Game Theory, Cheap Talk and Bragging

 “To brag the right way is to talk about yourself (interests, ideas and accomplishments) in a conversational story-like manner with pride, enthusiasm and passion. Telling a short story―or what I call a “bragologue”―is far more compelling and interesting than rattling off your accomplishments in laundry-list fashion.”

-Peggy Klaus, Forbes Magazine

Asymmetric information market is a situation in which one party in a transaction has more or superior information compared to another. One way to bring about symmetry is to send signals ex. qualifications from premier university is a strong signal to employer about your qualifications. Signalling has lot of applications in game theory.

cheap

Signalling is expansive as person incurs cost of training. Cheap talk is opposite of signalling. In game theory, cheap talk is communication between players which does not directly affect the payoffs of the game and does not cost anything. This is in contrast to signalling in which sending certain messages may be costly for the sender depending on situation. While signalling has its own advantages, yet most information sharing is done through ordinary, informal talk.

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One way to benefit from cheap talk is to indulge in bragging. Leadership Coach Peggy Klaus gives lot of importance to bragging in your career growth. She differentiates bragging in crude way from bragging in polished way. Polished bragging is must from your own growth. Example given below shows the difference.

Bad bragging: “I’m a great sales manager because I am good with people. At the end of the month, I always get the top numbers.”

Good bragging: “You know when I was first hired as a sales manager; I never knew what a great fit it would be for my skills and personality. The job brings together my organizational skills, an ability to bring out the best in people through coaching and mentoring, and years of hands-on industry experience, which helps me really understand what my team is going through.”

brag

In today’s corporate world responsibility of selling yourself lies with you, you cannot expect your boss or peers to do selling for you, as it may not be on top of their priority list.

“I think it’s really important for everyone to credit the people that they work with (boss, colleagues, direct reports) but you have to weave in what you are responsible for—what you have done, what your job is—because if you don’t, no one knows what you have done.”

-Peggy Klaus, Author of “Brag”

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Game Theory, Braess’s Paradox and Hotelling’s Law

“Whether one street is preferable to another depends not only on the quality of the road, but also on the density of the flow. If every driver takes the path that looks most favorable to him, the resultant running times need not be minimal.”

–  Dietrich Braess, German mathematician

Two mathematicans Horald Hotelling and Dietrich Braess have made significant contribution to Game theory.

Dietrich Braess came with concept of Braess’s Paradox, which is useful in traffic management. Sometimes building a flyover or bypass road may not result in less travel time, infact if traveller uses flyover or bypass road it may take more time than travelling by normal road.

Following example will explain Braess’s paradox.

braess paradox

Suppose T is the number of drivers and 5000 drivers want to travel from start point to end point. One route is Start-> A-> End, other route is Start-> B-> End. Let us assume that drivers give equal preference to both the routes so 2500 divers will take first route and equal number will take second route.

In first case travel time is equal to 2500/100+45 = 70 minutes, in second case travel time is equal to 45+ 2500/100 = 70 minutes. Now suppose due to political pressure, municipality constructs a flyover from A to B and travel time between A to B is not even a minute, let us take it as 0 minute.

bandra flyover

Now all drivers ( in game theory players think rationally) decide to travel from start to A, A to B and B to End, to take advantage of flyover. But now travel time is 5000/100+ 5000/100 = 100 minutes. In other words if all drivers think rationally they will end up taking more time. This is Braess’s paradox, without flyover, drivers were taking less time; with flyover (constructed to reduce travel time) it takes more time.

So constructing a flyover or bypass road may not always be answer to traffic congestion.

42nd_Street_in_New_York

On Earth Day, New York City’s Transportation Commissioner decided to close 42d Street, which as every New Yorker knows is always congested. “Many predicted it would be doomsday,” said the Commissioner, Lucius J. Riccio. “You didn’t need to be a rocket scientist or have a sophisticated computer queuing model to see that this could have been a major problem.” …But to everyone’s surprise, Earth Day generated no historic traffic jam. Traffic flow actually improved when 42d Street was closed

–   New York Times, 25th December 1990

Have you ever wondered why, if there are two medicine shops on street, they are always in the middle of street and next to each other and not at the ends of street?

This is explained by  Horald Hotelling’s Law.Take example of two ice cream sellers on beach ( assuming both sell same quality  of ice cream). Assume one starts at the south end of the beach and one starts at the north. Again assuming a rational consumer and equal distribution along the beach, each cart will get 50% of the customers, divided along an invisible line equidistant from the carts. But, each cart owner will be tempted to push his cart slightly towards the other, in order to move the invisible line so that it encompasses more than 50% of the beach. Eventually, the ice cream sellers end up next to each other in the centre of the beach.

0198606737_hotelling-model_1

 

What if they put their ice cream carts at two ends of beach? Theoretically each would still draw half of the customers (the northern or southern half) and the customers would enjoy a shorter travel distance. However, neither would be willing to do this independently, as it would then allow the other seller to relocate and capture more than half the market i.e. 50% of his side, plus say 25% of other’s market i.e. one in middle will have 75% market and one at end will have only 25% of market.

