Risk and role in conflict

[sigatoka]

This is from Games of Strategy 2nd Edition Avinansh Dixit and Susan Skeath pg 307-309

Risk is not always bad; in some circumstances it can be used to 1’s advantage. A prominent instrument that uses risk is an option.

An option gives the holder the right but not the obligation to take some stipulated action. For e.g. a call option on a tock allows the holder to buy the stock at a preset price, say 110. suppose the stock now trades at 100, and may go to 150 or 50 with equal probability. If the former, the holder will exercise the option and make a profit of 40; if the latter, he will let the option lapse and make 0.

Therefore the expected profit is

0.5*40+0.5*0=20

if the uncertainity is larger that is, the stock can go to, say, 200 or 0 with equal probabilities – the expected profit from the option is

0.5*90+0.5*0=45

Thus the option is more valuable the greater the uncertainty in the underlying stock. The market recognizes this, and the price for which one can buy such an option itself fluctuates as the volatility of the market changes.

Manipulating Risk in Contests:

A prime e.g. is contests such as R&D races between companies to develop and market new information technology or biotech products; many sporting contests have similar features.


The outcome in sporting and related contests is determined by a mixture of skill and chance. You win if

Your skill + your luck > rivals skill + rivals skill

Or

Your luck – rivals luck > rivals skill – your skill

Denote the left hand side by the symbol L; it measures your “luck surplus” L is an uncertain magnitude; suppose its probability distributions s a normal, or bell, curve, as in Figure. At any point on the horizontal axis, the height of the curve represents the probability that L takes on that value. Thus the area under this curve between any two points on the horizontal axis equals the probability that L lies between any two points on the horizontal axis equals the probability that L lies between those points. Suppose your rival has more skill; so you are an underdog. Your “skill deficit”, which equals the difference between your rival’s skill and your skill, is therefore positive, as shown by the point S. you win if your luck surplus, L, exceeds your skill deficit, S. therefore the area under the curve to the right of the point S, which is shaded in Fig represents your probability of winning. If you make the situation chancier, the bell curve will flatten because the probability of relatively high and low values of L increases while the probability of moderate values decreases. Then the area under the curve to the right of S also increases. In Fig, the area under the original bell curve is shown by grey shading and the larger area under the flatter bell curve by the red hatching. As the underdog, you should therefore adopt a strategy that flattens the curve. Conversely, if you are the favorite, you should try to reduce the element of chance in the contest.


Okay I couldn’t get the diagram in but it’s easy to visual. Draw a horizontal x axis, and in the middle of it draw a straight line up.

Then draw two bell’s curve with both their means where the vertical line is. One of the bell’s curve has condensed distribution than the other (that is it is more bunched up) the other has less condensed distribution but the area underneath the curves is equal.

To the right of the vertical line draw another vertical line called S.

It can be seen that the area of the less condensed distribution has a greater area to the right of S than the more condensed one. This means that the chance of victory is greater for the more risky strategy than the less risky one for the underdog.


Thus we should see underdogs or those who have fallen behind in a long race try unusual or risky strategies: it is their only chance to get level or ahead. On the other hand, favorites or those who have stolen a lead will play it safe. A practical piece of advice based on this principle: if you want to challenge someone who is a better player than you in tennis, choose a windy day.

You may stand to benefit by manipulating not just the amount of risk in your strategy, but also the correlation between the risks. The player who is ahead will try to choose a correlation as high and positive as possible: then, whether his own luck is good or bad, the luck of his opponent will be the same and his lead protected. Conversely, the player who is behind will try to find a risk as uncorrelated with that of his opponent as possible. It is well known that in a two sailboat race, the boat that is behind should try to steer differently from the boat ahead, and the boat ahead should try to imitate all the tacking of the one behind.


P.S. this book should be compulsory reading by all in the Pakistani military and admission to become an officer should include an examination on this book. This should not take more than 120 hours but the knowledge and concepts are essential in understanding situations of conflict and cooperation. I would advise everyone to read this book.

Specifically I put it up in response to Keroze claiming that Pak. Shouldn’t bother with armour, that is wrong because avoiding amour is too “safe” or risk averse strategy which doesn’t maximize payoff. But doesn’t this fly against my opinion of greater artillery capability? After all isn’t artillery a low risk strategy? Not really, greater artillery capability is essential for Pak. armour to have any chance of punching through and artillery is easily manufactured domestically which cant be said about those expensive imported F-16’s which wont even have the JDAM’s that is essential in anti-ground role. A combination of Al-Khalid and more artillery is a devastatingly powerful strategy which can be acquired on the cheap and boost GDP and domestic industry and which will be essential in unbalancing India’s military strategy vis-à-vis Pakistan due to increase in risk. Instead of those expensive F-16’s five hundred more Al-Khalid’s could be manufactured along with hundreds of fixed artillery pieces.