How to get that blonde in a Bar?

Economists are fascinated by social interactions. And there is nothing more satisfying than being able to predict outcomes of such behavioral interactions.

Recall the last time you went to a bar. You are sitting with your mates when a group of beautiful ladies walk in. All but one of them, brunettes. You are immediately drawn towards the Blonde, but just as you are about to go and chat her up, you realize your mates are thinking the same.

In a situtation, right out of the movie "A Beautiful mind", you have a couple of options. You can either disregard your competition, and try to reach her first. But failing would also mean losing the chance to go home with the Brunettes, who hate to be the second choice. Also, if all of you make a move towards the Blonde, it's sure to scare her off and everyone ends up going home alone.
Alternatively, you and your mates could collectively decide not to go for the Blonde, and approach the Brunettes. Lastly, just one goes for the blonde, whereas the rest go for the Brunette. So which is the best strategy?

Game theory gives the players solid recommendations on their optimal strategy and provides an external observer with a prediction of the outcome of the interaction.

Now, let's evaluate. First choice is right out of Adam Smith's book, "in competition, individual ambition serves the common good". This lesson of the father of modern economics suggests that it would be best for the group if all the boys go for the blonde girl.

In the movie, Nash's character argues that the above theory needs a revision and in fact the best strategy is everyone going for the Brunette since it ensures no one goes home alone.

Now let's apply game theory into it. Strategy 2 is a good strategy since the group is collectively better off than going home alone (Strategy 1). However it is not Pareto Optimal. Any guy could be made better off by going for the Blonde, without making someone else (in his group) worse off, which brings us to the last strategy -one for the blonde and rest for the brunettes.

So how does the game end? Who goes with the Blonde? Who do "you" go home with? Do you go home alone?

Let's put all the pieces together. Nash, in the movie suggests stratergy 2, with all implicit intentions of just himself going for the blonde, which clearly is the group-optimal (Pareto) strategy.

If all your mates are economists and have similar personalities, toss a coin to decide who goes after the blonde. Economists have great personal integrity ;)

In real life, however, the prediction also relies a lot on other factors. Since it is a co-operative strategy agreed with your mates, we have excluded external suitors. Say if Brad Pitt (or someone more attractive than your group), is drinking in the same bar. Then just go for the Brunette, since Brad Pitt always gets the blonde (infact all the blondes).

To sum up, you get the blonde if and only if,
- There is no Brad Pitt in the same bar eyeing for the blonde and,
- You won the toss and your mates decide to back off

Happy Pubbing..

PS: The above sterotyping women based on their hair color was purely to illustrate a point. I personally prefer Brunettes and wouldn't have gone for the blonde :)


Arms Race, Defense Budget Allocation and Prisoner’s Dilemma

In an earlier post we discussed the classic Prisoner’s Dilemma problem where rational unilateral (or individualistic) decisions fare worse than co-operative actions. A common real world example is the increasing defense budget, observed across the world. Defense Budgets are generally allocated as a fixed % of GDP. Countries spend on an average 2-4% of their GDP on military preparedness and defense. What is the optimum spend and can this be reduced and reallocated more efficiently towards other growth promoting government actions?

As a tax payer, I am often fascinated by the state’s allocation of the Budget. I belong to the school of thought where Budget should be allocated efficiently keeping the principles of Cost-Benefit in mind. Benefits should be improved Social welfare, equity, Health Status, Education level, employment, GDP growth, Political influence (indirectly for Strategic advantage culminating into other Direct Benefits) etc.

I pulled out Defense Spend and GDP for 9 countries and ranked them based on their absolute spend (in US Billion$). Before we look at the actual data, let us form some intuition on what we should expect.
a) Poorer countries (Yemen, Eritrea) would spend less on Military and more on socio-economic growth drivers like Infrastructure, Health, Education, Housing etc.
b) Developing countries with a history of war (India, Pakistan), international and domestic conflict, would spend more on Defense.
c) Developed smaller countries (Luxembourg, Singapore) with very high per capita income, would spend less on Defense and more on social security, Health and unemployment benefits.
d) Due to recent acts of terrorism and their participation in resolving international conflicts, larger Developed Nations (US, UK) would allocate more on Defense. Military spend to flaunt Political power and influence.

