Category: Game Theory

In trust we god


Can trust affect the outcome of political events (war), business transactions (pricing) and economic affairs (poverty)?

This is a problem that I’ve been very interested in for many years.

A few years ago I came across papers in economics and game theory that supplied the mathematical tools that we need to analyse such problems.

So, I’ll take each area of interest 1) politics 2) business and 3) economics and explain how trust matters in each case.

1.  Politics

Can the outcome of something like war be determined by trust?

Let’s assume an army of 2 soldiers.

In a war, the benefits to each soldier can be modeled as a bi-matrix (normal-form game) as follows:

soldier 2 fights soldier 2 flees
soldier 1 fights 5, 5
–5, 0
soldier 1 flees 0, -5
0, 0
Normal form or payoff matrix of a 2-player, 2-strategy game

The first of the two numbers in the matrix represents the payoff to soldier 1.

The second of the two numbers in the matrix represents the payoff to soldier 2.

(The soldiers win something (represented by 5 points) if their army wins; they win nothing if their army loses; and they lose their life (represented by -5 points) if they do not flee and their army loses; we assume the army wins if both soldiers do not flee and loses if one or both flee).

If soldier 1 trusts soldier 2 not to flee the battlefield, the best strategy for soldier 1 is to stay and fight as well (since he will then get more benefits than if he flees).

If soldier 1 does not trust soldier 2 to stay on the battlefield (if he suspects that soldier 2 will run away), then the best strategy for soldier 1 is to run away himself (so that he does not remain on the battlefield and get killed).

So, this model shows that if two equal 2 man armies meet on a battlefield, the one whose soldiers trust each other more will win.

2.  Business (Pricing)

There is a very interesting paper by George A. Akerlof (‘The Market for “Lemons”: Quality Uncertainty and the Market Mechanism’).

It tries to explain why the price of a new car in a show room is so much higher than the price of a new car in the second-hand car market.

For example, a car costing $25,000 fresh out of the showroom, might fetch $18,000 if sold as a used car in the used car market.

Akerlof’s paper tries to explain why the price dropped so sharply.

Akerlof suggests that the price drop is a result of the uncertainty surrounding the quality of the car in the used-car market.

A certain percentage of cars in a used-car market will be defective (since anyone can sell a car in an unregulated market, and unscrupulous people would have put defective cars up for sale).

Let’s say 50% of the cars in the used car market are defective.

Now, a person buying a used car a day old will only be prepared to risk paying 50% of the showroom price for the car (because of the 50% chance that the car is worth nothing).

The Price of Trust

This result has the following unintended consequence:

The more a person trusts a seller, the higher the price he will be willing to offer for a car.

I’ll give you an example of that.  (I’m sorry, but this is a bit racist).

When I was a student in North Carolina, and I was looking to buy a used car, I was given the following piece of advice by my fellow students.

They said, “Go for a car that an American is selling because they will tell you about any problems that it has.  Don’t buy a car from an Asian or an Indian unless you know them well.  They won’t tell you if there are any problems.”

I see the same effect even when doing business in India today – a lot of business happens through connections.

Price Sensitivity

It might also explain why Indians are so price sensitive.

Indians are said to be very price-sensitive, preferring the less expensive offerings over more expensive ones that promise better quality (I recall Richard Branson said that at one point while explaining why he didn’t want to enter India).

I think the price sensitivity is a result of Indians not being able to trust promises of higher quality from their countrymen.

Price becomes the only measure that Indian buyers are able to trust to when making a purchasing decision, leading to extreme price-sensitivity in the Indian market.

Hiring and ‘Brain Drain’

Even in hiring, this can have the effect of driving down salaries.

When hiring someone, an Indian firm is likely to offer a lower salary than the market, because they don’t trust in the abilities of the person being hired.

In Akerlof’s paper, he talks about a side-effect of a lack of trust.  He says that good quality cars will just stop being sold on the low-trust markets.

The applies to the job market in India as well:  Indian firms tend to offer lower salaries, which might lead to the best engineers choosing MNCs over Indian firms or leaving Indian shores altogether.

3.  Economics

I’ve described in an earlier blog how man-in-the-middle systems of government can fail to work efficiently if the man-in-the-middle is corrupt.

I’ve described in that post how resources can be wrongly allocated in the presence of corruption.

The result of an inefficient allocation of our resources is poverty.

