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

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!

Iceland has been the world’s whipping boy for the last few years.  The collapse of its banking system uncovered huge international systemic failures leading to the economic crisis.  The snowy nation has had a rough time of it.  But as we begin 2011, I ask the question, are they really still in that much trouble?  Figures released by the International Monetary Fund in December 2010 showed that Iceland’s GDP grew by 1.2% in the third quarter, ending the recession caused by the actions of those in its banking sector.  What about those European countries still in economic strife?

In direct contrast to the actions taken by almost all other western countries and most significantly Ireland, Iceland let its banks fail.  It was able to do so because the international risk of contagion is comparably lower than many of the European countries currently receiving bail-outs.  This forced foreign creditors and the banks themselves to foot the bill of failure, rather than the taxpayer.  Essentially, Iceland stuck to free market principles.  Those institutions that operated in an economically viable manner were able to survive; those that chose to take on too many liabilities in foreign currency must face the consequences.  In a system such as banking where when times are good, the mechanisms of capitalism and free market economics define the actions of agents in market, why should those mechanisms not also define what happens when it goes wrong?  In addition to the economic reasoning, there is also the moral issue of the taxpayer having to pay for the mistakes of a small elite.  The actions of many other governments in bailing out the banks served as an attempt to prop up an already unsustainable bubble.  These actions have exacerbated existing public finance problems further, the implications of which are to be felt by those who have not caused the problem.

During the recession Iceland’s economy shrank 11 – 15% depending on your source, but it did so with inflation peaking at 18%, which devalued its debt.  The soaring inflation was furthermore caused by the Icelandic central bank’s decision to halve the value of its currency, the Kroner.  The difference in terms of inflation between Iceland and those euro-zone countries thought to be in the worst economics position, the PIGS (Portugal, Ireland, Greece and Spain), is quite stark.  Iceland’s inflation soared whilst Ireland, for example, is still going through through a sustained period of deflation

Iceland’s inflation is now down to a respectable 3%, hence interest rates are now at 4.5% from an 18% peak.  These inflation rates are, however, higher than the PIGS.  Iceland’s debt situation is also looking up.  Forecasts for 2011 predict a deficit of 6.3% which will soon turn to surplus approaching the mid-point of the decade.  The IMF said Iceland has turned a corner and that its economic performance “compares favourably against other countries hard hit by the crisis”.

Iceland’s current account balance suffered greatly at the beginning of the crisis with the nation running a 26% of GDP trade deficit with the rest of the world, which is much greater than any of the PIGS.  However, due to the high inflation rates and devaluation of its currency, the trade deficit in 2010 fell to just 0.9% of GDP, with a surplus forecasted in 2011.  Comparably, the PIGS are still running significant deficits approaching and exceeding 10% of GDP.  The long-term effects of these deficits are yet to be seen.  One thing is clear, the PIGS do not have the monetary sovereignty of Iceland and hence cannot devalue their debt, they must in effect, toe the economic line of the European Monetary Union and European Central Bank.

Many have portrayed the path chosen by Iceland and subsequent recovery as a model for other beleaguered economies, such as the PIGS group in the EU.  However, such comparisons must be contextualised.  Iceland’s economy is comparably tiny and would have little chance of bringing the entire world economy down if it walked away from its liabilities compared to the aforementioned PIGS.  Defaulting in one of those economies would risk contagion throughout the euro zone and possibly beyond.

Iceland’s monetary independence from the European Monetary Union has been sighted by many as a possible reason for its recent good performance.  Having experienced the worst financial crisis in memory, the country has emerged ahead of many of its contemporaries having endured less punishment than many EU member states.  Greece and Ireland have already been forced to accept bail-outs, and it appears Portugal will soon follow with an €80bn rescue package mooted.

But how sustainable is this recovery?  Iceland’s public debt has reached in excess of 115% of GDP, over four times what it was in 2007.  Furthermore, Government bonds issued in foreign currency are becoming more and more expensive to repay due to the devaluation of the kroner.  Domestic austerity was aided by this devaluation and the subsequent increase in inflation; however, many commentators have indicated this had little to do with the recent return to positive growth.  The turnaround is attributed to the return to current account surplus from deficit.  Moreover, the aforementioned debt burden is not only applicable to government finance; house prices have plummeted in the crisis leaving many homeowners in negative equity.  By no means is Iceland out of the woods, its current account turnaround from deficit to surplus has been accredited to falling imports rather than a surge in exports.  More tough times are ahead.

The implications of bail-outs on the PIGS are also uncertain.  What is obvious is the political motivation behind their economic choices; the European Union needs the single currency.  It is those with vested interests in the Union that have the most to lose; there is an unnerving air of inevitability in what is happening.  Interest rates are remaining low, aimed at a sluggish Germany, whilst those euro-zone countries experiencing increasing inflation desperately need interest rates to rise.  Where the European project falls down is, in throwing hugely different nation economies under a single monetary policy, it lacked the complete supranational economic governance and social mobility required.

On balance, Iceland has taken a radical path of devaluation which saw violent shifts in economic measures, which all looked terrible whilst it was happening.  It may however appear preferable to the long-term damage that may be seen in those countries which have chosen austerity, debt deflation and bail-outs, but like driving a car using only the rear-view mirror, we will not know until it has happened.

About the author: Harry is a first year undergraduate studying Politics and Economics (BA) at the University of Leicester.