快猫短视频

ON GOOD FRIDAY two years ago, an event took place in Northern Ireland that
many thought they would never live to see. After months of negotiation, years of
conflict and centuries of mistrust, the various warring parties finally agreed
on a power-sharing accord to bring peace to that troubled province.

More than thirty years of conflict between the British Government, the Irish
Republican Army (IRA)鈥攚hich is determined to make the province part of the
Republic of Ireland鈥攁nd the Ulster Unionists, who are equally determined
that the province remain part of the UK, had left 23 000 killed or injured. But
on 10 April 1998, the conflict finally seemed to be at an end.

Then in February this year, the whole peace process seemed to fall apart.
Following the failure of the IRA to hand over its weapons, power-sharing was
suspended, and the province was once more ruled from London. Now it all appears
to be back on track, with the IRA allowing independent observers to inspect some
of its arms dumps to show that the weapons have not been used.

So is this really the end of the conflict? Surely there is no way of even
guessing where the roller coaster of events in the province will go next.

But perhaps there is. At the end of December last year, two scientists
published a mathematical analysis of the Northern Ireland conflict that seems to
fit most of its twists and turns. It is based on a mathematical method of
analysing conflicts known as the theory of moves (TOM), invented by Steven
Brams, a political scientist at New York University. TOM is causing a stir for
its power to illuminate situations ranging from the eponymous dilemma of Joseph
Heller鈥檚 novel Catch-22, to the all-too-real issue of how people
respond when confronted by a mugger in a backstreet.

For years, the standard way of analysing such situations has been game
theory, a mathematical bag of tricks that casts some light on conflicts and how
they might be resolved. Brought to prominence during the Cold War, game theory
has been applied to a host of deadly confrontations, from drunk teenagers
playing chicken through to the 1962 Cuban missile crisis. It has acquired a
reputation for being a clever way to boil down complex situations to their
essence.

Game theorists start by looking at the options available to each protagonist
in a given confrontation. An example is the 鈥減risoner鈥檚 dilemma鈥�, where two
criminals can each choose to betray the other by confessing their crime, or to
stay quiet. If they both stay quiet, they get short prison sentences; if they
both confess, they get intermediate sentences; but if only one confesses, the
rat goes free while the other stews in prison for many years. These consequences
can be summarised in a 鈥減ay-off matrix鈥�, showing the desirability of the
different outcomes for both protagonists. Game theory then analyses the
situation to see what the best strategies are. In a one-off game, a prisoner
always does best by betraying their partner in crime. No matter what the partner
decides, each prisoner can do better by confessing than staying quiet.

So standard game theory is static. It assumes that adversaries find
themselves in some situation, decide what best to do, and stick to their
decision. But real conflicts are more dynamic. Those involved look for signs of
what their opponents are likely to do, changing tack and preferences, and
responding to their opponents鈥� changes in turn. 鈥淲e all know intuitively that
politics is sequential, that moves and countermoves are what drive such
phenomena as negotiations, revolutions and war,鈥� says Jeffrey Togman, a
political scientist at Seton Hall University in South Orange, New Jersey.

Since the early 1980s, Brams has been putting this intuition onto a
mathematical footing. 鈥淭OM adds a dynamic dimension by assuming that players
look ahead before making a move,鈥� says Brams. This injection of dynamism, he
says, allows TOM to capture a host of subtleties beyond the reach of the
standard theory. Over the past few years, Brams has explored these subtleties in
a book and a series of papers which use TOM to probe well-known conflicts. TOM
often reaches different conclusions from standard game theory鈥攁nd the
difference can be as stark as handshakes all round versus all-out war.

The matrix

Brams and Togman begin by constructing the same pay-off matrix as in standard
game theory. Where TOM differs is in analysing how these pay-offs affect
strategy. Take armed mugging. The victim has two choices鈥攖o resist or give
in鈥攚hile the mugger can either just threaten physical violence or actually
use it. The payoff matrix (see Diagram)
shows the ratings given by the two players to each state they can find themselves in,
from 鈥�4鈥� for the best to 鈥�1鈥� for the worst.

For example, the victim鈥檚 best state is that of resisting a mugger who
doesn鈥檛 resort to violence (giving a 鈥�4鈥� for the victim at the intersection of
鈥淩esist鈥� and 鈥淒on鈥檛 use violence鈥� at the top right-hand corner of the matrix).
Then the victim gets to keep their money and doesn鈥檛 lose any teeth. This state
is the worst of all for the mugger, however, who rates it as 鈥�1鈥�. This outcome
is denoted as (4,1).

Standard game theory portrays the situation as static, with the victim and
mugger simultaneously deciding on what best to do, and sticking with that
decision. It predicts that the most likely outcome will be a state in which
neither player can do better by changing strategy鈥攁 so-called Nash
equilibrium. In the mugging conflict, this occurs when the victim resists and
the mugger uses violence, which has a (2,2) rating. Victims who choose not to
resist, on the other hand, would end up with their worst option, rating just 1,
while muggers who didn鈥檛 use violence would also end up with their worst
outcome. So standard game theory predicts that muggers will use violence, and
victims will resist.