For example, the Indian government has tripled defence spending in the last 10 years – through heavy borrowing – when it is possible to show that we need to allocate whatever money we have to education (see our arguments for that

World Bank studies (that you can get off an Indian Reserve Bank website) show that corrupt governments spend more on arms (because of how easy it is to hide kickbacks from arms deals) than honest governments.

So, the economic prosperity of a country can be impacted by corruption.

Causes of Corruption

But we can ask a deeper question:  “What causes corruption?”

I’ll try to show right here that it is a lack of trust.

Take for example two players in a bidding war (let’s say that they are bidding for a government contract).

Each has the choice to give a bribe or not to give a bribe.

Player 1 is more likely to give a bribe if player 1 does not trust player 2 to not offer a bribe to the government official.

It’s the same decision matrix that I have used for the case of the 2 soldier army.

So you get it?

Everything depends on trust.


I am probably way out of my depth on this, but the ancient Greeks seem to have had two views on the supreme ideal that man should strive for.

According to the Wikipedia article on Dialectics:

“The Sophists taught arête (Greek: ἀρετή, qualityexcellence) as the highest value, and the determinant of one’s actions in life.”

But there lived in Greece a man who disagreed with that notion:  ”Socrates favoured truth as the highest value, proposing that it could be discovered through reason and logic in discussion: ergo, dialectic.”

But the above models seem to suggest that truth (honesty) results in trust (you know that the guy next to you is honest and won’t lie about the quality of a car or bribe a government official to get ahead of you).

And what the Akerlof paper shows is that trust rewards and promotes quality.

In other words, the two Greek concepts of quality (of the values mankind must uphold for its own good) are probably one and the same.

Related Posts:

1.  Framework for evaluating values

2.  What traffic can reveal about society

3.  Who betrayed Ekalavya?

4.  Can economics change the world?

5.  Is there an algorithm to combat poverty?

6.  Why dance is undervalued

7.  Is 5 very far from 4?

Related Far-out Posts:

1.  Splitting the Truth into Precision and Recall

2.  Does AI have Buddha nature?

[The image in this picture was taken from a circulated Facebook post.  The copyright owner of the image is unknown at this time and if anyone knows him/her I’d like to make sure they’re ok with my using the image and acknowledge them].

What traffic can reveal about society

The last post was about Socially Optimal Solutions and the Nash equilibrium.

In this post, we examine traffic patterns under the same lens.

It appears bad traffic situations might be avoided if road users a) play by the rules or, b) play fair or, c) are trusted by other participants.

Scenario 1


In Scenario 1, the North-South traffic is waiting for the light to turn green.  Cars 1 and 2 are going South.  Cars 3 and 4 are going North.

Now, if the drivers of Cars 2 and 4 try to cheat by overtaking on the wrong side of the road, you could end up with Arrangement 2 (everyone is blocked).

This is what you would get at the Nash equilibrium assuming that there were no policemen at the intersection (the Nash equilibrium is one of many possible equilibriums that can be reached if people don’t cooperate, but just act in their own self-interest).

So, it is only if the drivers all respect the law,  without any trying to cheat, that they would end up with the socially optimal solution (Arrangement 1 rather than Arrangement 2).

Scenario 2


Here, the intersection does not have traffic lights.  The North-South traffic has stopped.  Cars are accumulating in the North-South road, and so Cars 1, 2, 3 and 4 are not going anywhere.  Now, 3 can choose to leave a gap for 5 to pass through.

The game here is between Cars 3 and 4.  If Car 3 feared that Car 4 might try to overtake by taking advantage of the gap, it would move forward and block the intersection.

So, in this case, an expectation of unfairness could lead to a solution that is not socially optimal.

And that would be the Nash equilibrium.

However, if people considered each other to be fair, there could be a socially optimal solution that is better than the Nash equilibrium.

Scenario 3


No traffic lights.  There are two lanes going in the same direction (South to North).  Traffic is stalled in the North-South direction (Cars 3, 4, 8 and 9 are going nowhere).  Cars 3 and 8 have the option of leaving a channel open for Car 5 to pass through.

What’s interesting here is that if Car 3 suspects that Car 8 might close the intersection, Car 3 would do well to close the intersection itself (preventing Arrangement 2).