Now let us look at the data,
Rank Country SIPRI Military spend in USD $B (2009) IMF GDP in USD $B (2009) Military spend as % of GDP
1 United States $ 663.26 $ 14,119.05 4.7%
3 United Kingdom $ 69.27 $ 2,178.86 3.2%
10 India $ 36.60 $ 1,235.98 3.0%
25 Singapore $ 7.97 $ 182.23 4.4%
35 Pakistan $ 4.82 $ 161.99 3.0%
40 Malaysia $ 4.08 $ 192.96 2.1%
68 Yemen $ 1.20 $ 25.13 4.8%
87 Luxembourg $ 0.41 $ 52.43 0.8%
94 Eritrea $ 0.33 $ 1.87 17.5%

In most cases, our observations are quite consistent with our intuition. US has above average spend on Defense, which has been a topic of serious debate in recent times. Trends suggest, a drop in oversees bases in Iraq and Afghanistan, and more spend on Job Creation and Health.

Eritrea, an impoverished country in the horn of Africa is an interesting case study. It has been in constant conflict with it’s neighboring nations of Yemen, Sudan and Ethiopia. It is an Authoritarian state, with a population of over 5Million with a GDP just around 1.9Billion.  Yemen on the other hand is a presidential republic and started economic reforms in late 90s with aids from IMF and international donors. Yemen also has a significant Geopolitical influence with it’s strategic location and oil reserves.

Singapore, stood out, in my view as well. Singapore spends 4.4% on Military, a percentage which has stood somewhat constant over the years. The Government deems it necessary to maintain the sovereignty of this small city state. Singapore fears sudden political developments in the region, particularly in the neighboring states of Malaysia and Indonesia, which might require its armed forces to be used either as a deterrent, or as a means of national defense. The fact that it takes a very long time to build up such capabilities has meant that Singapore's military development has been continuous and sustained. This development also reflects other factors, such as political will, aided by the longevity of the same regime in power since independence; Singapore's sustained economic development which has given it the ability to devote resources to defense.

India and Pakistan have had 4 major wars (‘47,’65,’71,’99) along with frequent border conflicts. Both had a similar % spend (3%) of GDP for military spend, which as a % of GDP is at par with Global average.
A thing to note is, that since Defense spends are in most cases incurred by Government, this when translated into a % of their annual budget could be a really high figure. For instance, US Government spent 19% of their budget last year in Defense.

Economists worldwide agree that ~1.5 Trillion USD (2009 estimate) spent collective by all nations on military spend could have been put to better use, had their been more effective multilateral agreements on peace and cooperation. The Prisoner’s Dilemma is applicable here for precisely the same reason. Since countries don’t trust each other and often question the UN’s ability to mediate conflicts, decisions on military spend are thus unilateral. Each country puts up the most it can spend on defense. Had they all co-operated, they needed just enough to resolve internal domestic conflicts, leaving the rest to a better use.

Also, if in a particular year, India decides to raise its Military budget to say 3.1% of its GDP, this will trigger panic among its neighbors. It could be both Positive (against fear of new threats) and Negative (Geo-Political influence, war, territorial conflict). Pakistan and China would raise their spend just to signal their willingness to counter India’s move.

Thus the pareto-optimal solution would have been no one spends anything on international/cross-border defense, had countries cooperated and had there been an effective way to enforce it. However the NASH equilibrium we always end up is each country spending the maximum they can afford to spend.

Prisoner’s Dilemma: Where Equilibrium is not always Socially Optimum

interrogatorPrisoner’s Dilemma is a very popular situation enacted innumerable times in modern cinema and television shows. The situation is very simple.

  Two suspects Shawn and Gus 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 make the choice of whether 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. How should the prisoners act?

A prisoner’s action depends a lot on how the other convict reacts to the same situation. Game theory can be used to predict the outcome. However, we will see, Prisoner’s Dilemma is a bit unique.

Sentence for (Shawn, Gus) Gus Defects Gus remains silent
Shawn Defects 5 years, 5 years 0 years, 10 years
Shawn remains silent 10 years, 0 years 6 months, 6months

From the payout matrix, if they were great friends and trusted each other, they know that the other wouldn’t defect. Hence they could play a co-operative strategy with both remaining silent and be sentenced for 6 months each. This is the Pareto Optimal solution where both benefit.

A Pareto optimal solution is one where no “one” person can be made better off without making someone else worse off than before. The Pareto Optimal solution is that both remain silent (Silent, Silent). Their combined sentence is 1 year. For Shawn to be made better off (go free), he has to defect making Gus worse off than before.

However, if both of them were rational and not confident of the other’s reaction, they would try and maximize their individual payoffs. Thus they will always defect since, irrespective of the other person’s decision, defecting always results in a comparatively better payoff (5 years vs. 10 years or 0 vs. 6 months). Defect, Defect is the dominant strategy for both.

The NASH equilibrium is this self-interest maximizing solution, which is both of them confessing and ending up with a sentence of 5 years each. The beauty of this non-iterated Prisoner’s dilemma problem is that this equilibrium is not Pareto optimal as before.

