Home Opinion The Nash Equilibrium: Applications in the Security World

The Nash Equilibrium: Applications in the Security World

by Brian Sims
Mike Hurst CPP

Mike Hurst CPP

In Game Theory, the Nash Equilibrium, itself named after the mathematician John Forbes Nash Jr, is a proposed solution of a non-co-operative game involving two or more players in which each player is assumed to know the equilibrium strategies of the other players and no player has anything to gain by changing only their own strategy. Is there any application for this in today’s security environment? Mike Hurst investigates.

Many of you will have read the book or seen the film entitled ‘A Beautiful Mind’ which is all about the brilliant, but troubled mathematician John Nash, who’s work on Game Theory was ultimately to lead to him being bestowed with the huge honour of a Nobel Prize in Economics.

In terms of Game Theory, if each player has chosen a strategy, and no player can benefit by changing strategies while the other players keep theirs unchanged, then the current set of strategy choices and their corresponding pay-offs constitute a Nash Equilibrium.

Like many concepts, Game Theory can be incredibly complicated, but there are ideas that security businesses could benefit from simply by being aware of them. The classic example of the Nash Equilibrium is the prisoner’s dilemma.  Two men are arrested in relation to  a gangland killing. The police may not have sufficient evidence to obtain a conviction. The men are held and questioned in separate police stations such that they cannot communicate with each other. If they both confess to this brutal murder, they each face a nominal ten years in jail.

If one stays quiet while the other confesses, then the confessor will be able to go free, while the other will face a lifetime in jail. If both stay quiet, then they each face a relatively minor charge and only a year in custody.

If they could confer, it would be best for both to keep quiet. Given the situation, an economist armed with the concept of the Nash Equilibrium would predict the opposite: the only stable outcome is for both to confess.

Making the best decision

In a Nash Equilibrium, every person in a group makes the best decision for themselves based on what they think the others will do and every member of the group is doing as well as they possibly can. In the case of the prisoners’ dilemma, keeping quiet is never a good idea, whatever the other criminal chooses to do. Since one suspect might have come clean and told the police what happened, informing avoids a lifetime in jail for the other.

If the other does keep quiet, then confessing sets him free.

How can this work in real business life? Companies may strategise on the outcome if a competitor raises or lowers prices, for example. An economist can help predict this using the Nash Equilibrium. This works particularly well in an oligopoly, where, for example, two large CCTV manufacturers are deciding on pricing strategies to compete against each other. In this situation, they will probably put more pressure on their customers than they could/would do if there was fierce competition from many major competitors.

Sometimes, of course, decisions that are good for individuals can be very bad for a group/society. The Nash Equilibrium can be used to help explain why we emit too much carbon dioxide or over-exploit the rain forests or over fish the seas. However, this simple idea can also aid economists to advise Governments on how to design auctions to maximise the most from bidders and benefit their exchequers. An example of this is the sale of 3G licences in the UK that raised no less than £22 billion.

Mike Hurst CPP MSyI FIRP is Vice-Chairman of ASIS UK and Director of HJA Consult

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