Again, that would be the Nash equilibrium.  However, if everyone agreed and cooperated to keep the intersection open, you would get a much better result (a social equilibrium) than you would with the Nash equilibrium.

So, the socially optimal solution is obtained only if there is strong mutual trust between the participants in this traffic pattern game.


I find these traffic patterns interesting because they could be indicators of local ethics. When you visit a new place, you might be able to get an idea of how fair, trustworthy and rule-abiding the local people are, just by observing the traffic?

What game theory says about why gas stations are built next to each other

This lovely video tells you about the concept of a Socially Optimal Solution – a solution that works very well for society – and why such solutions are often not stable.

It also explains the concept of a Nash Equilibrium – a solution that is stable, but not always optimal for society.

It also tells you how aggressive competition can lead to results that are not optimal for society.

Frameworks for evaluating values

I recently came across a very interesting 2001 paper by Daphne Koller that dealt with influence diagrams and how they could be applied to game theory.  I came across the paper while doing some background reading on a talk on decision making in accordance with our core values by a friend of mine, Somik Raha.

Influence diagrams are a formalism (very similar to probabilistic graphical models) that are used for making decisions.

What Somik Raha has attempted to do is come up with a framework for making decisions while also taking one’s values into account (either as constraints or as inputs into the decision model).  To do that he proposes extensions to influence diagrams.

What I found interesting when I thought about Daphne Koller’s work and Somik’s together, is that they could possibly give you a framework to evaluate your values.

Koller’s formalism reduces to a game theoretic model, which can be evaluated to determine the outcome of the decisions made by a group of people.

Plug in a formalism based on Somik’s ideas and you just might be able to create a way to quantity the benefits of values.

The Importance of Values?

I have been thinking a bit about values these days because there has been a horrific gang rape in Delhi, and there have recently been numerous incidents of bad driving where friends of mine have been injured in Bangalore.  Then there is corruption.  Our society seems to be quite happy with inequality and vast differences in the distribution of wealth.  It make me wonder if our values are to blame.

I have often wondered whether some of our problems originate in our value systems and whether the value systems that we consider sacrosanct in India are really very good ones.

Let me take just a couple of values that most Indians would consider to be very good values

  1. Non-violence
  2. Obedience

and let’s discuss them in more detail.

  1.  Non-violence

This value appeals not just to people in India.  You see variants of the value of non-violence appear in Tolstoy’s writings and in Semitic religions, as you can see from the Bible (“turn the other cheek”) and the Quran (“give alms to one who begs from you, even if he comes on the back of a horse”).

The issue with this sort of value is that it makes a person (and those around him/her) extremely vulnerable to injustice.

In India, we restrict the liberty of women – in their choice of clothing, company and lifestyle – for fear that they could be in danger if they violated societal norms.  This shows that none of us want to fight society or cross swords with someone who might make disparaging comments about personal choices.

Moreover, possibly as a result of the value of non-violence, very few Indians if any are taught fighting skills in school.  So, even if a person really wanted to act, say to protect a friend, he or she might not really have the skills to take down an aggressor.

So, instead of protecting and standing up for people who might be vulnerable, we become their tormentors and make their lives more miserable, just so we don’t have to get our hands dirty, or because we don’t have the skills and strength to do squat.

I’ve written about how bribes are openly collected by traffic policemen.  It should be very easy to put a stop to such behavior if you’re willing to fight.

If non-violence is not a core value, then how do we protect people from tearing each other to bits?

We could start with a question like:  non-violence for what purpose?  (turning it into an extrinsic value)

If the answer is something like, “so that the weak feel protected”, why not make protecting the weak our core value?

I’d prefer teaching kids values like “Don’t ever turn your back on a bully” rather than values like “Don’t fight anybody, and just come home safe, child!”

2.  Obedience

Indian parents love to boast that their child is “such an obedient child!”

Is that a good thing?

Obedience is different from politeness or respect.  The latter are mutual but the former is one way.

So, the politics of obedience creates a hierarchy of subservience.

In India, Parents expect complete obedience from Children.

The Police expect complete obedience from People.

The Politicians expect complete obedience from Police.

Teachers expect complete obedience from Students.

Managers expect complete obedience from Employees.

The creation of the hierarchy (through expectations of obedience) can be very dangerous in many ways.