The economic moral of the puzzle is that a group whose members pursue rational self-interest may all end up worse off than a group whose members act contrary to rational self-interest. More generally, if the payoffs are not assumed to represent self-interest, a group whose members rationally pursue any goals may all meet less success than if they had not rationally pursued their goals individually.

Simply put, in most situations at least one would always confess (driven by self interest) and the cops eventually have someone to frame and they solve the case :)

Now, look around you for instances of Prisoner’s Dilemma. You would be surprised how common it is. But then, that’s for the next post.

For the math lovers,

If Shawn and Gus were two rational mathematicians, they would gauge the relative probability of the other person defecting and decide accordingly based on the total payoff. And the probability would be based on how much they can trust each other. However, sadly, in this particular instance (in Prisoner’s Dilemma problem), defecting is the dominant move irrespective of the probabilities.

It can be easily shown that Payoff for Shawn if he defects is always higher.
Sentence for Shawn if Shawn is Silent > Sentence for Shawn if Shawn defects
[10x + 0.5(1-x)] > 5x + 0 * (1 – x)
4.5x + 0.5 > 0
For all +ve value of x

where x is the probability between 0 and 1, of Gus defecting
Thus irrespective of Gus’ move, Shawn will always defect.

Why does check splitting cause people to spend more?

Friends or colleagues who dine together at restaurants commonly split the bill. This is a lot easier compared to consolidating each one's 'right' share.

Back in days when I was still a vegetarian, I would find this practice highly unfair since chicken kebabs and roasted pork is lot more expensive than fried rice and lentils. Thus check splitting often does lead to disproportionate distribution of bill. But apart from this, there is yet another consequence.

It gives everyone an incentive to spend more than if each had dined and paid separately. Why does this happen?

Let's talk about the concept of perceived value again. Say I am dining with 5 friends and we have decided to split the bill in the end. I am trying to make up my mind between mac n cheese listed at $10 and a lasagna at $20. Assuming my perceived value/willingness to pay for the lasagna is $15. That is, for me the lasagna gives me $5 of additional benefit compared to the former. But any price more than $15, I am better off ordering the former.

Had I been dining alone, I would have settled for the Mac n cheese. However, I know that since I am sharing the bill with 5 others, my marginal increase in share is just $2 (one fifth of the additional $10) which is still lower than the incremental $5 benefit. Thus I will order the lasagna.

Economist call such decisions inefficient as my $3 benefit is against a -$8 for the rest of the 4 diners, giving a net group benefit of -$5, resulting due to my decision of ordering a more expensive dish.

Then why do people still split their bill? Simple. Imagine if each of us do the same (with/without anticipating similar behavior by the rest). All 5 of us order more expensive dishes than we initially intended. The Result would be a larger total bill but also a smaller nett surplus loss. Each of us would benefit from our actions and lose from the rest's. It is still inefficient since now on an average you may end up paying more. Also depending on what item each ordered some could really gain and some lose.

The other obvious reason is the convenience that check splitting brings in.

So do you like splitting bills or paying your own share? Do leave your comments. Happy dining!

- Posted using BlogPress from my iPhone

Why do women endure high heels?

High heels are painful and make walking uncomfortable. Prolonged use can injure the feet, knees and back. Then why do they continue to wear them?

A rational explanation is to look at the subsequent benefit realized for the incurred cost. The benefits are quite apparent. "Men like an exaggerated female figure", writes fashion historian Caroline Cox in "Stilleto" where she describes the compelling lure of the needle heel.

Women in heels are more likely to attract favorable notice. In addition to making women taller, high heels force the back to arch thus accentuating the female form.

The problem is that height and appearance is a relative phenomenon and if all women wear high heels, such advantages tend to cancel out. It may be advantageous to be a few inches taller than before, but the relative height distribution is unaffected. So no one appears taller than if all had worn flats.

For fun, let's model this in game theory. Taking the simplest case of 2 women- Betty and Jane. The four possible options for (Betty, Jane) are (Flats, Heels), (Heels, Flats), (Heels, Heels) and (Flats,Flats).

Interestingly, game theory gives us  two optimal solutions to this problem. Either both wear high heels and nullify each others relative advantage or collectively decide to wear flats and stop enduring the pain.

Thus collectively if all women in the world decide to forgo high heels, they are all better off than before. Rationally, the latter is a better solution since they don't endure the pain for no incremental advantage.

But then why do we still see them wearing high heels?
Firstly, not everyone thinks like an economist. Collective decisions are nearly impossible since each one is driven by their own personal incentives, and any individual can gain relative advantage by violating the collective consensus by wearing heels. At least for a short period of time, till everyone realizes they need to follow suit to nullify their disadvantage.
Secondly, well, women are just too darn hard to understand :)

So why do you wear heels? Please do leave your comments