Economics in Action

Following my last post, I have been given a great article by Peter Sozou and Robert Seymour (titled “Costly but worthless gifts facilitate courtship“) about the application of game theory in relationship issues. This unconventional article on game theory shows the great power economists have to solve social problems. It is free and worth reading if you are keen on studying game theory.

And apparently, intrinsically worthless gifts (e.g. an engagement ring?) are great signals.

So, one week of micro basic game theory revision can drive you to the edge of insanity… Talking to certain people about their love problems has definitely pushed me over that edge. Here is my analysis of love as a dynamic game of imperfect information. Enjoy!

THE SETUP:

I will base my analysis on a simple two-players model, which can be extended to create love triangles, quadrangles, etc… We have players A and B, who have concave utility functions, and hence are both risk-averse (i.e. they prefer certainty over an uncertain prospect). People are risk-averse to different degrees, and this will affect the payoffs each player faces, and as a result, the way the game is played. In this game, I will assume that both players are very risk-averse (which is true in most cases). Both players are trying to maximise their payoffs.

Firstly nature chooses whether player A will like player B (we have an information set). The subjective probabilities (something B may believe in) that A likes B and A does not like B are p and (1-p) respectively. This probability will affect the final equilibrium as shown later. Player B really fancies player A, but does not know whether player A will reciprocate. Player B has two strategies: profess and not profess his/her love. Player A’s action is to reciprocate or not reciprocate. However, player A will only reciprocate if nature has made him/her like B and vice versa, i.e. A cannot determine whether he/she will reciprocate. Each player’s payoff will depend on where player B is in the game, and what he/she chooses to do. The potential payoffs are as follows:

1) Player A reciprocates and player B professes: A gets 20 and B gets 20 (both players end up happily together, yay!!!).

2) Player A reciprocates and player B does not profess (sad times hah?): A gets 0 (he/she will never find out that he/she could have been a lot happier, but this can not be treated as a loss either) and B gets -10 for being an idiot (a rational fool) and not professing.

3) Player A does not reciprocate and player B professes (the worst thing ever right?): A gets -10 because suddenly he/she is facing an incredibly awkward situation, which clearly causes a lot of distress (like you need to be nice to that other person, explain why you will not reciprocate blah blah blah), B gets -100 for taking the risk whilst being so risk-averse (in other words for being an irrational fool). This is the most embarrassing scenario for both players.

4) Player A does not reciprocate and player B does not professes (a really boring scenario): A gets 0 again for very similar reasons (the lack of knowledge means he/she will never find out that he/she could have been a lot more stressed), B gets -5 for being a rational fool again (he/she will forever question whether A would have reciprocated).

It is probably easier to see the payoffs if you just draw the normal and extensive forms of the game.

POSSIBLE EQUILIBRIA:

Note that there is no strictly dominant strategy in this version of the game due to player B being very risk-averse.

We now look at best responses. It is pointless trying to look for A’s best responses because whether he/she reciprocates is decided by nature. Thus, we look for B’s best responses:

Best response for B given A reciprocates = profess.

Best response for B given A does not reciprocate = not profess.

Thus, we have two equilibria: (reciprocate, profess) = (20,20), (not reciprocate, not profess) = (0,-5). These are not strictly Nash’s equilibria as A’s action is predetermined by nature. Clearly though, the first equilibrium brings more utility to both players.

THE EASIER SOLUTION (i.e. under perfect information):

If we have a third party to provide (signal) player B information about his/her position in the game, then the game is pretty straight forward. Player B, knowing at which node he/she is, will be able to make the best decision for himself/herself. There will be two Nash equilibria. If player B knows that player A will reciprocate, then he/she will profess, making both players happy. On the other hand, if player B knows for sure that player A will not reciprocate, he/she will not profess and avoid the potential embarrassment. This happens sometimes (as I have seen recently), but most of the time people are in the dark about whether the other person like him/her or not.

THE SOLUTION UNDER IMPERFECT INFORMATION:

There are no mixed strategies in this game as player B can profess only once. However, it is probably possible to have mixed strategies if signalling is introduced. Since B knows nothing about A’s feeling, he/she will have to form expected utility from professing and not professing:

E [U(B)/B professes] = 20p – 100(1-p) = 120p – 100

E [U(B)/B does not profess] = -10p – 5(1-p) = -5p – 5

In order for B to profess, the first equality must be greater than the second. Basic calculations give that p must be greater than 0.76. However, remember what I said in the beginning about p being a subjective value and B being very risk-averse, most people will not say that the probability that someone likes them is that high (unless they have better knowledge after interacting).

SIGNALLING?

Signalling in this game can be slightly more complicated as after player B sends a signal, player A will likely send a signal back, and both players will have to form beliefs functions. Sending a signal can incur costs (say buying flowers and presents or trying to look more physically attractive) or no costs (just showing affection). The signal also may or may not increase the probability that player A will reciprocate player B’s feeling. This is probably too difficult for me to analyse right now, so I will leave this for another note in the near (indefinite) future.

MORE PLAYERS?

