasons. Students who joined in 2008 and who should have got diploma by 2011 are still yet to complete diploma, while batch which joined in 2009 has already completed diploma. These students are still staying in FTII’s hostel putting pressure on inadequate infrastructure of the institute. Reasons for delay according to students are many -incompetent faculty, change in syllabus, lack of infrastructure and “swine flu” etc.

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Students of 2008 batch have assumed leadership in ongoing strike, while reason for strike is appointment of Gajendra Chauhan as director of institute,  it does not address  the deeper issues- lack of infrastructure, lack of discipline in students, lack of quality faculty etc. Whether Chauhan is capable of resolving issue is different story, what is worrying is falling standards of this premier institute.

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Two players director and students instead of resolving the issue are more interested in playing games. First students went on strike and  then current director Prashant Patharbe was “gheroed” by students when he decided to do assessment of 2008 batch, resulting in police entering campus and arresting 5 students. So far game strategy is tit for tat, if students defect, the director also defects to ensure that students cooperate. But if situation does not improve i.e. students refuse to cooperate, then director will be forced to use what is called as grim trigger strategy, resulting in series of actions/punishments that will continue till students cooperate.

Hope good sense will prevail and game will end at tit for tat stage itself and not get into grim trigger strategy.

 

Nehru, Patel and Princely States

“As you are all aware, on the lapse of Paramountcy every Indian State became a separate independent entity and our first task of consolidating about 550 States was on the basis of accession to the Indian Dominion on three subjects. Barring Hyderabad and Junagadh all the states which are contiguous to India acceded to Indian Dominion. Subsequently, Kashmir also came in…”

-Vallabhbhai Patel in 1948

India became independent on 15th August 1947; India then consisted of areas directly ruled by British, Princely States and some territories ruled by other European powers like French and Portuguese.

Post-independence and partition of India, question remained as to what happens to princely states and European colonies. Then home minister of India Sardar Patel and his secretary V.P. Menon were given task of integrating princely states with India. Many states like Travancore, Hyderabad, Kashmir and Bhopal wanted to remain independent, some like Junagarh wanted to join Pakistan etc.

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Vallabhbhai Patel and V.P Menon did wonderful job of integrating more than 500 states with India using diplomacy and at times force. They did not hesitate to use force when required ex. in case of Kashmir and Hyderabad.

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Recently a trend has emerged to criticise Nehru for not allowing Patel to handle Kashmir and his inability to handle Kashmir issue himself. They even accuse Nehru of sacrificing national interest for sake of international image. Their arguments are not correct.

Congress was clear in its policy towards princely states, any movement against ruler should come from local subjects, Congress may use diplomacy or force, but willingness of local people to integrate with India was vital and this helped in plebiscite, when locals voted for India.

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Policy used by Nehru in case of Kashmir was no different. While some parts of Kashmir like Gilgit, Baltistan and Azad Kashmir went to Pakistan, Kashmir Valley under Sheikh Abdullah, Jammu and Ladakh became part of India. Next step was UN monitored plebiscite to decide future of entire Kashmir, while India was ready for it, Pakistan refused. Asking for UN monitored plebiscite shows confidence of Nehru in locals of J & K. Ironically after six decades Pakistan now reminds India of plebiscite.

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When it came to annexation of Goa in 1961, his methods were not different from those of Sardar Patel (Patel died in 1950). At no stage was he an impractical idealist as he is portrayed. Local population of Goa was against Portuguese rule and wanted to integrate with India. When diplomatic talks failed, Nehru did not hesitate to use armed forces to annex Goa, though most of the western countries were supporting Portugal. Nehru did not care about international image when it came to national interest.

“With his invasion of Goa Prime Minister Nehru has done irreparable damage to India’s good name and to the principles of international morality.”

-New York Times 19th December 1961

“You spend the last fifteen years preaching morality to us, and then you go ahead and act the way any normal country would behave… People are saying, the preacher has been caught coming out of the brothel.”

-President Kennedy on annexation of Goa

Most interesting was reaction of Pakistan, who wanted UN monitored plebiscite in Goa, while they themselves refused to participate in UN monitored plebiscite in Kashmir.

“The forcible taking of Goa by India has demonstrated what we in Pakistan have never had any illusions about—that India would not hesitate to attack if it were in her interest to do so and if she felt that the other side was too weak to resist.”

– Pakistani President General Ayub Khan

Policy of India remained unchanged even in 1975 during prime ministership of Indira Gandhi, when people of Sikkim wanted to get rid of monarchy and integrate with India. Indian army disarmed guards of Chogyal (hereditary ruler of Sikkim) and plebiscite was held wherein in 97% of people voted in favour of joining India.