1.  It can stifle creativity and problem-solving ability.  There is a bias against ideas flowing up a hierarchy because those higher up the hierarchy claim their place above those required to be obedient to them on the premise that they are somehow superior to those below them.  A good example is how parliament will not accept that people have a right to demand a bill against corruption (members of the Indian parliament claim that parliament is supreme in a parliamentary democracy – not the citizens that the parliamentarians represent).

2.  It can leave young people ill-equipped to defend their personal spaces.  I read in a paper on rape that many rapists approach victims by testing their boundaries.  They make comments and otherwise violate the intended victim’s personal boundaries.  If these are not strongly resisted, the probability of an assault becomes greater.  Another strategy used by rapists is to move their intended victim to a new location where they are more vulnerable. It is very important for people to be conditioned so that they do not obey an order by an attacker to relocate under any circumstances.

3.  The hierarchies perpetuate the power of stronger (bigger, older or richer) parties by providing social sanction to their dominant position, and so hinder social mobility.

4.  The obedience hierarchy could allow a few people at the top to amass too much power. It might have, for example, prevented cops from disobeying those in power during the Gujarat riots.

5.  Obedience means valuing rules above truth.  Obedience implies not challenging the rules or the status quo.  So there is little scope for discovering if the rules really are good ones for everybody.  People often defend something they assert with a “because I said so.” – that is, you are expected to believe them because of their authority, and not because they can substantiate their assertion.

Obedience as an absolute value is not entirely harmless.  It could be dangerous to us as a society because corrupt politicians can use the pliability and obedience of people around them to get away with evil (remember the activist who was hacked to death on the orders of a corporator from Bangalore, the journalist who was burnt to death in Uttar Pradesh, or the shutdown that the former Chief Minister of Karnataka State ordered when he was about to be investigated for corrupt dealings?).

I’d love to replace “obedience” with something else, perhaps “honesty” and “trustworthiness” and “pride”.


I understand that we as Indians are very proud of our values but I’ve tried to argue that our values need to be re-examined.

Personally, I’d love to see the day when we replace all our values with just the value of trustworthiness.

Trustworthiness as a value would mean we’d fight for each other.  It would mean we’d protect the weak.  It would mean we’d be on time.  It would mean we’d be honest.  It would mean we’d be capable and skilled and strong.  It would mean we’d be proud of each other.  It might mean we’d never lose another war.

Reading Koller’s and Somik’s work you get the feeling that one day you might be able to evaluate the comparative benefits of two sets of values, and pick the better one, using plain math.

And hopefully, by showing them mathematical proofs, you can convince people to change their values and pick better ones for themselves.

Digital Democracy and Cutting out the Middleman in Government

Can information technology in general and text analytics in particular help improve the quality of governance?

We believe they can.  In this article, we discuss one problem/weakness with the present system of governance that makes it very susceptible to corruption.  We then present a solution that relies on analytics to mitigate the problem.


Governance is a service.  An organization (government) provides people in a geographical area with a service called governance.  The organization that provides the service is for all practical purposes a service company owned by all the people to whom the service is provided.

Services provided by government include collecting money and using it to create infrastructure and services for the common good like roads and schools and city planning and waste disposal.

One weakness in the present approach is as follows.

The goals of the service provider may not always be well-aligned with the goals of the people being served.

When corruption exists, these goals may be very poorly aligned indeed.

Misalignment of Goals

Example 1:  Misalignment of Goals in Road Construction

For example, take the construction of a road.  To the people of the city who use roads, what they want in return for paying out money is better roads.  To the governing body who disburses the money, the goal – where corruption is rife – is high kickbacks.

Does Bangalore really not have enough money to build good roads?  It is very likely that our roads are bad not because we don’t have the money or the means to build roads that last, but because our governing body in charge of road repairs repeatedly doles out road maintenance contracts to people who do the road construction authorities favors in return for the contracts.

Example 2:  Misalignment of Goals in Allocating Budgets for Defence and Education

In an article on why India imports vast quantities of arms, we had described how the Indian government was under-spending on education and over-spending on defense procurement.

That article was based on a World Bank report that mentioned a study that showed that corrupt governments overspend on defence procurement because of the lack of transparency in such deals.

For example, in 2011 and 2012, India committed close to USD 50 billion to purchases of aircraft and ships alone whereas the expenditure towards education was around 12 billion per annum (woefully inadequate for our country).