 

 

 

 

 

Game Theory, Market for Lemons and Management Institutes

“George Akerlof’s Nobel prize is richly deserved. He and his co-laureates led a revolution in our understanding of how markets behave when different participants have different information about the qualities of commodities being traded. He showed that in the absence of adequate mechanisms to assure quality and verify and enforce contract provisions regarding quality, markets may fail to form or may do a poor job of allocating resources.”

-Daniel McFadden, Noble Prize winner in field of economics.

 

I did post graduation course in management from Nagpur University, though it was not at par with MBA course of premier institutes, it was adequate to get job. Course structure was simple, consisting of 5 basic courses in 1st year and 4 elective papers in 2nd year.

Our class consisted of mix of talented and average students. But since this course was not highly rated by industry, companies were not interested in visiting campus and there was nothing great about pay package. While average students did not complain, talented students felt that they were underpaid because of reputation of management course.

management grads

This happened because of what is called as asymmetric information i.e. student knows what he is capable of, but the marker (buyer) has no knowledge about student’s talent or quality of his education.

Economist George Akerlof did lot of research in area of asymmetric information and won Nobel Prize in 2001. He gives example of used car market to explain concept of asymmetric information.

cars

A used car market is mix of cars which are of poor quality (lemons) and cars which are in good condition (plums).  For average buyer it is difficult to know the quality of car he is buying (assuming they are not expert in automobile engineering) so on safer side he will always offer average price (average of bargain and premier price). Result is lemon car owner gets higher than his expectations while plum car owner gets lower than his expectations, so he stops selling his car in used car market, this further brings down the average price, resulting in more and more owners of good quality cars quitting the market, this keeps happening till market is left with only lemon cars.

used cars

Let us take an example, suppose lemon car costs Rs.1, 00,000 and plum car Rs.3, 00,000. Since buyer cannot differentiate due to lack of information, he will play safe by offering  average price i.e. 1,00,000+3,00,000/2 i.e. 2,00,000 lakhs. While lemon car owner ends up getting nice profit of 100%, the plum car owner quits market as he will make loss if sells, while buyer feels cheated and loses faith in market. If plum car owners start quitting market, soon market will be left with lemon cars with no buyers.

This theory has lot of applications in various industries esp. banking and insurance industry.

Solution to overcome this problem is to spread more information (reduce asymmetry) and establish agencies who can rate the quality of products being sold, so that buyer and seller benefit.

student loans

Coming back to example of management course, there is need to have a reliable agency which will rate the management institutes, so that student after spending 2 years studying with liability of student loan does not end up with pathetic job.

 

 

 

 

 

 

Lotka–Volterra equation, Paradox of enrichment and Communism

“Under capitalism, man exploits man. Under communism, it’s just the opposite.”

– John Kenneth Galbraith, American Economist.

Two mathematicians Alfred Lotka and Vito Volterra applied mathematics to biology esp. study of population giving rise to what is known as Lotka-Volterra equation.

This equation is very useful to study population of prey and predator ex. if density of prey ex. hare is x and density of predator ex. lynx is y, then equation giving their relationship is

Growth of prey over period time t is dx/dt= ax+bxy, while that of predator will be dy/dt= cxy-dy.

We will not go into details (plenty of information is available on web); application of these equations helps us to understand what is known as paradox of enrichment.

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Suppose population of hare goes up, this will result in plenty of food for lynx, as a result it will increase the number of lynxes, but this situation i.e. plenty of hare and lynxes does not last for long. Hunting by lynxes brings down population of hare, resulting in shortage of food and ultimately resulting in deaths of lynxes due to starvation.  Reduction of number of lynxes again increases population of hare, resulting in increase in population of lynxes and so on. This cycle has been going on for centuries i.e. decline and growth of prey and predators is cyclic and correlated.

lynx hare

One more application of this is paradox of insecticide. To kill pest a farmer sprays insecticide, the insecticide due to rains reaches soil and water table killing natural predators of these pests. Over a period of times pest develop resistance to pesticide and by then all its natural predators are eliminated, so population of pests grows more than before.

insecticide

In economy you have cycles of boom and recession. Communists believed that they could do away with such cycles through planned economy; unfortunately it was a very costly experiment which ultimately resulted in downfall of most of the communist regimes in the world.

communism

Game Theory, Median Voter Theorem and Kejriwal

“The story of Detroit’s bankruptcy was simple enough: Allow capitalism to grow the city, campaign against income inequality, tax the job creators until they flee, increase government spending in order to boost employment, promise generous pension plans to keep people voting for failure. Rinse, wash and repeat.”

-Ben Shapiro

If we were to measure height of Indian males and plot it on a graph, we will find few are 5’ tall or 6’ tall, majority will fall in between of 5’4” and 5’6” i.e. we get a normal curve ( bell shaped) due to normal distribution, similarly in case of politics few voter subscribe to extreme right ideology or extreme left ideology, most of them are centrist i.e. those opposing political changes which would result in a significant shift of society either strongly to the left or the right. You also have combinations like left of centre (Congress Party) and right of centre (BJP).