 

Game Theory, Cooperation and Shapley Value

The only thing that will redeem mankind is cooperation.”

– Bertrand Russell

Lloyd Shapley is an American economist. He has made significant contribution to fields of mathematical economics, especially game theory. In 2012 he won Nobel Prize in Economics (which he shared with Alvin Roth.)

In game theory, a cooperative game is a game where groups of players or coalitions behave in cooperative manner while choosing strategy ex. they may work on project which is mutually beneficial to them and workout strategy to fairly distribute both gains and cost among themselves.

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Distribution of gains or cost is easy if contribution of all players is equal. But if it is unequal then some other method is required. Shapley has made significant contribution in this area of game theory. The Shapley value applies primarily in situations when the contributions of each actor are unequal. The Shapley value ensures each actor ends up spending less, than they would have if they had acted independently. This is important, because otherwise there is no incentive for actors to collaborate.

“Competition has been shown to be useful up to a certain point and no further, but cooperation, which is the thing we must strive for today, begins where competition leaves off.”

– Franklin D. Roosevelt

A famous example of the Shapley value in practice is the airport runway problem.

In the problem, an airport needs to be built airstrip to accommodate a range of aircraft which require different lengths of runway. Cost of building each runway is different. The question is how to distribute the costs of the airport among all actors in an fair manner.

The solution is given below, which calculates the Shapley value.

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If players do not cooperate then they will have to build runway on their own ( cost will vary from 4 units to 16 units), but if they cooperate then they have to build only one strip that will cost them 16 units, now question is how do they share the cost among themselves.

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First player A’s (4 units, also least cost) cost is equally shared among all players. Next marginal cost of player B is equally shared among 3 players, then marginal cost of player C is shared among 2 players and finally player D bears the remaining marginal cost. Adding marginal costs (row wise) will tell how much each player will have to pay (which is the Shapley value).

In the end, actors requiring a shorter runway pay less, and those needing a longer runway pay more.

We find that Shapley value for each player is not only fair, but also less than what they would have spent individually if they had not cooperated.

How to play games- Psychology vs. Economics

“Knowledge of game theory does not make one a better card player, businessman or military strategist.”

-Anatol Rapoport

Let us assume that there are two players- Schlemiel and Schlimazel. Schlimazel invites Schlemiel for party in his house. Schlemiel does all sorts of things that will irritate Schlimazel like spills wine on hostess’s dress, break things, spoils curtains and rugs with food etc. Every time he commits blunder he apologizes to Schlimazel. Schlimazel is sure that Schlemiel is doing it on purpose.

'Hey! You look fabulous with your dress clinging to you like that!'

What should Schlimazel do?

Economics and Psychology offer different solutions.

Anatol Rapoport was a Russian-born American mathematical psychologist who came up with game of tit for tat. Game is similar to that of prisoner’s dilemma, where each player will follow a course of action which is consistent with his opponent’s previous turn. For example, if provoked, a player will subsequently respond with retaliation, but if not provoked, the player will subsequently cooperate.

Tit-for-tat strategies are based on the concepts of retaliation and altruism. When faced with a prisoner’s dilemma-like scenario, an individual will cooperate when the other member has an immediate history of cooperating and will default when the counterparty previously defaulted.

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So Schlimazel’s next move should be similar to Schlemiel’s earlier move. If he misbehaves, then Schlimazel too behaves similarly at Schlemiel’s house. He can repeat this game till Schlemiel changes his behaviour.

“A schlemiel is one who always spills his soup, a schlimazel is the one on whom it always lands.”

-Anon

Psychology offers a different solution on how to end this game. Eric Berne, a renowned psychologist has written book called “Games people play”.

He calls the game as “Schlemiel”. In this game Schlemiel is a cunning fellow while his victim Schlimazel is simple, good natured fellow. He forgives Schlemiel each time he commits blunder. Schlemiel takes advantage of Schlimazel’s self-control and enjoys game of damaging his property. Schlimazel on the other hand suppresses his anger to keep friendship intact.

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Eric suggests an interesting solution to this game. Actually Schlemiel is more interesting in obtaining forgiveness for his misbehaviour than destroying property. Schlimazel can end game like this. When Schlemiel first apologizes, instead of forgiving by saying “It’s OK” he should say, “ Tonight you can embarrass my wife, ruin the furniture and wreck the rug, but please don’t say I’m sorry.'” Here he switches from being a forgiving Parent to being an objective Adult who takes the full responsibility for having invited Schlemiel in the first place.

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Child in Schlemiel will keep saying, “You have to forgive things which appear accidental.”, and would want game to continue, but Parent in Schlimazel can end this game by saying, “You are right. But I have to show you what good manners are.”