Here again, we see a complete misalignment of goals.  People in India need education.  The government, however, when given a choice between putting our money into education or into arms, picks the choice that gives it a higher chance of receiving kickbacks.

Both are examples of something we call man-in-the-middle corruption.

One possible solution is to allow people to allocate portions of their income tax to categories of services that we expect our government to provide us.

Goal Alignment

For example, if I am paying Rs. 20,000 in income tax, I might quite reasonably be allowed to allocate say Rs. 10,000 of it to areas of infrastructure that I feel we need to invest in.  I might allocate of 5000 to education and 5000 to health services.  This would give people some measure of control over the use of our money by the governing body.

Moreover, it would give the governing body a deeper insight into the needs of the people, and also put some pressure on it to allocate all public funds according to a similar ratio.

For this to work, the allocation choices offered to people would have to be meaningful.  Meaningful choices may be determined by public discussion and/or referenda.

Any public discussion on the matter would require the use of debate support tools – text analytics tools that help large numbers of people communicate.

We’ve described one such tool that we call an MCT (Mass Communication Tool) in our lab profile.

In essence, what might be needed are text analytics technologies that can support legislation (proposing legislation, modifying legislation, or conducting a referendum on legislation).


Much to the point, at this year’s Coling conference, we came across a paper by a student of the Singapore Management University (Swapna Gottipati), on how one might detect suggestions (thoughtful suggestions) in social media messages.  The paper was titled “Finding Thoughtful Comments from Social Media”.  Unfortunately the paper is not yet available online.

There have been attempts to allow people to propose legislation through online communities that don’t seem to work very well as the following article shows you:

But a more successful attempt at using social media is described in this BBC article Why not let social media run the country?, and I quote: “But Nick Jones, deputy director of digital communications at Downing Street … points to the Red Tape Challenge, which has received more than 28,000 comments since it was launched by the prime minister last year and which has a ‘social media element’.  More than 150 pieces of legislation identified by the public as unnecessary have been so far been scrapped.”

I also really like Clay Shirky’s talk on how the internet will one day transform government.  He talks about how freedom of expression is promoted by social media.  What does freedom of speech do?  Well, it allows more ideas to circulate.  The more ideas there are in circulation, the better things (possibly governance) can become.

He talks about a need for an open-source model for generating agreement on ideas and proposes large scale discussion using something like the GIT version control.

He provides examples of legislation dumped on GITHub and his big takeaway seems to be the idea of collaboration without coordination.

He also talks about the need for openness working in two directions (about participatory legislation and not just legislation being visible to everyone), and about the invention of new methods of argument.  Very interesting.


Another use of social media in governance is to collect feedback on government policies and decisions.  In that context I want to mention Project Dreamcatcher, an analytics project with a social media component that was used by the Obama campaign in 2012.  Here is an article on Project Dreamcatcher.  It seems to be an extension of feedback monitoring which has been used for customer service.


There seem to be new possibilities opening up for the use of technology, possibly text analytics technology, in governance.

Quantum of Punishment – Or Should Draconian Punishment Ever be Used?

One of my friends – Nishanth Ulhas Nair – wrote up a set of suggestions on how one might go about solving the problem of violence against women in India, specifically rape (there have been some horrific occurrences lately in Delhi, Bombay and Bangalore).

Here is one of his suggestions that I particularly liked:

a) In schools, make students do the cleaning and if possible cooking/washing-dishes also. Boys should especially be made to do this. So that they learn to do work which are typically considered to be the job of a woman in India. Moreover this will reduce the class divide in India where there are some ‘inferior/poor’ people who will work for us. Why should there be a mess in schools/colleges? Students should cook their own food and clean their own plates.

But what I really want to talk about today is the counter-suggestion he had made:

The problem with death penalty is that the rapist may end up killing the victim because he feels it will be easier for him to get away with it (since death is anyway the worst penalty he can get, there is more incentive for him to kill her after the rape).

Stricter measures (for example, applying the death penalty to the crime) have been floated around a lot lately, but how do you decide what is an appropriate quantum of punishment?

I am going to see if it is possible to arrive at Nishanth’s conclusion using game theory.