This concept can be summed up by Median Voter Theorem, which states that “a majority rule voting system will select the outcome most preferred by the median voter.”

voter

So winning of elections depends on how close your manifesto is to aspirations of median voter i.e. centrist. This forces all parties to include aspirations of median voters in their manifesto. Result is manifestos of all political parties look same.

voter

Any radical change is likely to alienate the median voter and thereby reducing chances of winning elections. Many fiscal reforms like reduction in subsidies, defence expenditure, reduction of staff in public sector, privatization of railways are not favoured by median voter, hence no party is keen to include this in their agenda.

kejriwal

Delhi elections are good example of how median voter theorem works. Voters wanted free electricity, free water, free Wi Fi, all illegal occupation of land by slum dwellers by legalised, women safety, reduction in corruption etc. Manifesto of AAP matched with expectations of median voter, while BJP was working on agenda which was of no interest to median voter, resulting in landslide victory for AAP. Kejriwal played the game quite well and won.

Queue, Buyer’s Mindset and Goldman Sachs

“Goldman didn’t like the idea of its people waiting on long lines to get their lunch. People are capital to Goldman. It wants to use its capital efficiently. Standing on line waiting for dumplings or salad or a burger is not an efficient use of Goldman’s capital. …”

-CNBC report, 17 October 2013.

Gad Allon is professor of operations research specialising in area of game theory and queues.

He used optimisation models to study impact of length and time spent in queue on mindset of buyer. He found that for every additional time a buyer spent in queue, he was to pay few cents less. This decline in spending power of buyer has impact on business, solutions could be having more counters, outsourcing task of taking orders etc.

“An industry maxim suggests that a seven-second reduction in customers’ waiting time increases a chain’s market share by 1 percent… each extra second of waiting time at the drive-thru window reduces the amount that customers are prepared to pay for their meals by at least four cents.”

-A study by Gad Allon, an associate professor of managerial economics and decision sciences at the Kellogg School of Management

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Company cafeteria too face problem of long queues during peak hours, this means loss of revenue for employer i.e. had employee done some productive work, instead of spending time standing  in queue, it would have earned revenue for organisation. Many organisations introduce staggered timings for different functions to cope with crowding of cafeteria. Administration head in one of the organisations I worked for ended losing his job when he could not handle mess created by crowding of cafeteria.

Both the price and waiting time parameters have a significant impact on the consumer’s decision… in the fast-food drive-thru industry customers trade off price and waiting time. In particular, to overcome an additional second of waiting time, an outlet will need to compensate an average customer by as much as $0.05 in a meal whose typical price ranges from $2.25 to $6.”

-Gad Allon

Goldman Sachs came up with innovative solution to tackle cafeteria problem. Those who come to canteen before or after peak hours were given 25% discount on food. Most of the financial professionals take pride in saving money, so this policy became popular as employee took pride in telling others how much money he saved.

 

queue

“The cafeteria has a set of timed discounts. If you show up in the cafeteria before 11:30 or after 1:30, you get a 25 percent discount on your food. Goldman incentivizes employees to avoid the rush hour.”

-CNBC report.

 

Game Theory, Handicap Principle and Vanity

Vanity and pride are different things, though the words are often used synonymously. A person may be proud without being vain. Pride relates more to our opinion of ourselves; vanity, to what we would have others think of us.

– Jane Austen

Why peacock displays its feathers to attract peahen was puzzle for Darwin. This display of feathers not only attracted peahen but also attracted attention of predators like tigers and leopards. By displaying his feathers peacock was risking his life.

peacock

Israeli biologists, Amotz and Avishag Zahavi came with an explanation called handicap principle. To support their hypothesis they applied game theory to biology esp. Michael Spence’s job-market signalling model, where a potential employee sends a signal to employer about his ability to do job by acquiring degree from a good college.

zahavi

Amotz applied this concept to behaviour of peacock. By displaying feathers the peacock sends a signal to peahens that he can afford this handicap of coloured feathers (inspite of risk) and therefore is ideal mate for peahen. Also those lacking such colourful display should not compete with him. This is similar to job market signalling model, where employer is ready to pay more to good employee (i.e. those with degree from premier college) than bad employees (those from average colleges).

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Another example in animal world is that of stotting of gazelles, when attacked by predator the gazelle starts stotting i.e. jump higher instead of running faster. By stotting the gazelle sends a signal to leopard that has lot of energy and is in good health, so leopard should not waste his time chasing him, as leopard is unlikely to hunt him. It has been found that leopards avoid going after stotting gazelles.

stotting

Handicap principle is also applicable to humans; ownership of goods of premier brands and showing off sends a signal to others that owner is capable of bearing expenses of goods and therefore is a desirable partner. Thus vanity may not be morally desirable, but it definitely has useful purpose.

showoff