But by capturing the dynamic aspects of this conflict, TOM reaches a
different conclusion. The victim faced by a mugger might initially think of
resisting, preventing any chance of suffering the (1,3) state, and possibly
achieving the best-possible outcome of (4,1). But it鈥檚 a strategy not without
its risks: seeing that the victim is stubborn, the mugger might use violence,
putting them in the (2,2) state.

If the victim has second thoughts and decides to hand over their valuables,
that gives the mugger an incentive not to become violent. The non-violent mugger
gets a reward of 4 instead of 3, while the victim gets 3鈥攏ot perfect, but
far from the worst outcome. In short, by including the effect of move and
counter-move by the two participants in a conflict, TOM predicts that victims of
muggings will typically not resist, and that muggers will typically not resort
to violence.

So what happens in real life? 鈥淥verwhelmingly, the victim chooses not to
resist,鈥� says Brams, adding that muggings also typically do not involve
violence, flatly contradicting the prediction of standard game theory.

Superpower games

TOM applies not just to street-level conflicts, it also gives pointers to on
how nuclear superpowers square up to one another. And once again its predictions
can be radically different from those of standard game theory.

For example, when the Yom Kippur War erupted in October 1973, with Israel on
one side and Egypt and Syria on the other, the response of the US seemed
dangerously reckless, at least according to game theory. As soon as Israel
started to get the upper hand, the Soviet Union鈥攚hich was supplying arms
to Egypt and Syria鈥攕aid it wanted to broker a peaceful settlement. Richard
Nixon, the pro-Israeli US president, was faced with the choice of
cooperating with the Soviets or intervening directly in the war. His response
was stunning: he put US military forces on global nuclear alert. Nixon thus sent
a clear message to the Soviets: if they continued feeding arms to Egypt and
Syria, he鈥檇 rather have war between the Superpowers than back off.

In the process, Nixon turned this conflict with the Soviet Union in to a
prisoner鈥檚 dilemma. Terrifyingly, the most plausible outcome according to game
theory would be for the superpowers to escalate the conflict. Was Nixon insanely
reckless to put US nuclear forces on alert?

History suggests not. Within three weeks the war was effectively over, and
the US and Soviet Union went back to routine cold war bickering. So why did
Nixon鈥檚 overreaction succeed when game theory predicted its catastrophic
failure?

According to Brams, TOM can explain why because, unlike standard game theory,
it recognises the crucial importance of the starting positions of the
adversaries in a conflict. Some starting positions are stable, in the sense that
there鈥檚 no advantage in switching to any other. But others are unstable, and if
the game begins in one of these, there鈥檚 an incentive to explore the
consequences of moving to other states.

In the prisoner鈥檚 dilemma created by Nixon, TOM reveals that if both sides
start in a state of no direct involvement, then they鈥檒l stay there: there鈥檚
nothing to be gained by switching to others. So by turning the conflict into a
prisoner鈥檚 dilemma, Nixon ensured that the Soviet Union would have no incentive
to shift towards a dangerous, direct confrontation with the US. And, mercifully,
they did stay put.

TOM shows that some conflicts are more pathological. In a paper published
last year in Rationality and Society (vol 11, p 139) Brams and computer
analyst Christopher Jones unveiled what they call Catch-22 games, after the
famous paradox in Joseph Heller鈥檚 novel.

Set in the Second World War, Catch-22 describes how US Air Force combat pilot
John Yossarian finds himself in a situation where he will no longer have to fly
dangerous missions if he can persuade an air force doctor that he鈥檚 insane. But
then he falls foul of Catch-22: that the very act of trying to persuade a doctor
of his insanity is an entirely sane thing to do, and thus proves that he is fit
to fly more missions. Yossarian is thus doomed to continue flying, as the other
player in this 鈥済ame鈥濃�攖he air force鈥攃an鈥檛 lose.

Using TOM, Brams and Jones found that the Catch-22 paradox lurks in more than
20 per cent of all the possible types of conflicts involving two parties. In
Yossarian鈥檚 game, the same side always wins, but there is another kind of
Catch-22 game in which neither side can get what they really want. These
conflicts are likely to rage forever, just switching between the various states.
Those finding themselves in such a situation can either slug it out endlessly,
and pointlessly, or recognise that compromise is as good as it gets.

All of which sounds like the situation in Northern Ireland. In fact, TOM
shows that this seemingly endless conflict is not like either kind of Catch-22
game, and this turns out to be both good news and bad.