We have never done anything like this in the lectures, and my brain is melting… so I will go and write a blues on my piano! But I hope that everyone has seen that love is a really complicated game because people are just rational fools!

Photo by Bayat on Flickr

Two odd pieces of economic research have been highlighted in the Ig Nobel Prizes, awarded each year by the magazine the Annals of Improbable Research.

The first study examined tips given to lap dancers. Unfamiliar with lap-dancing, Geoffrey Miller and colleagues read up on the relevant sociological and feminist literature before getting eighteen dancers to record their earnings for two months. They found that earnings were greater when the dancers were ovulating: the male patrons expressed a preference for dancers who were currently fertile, even if not consciously aware of the difference.

The other study was by behavioural economist Dan Ariely and colleagues, who found that the placebo effect of a pill was weakened when the pills were discounted in price. In other words, some medicines are more powerful in virtue of being more expensive.

The full references are Geoffrey Miller, Joshua M. Tybur, Brent D. Jordan (2007) “Ovulatory Cycle Effects on Tip Earnings by Lap Dancers: Economic Evidence for Human Estrus?” Evolution and Human Behavior, vol. 28, 2007, pp. 375-81; and Rebecca L. Waber, Baba Shiv, Ziv Carmon, Dan Ariely (2008) “Commercial Features of Placebo and Therapeutic Efficacy” Journal of the American Medical Association, March 5, 2008; 299: 1016-1017.

Matthew Reisz reports in the Times Higher Education about the rebirth of economics, ‘today the “dismal” science of economics is sexy’. Tim Harford and Stephen Levitt are held somewhat responsible for the distinct change in attitude, with simple economics being used to explain anything from ‘rational crime’ to ‘the teenage oral sex craze’.

The publication of The New Palgrave Dictionary of Economics compiles contributions from not only 1500 economists but also other fields, a Swedish zoologist for example, supporting the end of ‘dismal’ economics.

Read more: Matthew Reisz (2008) Figure It Out Times Higher Education

Human beings ability to cooperate with each other lies behind our success as a species. But since the skills of coalition-building are essentially for masculine activities notably hunting and warfare they have also been the key to mens subjugation of women.

That was the central message of Professor Paul Seabright when he delivered the 2005 Royal Economic Society Public Lecture on Thursday 8 December in Edinburgh and again on Friday 9 December in London.

Professor Seabrights lecture took his audience through a tour of the many ingenious strategies that males and females have used to manipulate their partners and rivals, from primates to prehistoric humans to modern men and women. He concludes:

Cooperative man was the key to our civilisation but he has used his success to isolate, confine and control the women in his life.

(more…)

This is the title of a research paper by economists Lena Edlund and Evelyn Korn, in which they consider the relative appeal of marriage and prostitution for women, and (closely linked) the relative appeal of wives and prostitutes for men.

Michael Noer in Forbes magazine shows wittily that the economic perspective on marriage is bleakly unromantic, but admits the point of the research is not to illuminate romantic feelings (for which we already have a culture’s worth of art and poetry) but to answer a specific question, namely, “Why do prostitutes earn so much money?” Is it compensation for the violence and disease which they are exposed to, or compensation for the fact that no-one wants to marry a prostitute?

Found via the book Economics Uncut: A Complete Guide to Life, Death and Misadventure, edited by Simon Bowmaker, which has many examples of economic research into topics like drugs, crime, abortion and gambling and includes Edlund and Korn’s original paper.

Economics research has a surprisingly large amount to say about dating, sex and relationships. Take Alan Collins, for whom personal ads are potential research data. Collins – an economist at the University of Portsmouth – researches topics including the economics of love, sex and dating. (Rock bands and cigarettes also feature in his research, but not at the same time).

He and his colleagues apply economic analysis to personal ads and to survey data. In “The Surrender Calue of Capital Assets: The Economics of Strategic Virginity Loss” he looks at the extent to which people lose their virginity because of being in love. He finds a reliable difference between male and female attitudes, with males more likely to pursue sex for its own sake and females more likely to use virginity “strategically” as a way to get romance.

It may be a common generalisation, but research like this can examine to what extent it is true, and how attitudes to virginity loss are affected by religion, age and the way in which subjects learned about sex.

Read More: (You may have to have university internet access to read these research papers)
“Surrender Value of Capital Assets: The Economics of Strategic Virginity Loss” Journal of Bioeconomics, v2 n3, October, 2000
“Gender Differences in Mate Search Effort: An Exploratory Economic Analysis of Personal Advertisements”, Applied Economics, 1998, 30, (10), 1277-85

Listen to the interview

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Providing family planning services for young people has little impact on pregnancy rates and may have contributed to the dramatic increase in rates of sexually transmitted infections (STIs) among young people. That is the conclusion of research presented at the Royal Economic Society annual conference by Professor David Paton of the Nottingham University Business School.

The research casts further doubt on the wisdom of the Government’s Teenage Pregnancy Strategy, following on from the announcement in February 2002 that the latest figures show an increase in teenage pregnancy rates, following several years of decline. (more…)