We are going to start with a set of simplified assumptions:

a)  You have two players in this game – the law-enforcer and the law-breaker.

b)  The law-enforcer has two choices – a) to punish the law-breaker with death and b) to punish the law-breaker with a few years in jail.

c)  The law-breaker has two choices – a) to kill witnesses to better his/her chance of not getting caught and b) to not do anything beyond the primary objective of the crime.

d)  The aim of the law might be assumed to be to maximize the number of potential crimes prevented.

e)  The aim of the law-breaker might be assumed to be to minimize the punishment if any that might result from the crime.

The Payoff Function of the Law-Breaker

The law-breaker’s payoff is the punishment, and so is a negative number.

It is set to -6 (maximum punishment) if the law-breaker does not kill the victim after the crime (which could be a burglary or a rape) but the punishment for the crime is the death penalty (to act as a deterrent).

It is only -2 if the law-breaker does not kill the victim, and the punishment is not draconian.

The law-breaker’s payoff is only -3 if (s)he kills the victim assuming the chances of detection decrease by 50% as a result of the murder.

Since the crime is compounded by the killing, the payoff is the same no matter whether the penalty for the original crime is harsh or not.

The Payoff Function of the Law-Enforcer

The law-enforcer’s model is simpler.  It is equal to the number of innocent lives saved.  It is 1 if the victim is not killed.  It is 0 if the victim is killed after the crime.


Now to start analyzing the game, you write the assumptions down in a bi-matrix (normal-form game) as follows:

the law (enforcer)
awards a few years in jail
the law (enforcer)
awards the death penalty
the law breaker
chooses not to kill the victim
-2, 1
the law breaker
chooses to kill the victim
-3zero -3, zero
Normal form or payoff matrix of a 2-player, 2-strategy game

The first of the two numbers in the matrix represents the payoff to the law-breaker.

The second of the two numbers in the matrix represents the payoff to the law-enforcer (or society).

Strictly Dominated Strategy

By examining the matrix, it is possible to see that there is no strictly dominated strategy for the law breaker.

A strictly dominated strategy is one that will benefit one of the players more than all his/her other strategies no matter what the other player does.  No strictly dominated strategy exists for the law-breaker in this particular game.

That is because if a draconian punishment strategy is used by the law-enforcer, killing the victim appears to be a better strategy for the law-breaker.  If the death penalty is not used for a lesser crime, then not killing the victim appears to be a better strategy for the law-breaker.

Nash Equilibrium

A Nash Equilibrium consists of a set of strategies for both players that are the best possible for each of the strategies an opponent might choose.

It turns out that this system contains two Nash Equilibrium points.

In this formulation, the strategy pairs that can yield a Nash Equilibrium are:

1)  the law-enforcer does not award the death penalty + the law-breaker does not kill the victim

2)  the law-enforcer awards the death penalty + the law-breaker kills the victim


So, what this analysis suggests is that if the death penalty is awarded for crimes like rape, there will be a strong motive for perpetrators to kill their victims.  Conversely, if the penalty for crimes like rape is less than the penalty for murder, there will be a strong motive for perpetrators not to compound lesser crimes with murder.

What is also interesting to note is that if law-enforcement is not very effective at identifying perpetrators without a victim’s assistance (if there were no DNA matching technology or if the police force were ineffective), a criminal would have a good incentive to kill his/her victims [the result would be obtained if you change the -3 to -1 in the law-breaker’s payoff function].  Ineffectiveness of policing would reduce the negative payoffs for a rob+murder strategy to the point where murder to compound the crime might become an appealing alternative to a law-breaker.

The Alternative Scenario

I had heard from a friend from another country that in his country, thieves would be killed by anyone who caught them (passers by would tie them up and kill them summarily and without trial – by ramming pins into their heads).  I can imagine that this strategy might cause law-breakers to do everything possible to hide the crime – including murdering anyone who might hinder their escape or later identify them to their captors.

So, in a way, the matrix justifies having an effective police force at public expense.


So, we’ve tried to show using some simple game theory that Nishanth’s intuitions about penalizing rapists with the death penalty are possibly right on target.

However, we have chosen a model that is very simplistic and not a very accurate fit for the problem.  The model chosen is of a static game with complete information, but that is a bit of a simplification.

If you liked this article, you might like some of our earlier writings that attempt to analyze game theoretic models of social media customer service.


We learnt a lot about the subject of game theory from a book that is absolutely-required-reading for anyone with the faintest interest in economics and game theory – “Game Theory for Applied Economists” by Robert Gibbons.