The origins of the conflict are complex, but in the simplest terms it can be
considered a struggle between two sides: the British government and the
Unionists on one, and Sinn Fein and the IRA on the other. Both sides can either
adopt a conciliatory approach to Irish unity, or take a hard line. Rating the
various outcomes of this simplified conflict, political theorists draw up a
pay-off matrix (see Diagram).
The first digit represents the payoff for
Sinn Fein/IRA, the second for the British government and Unionists. So, for
example, the best outcome for Sinn Fein/IRA is one in which they insist on
getting everything they want, and the UK government just rolls over鈥攖hus
giving a 鈥�4鈥� at bottom left corner of the matrix. Such a demonstration of
weakness in the face of terrorism is unacceptable to the British government,
however, leading to a rating for that outcome of 鈥�1鈥�, and thus an overall score
of (4,1).FIG-mg22414701.JPG

Completing the matrix using similar arguments, standard game theory then
shows that the most stable state is (2,4): the one in which the British
government maintains a hard line, refusing to negotiate, and Sinn Fein/IRA make
all the concessions: neither side can improve their pay-off by switching
strategies. So why has this state not prevailed over the past 30-odd years of
violence in the province?

Once again, the ability of TOM to capture the dynamics of the conflict seems
to offer an explanation, because it raises the possibility that the two parties
in the conflict do not have to stay put, but can move to other states. In the
case of Sinn Fein and the IRA, it shows they have a real incentive to force the
conflict out of the 鈥渟table鈥� state (the Nash equilibrium). And the obvious way
to do that is through violence. By adopting a campaign of violence, the IRA has
put the British government in its two worst states: (4,1) and (1,2). In the
past, the government opted for the less bad of these, adopting a hard line by
refusing to negotiate with the IRA. The result is depressingly familiar: a
province locked in conflict for decades.

So why did the IRA call a ceasefire in 1994? On the face of it, such a
conciliatory move makes no sense: it would simply move the conflict back to the
(2,4) state and leave it there, because the British government has no incentive
to shift from its hard-line strategy. To do so would reduce its pay-off to 3.
But TOM focuses attention on any ability the adversaries may have to move around
the matrix of possibilities.

Exercising power

In Northern Ireland, the IRA had already spent decades showing all too
graphically that it could move the conflict out of the supposedly stable state,
round to the (1,2) state. And when two years of ceasefire had produced no signs
of the British government moving from (2,4) to (3,3), the IRA exercised that
power by bombing Canary Wharf in east London in February 1996. For a year or so,
the conflict seemed to be back in its old confrontational (1,2) state. But in
July 1997 the IRA again called a ceasefire, and this time it seemed to work.

Why? Because, say Brams and Togman, things were different: the Canary Wharf
bombing had shown that the IRA would not allow the conflict to stay stuck in
(2,4). It was a threat that appears to have succeeded, for this time the
ceasefire was followed by a move to (3,3), and compromises on both sides. In
other words, to the Good Friday agreement.

Ever since, progress towards permanent peace has been hamstrung by the key
issue of disarmament. The unionists have insisted that the IRA surrender all its
arms, and the IRA has refused. Even now, with its offer to allow independent
inspection of some arms dumps, the IRA is a long way from actually relinquishing
all its weapons.

And, according to TOM, it is unlikely to. If the IRA gives up its arms, it
will lose the ability to prevent the current situation sliding back into the
(2,4) state, in which the British government gets everything it wants, and
staying there forever. So for the unionists and British government, the lesson
from TOM is clear: the current offer from the IRA is probably as good as it鈥檚
ever going to get.

Brams and Togman are the first to admit that TOM is a simplification of the
situation in Northern Ireland. For one thing, not all decisions are made
rationally鈥攂oth sides are driven by deep-seated emotions that TOM does not
reflect. It鈥檚 a limitation that Nigel Howard, a veteran game theorist and
consultant in conflict resolution, has tackled with his own extension of game
theory, known as drama theory
(快猫短视频, 10 October 1998, p 26).
Drama theory includes the effects of irrationality. For example, convincing your
opponent that you鈥檙e crazy can affect their thinking, sometimes to your
advantage.

Perhaps a combination of TOM and drama theory could represent conflicts even
more realistically? 鈥淭OM is a rationalisation that players, under the influence
of emotion, might use to eliminate dilemmas,鈥� says Howard. 鈥淚t鈥檚 a most
interesting and ingenious rationalisation, and I believe that real players might
use it.鈥� To see how well their refinements of standard game theory apply to real
people, Howard and Brams are discussing the possibility of working with
psychologists in a three-year project funded by Britain鈥檚 Ministry of
Defence.

Such reality checks are certainly needed: conventional game theory has often
fared badly when confronted with real life. But while a bunch of numbers will
never fully capture the complexities of human conflict, Brams believes that it
is still worth searching for ever-better approximations: 鈥淲hat game theory and
TOM can do is give insights into possible paths to peace, as well as into
difficulties that may be encountered along the way.鈥�

And if that can bring a glimmer of hope to the millions living under the
shadow of conflict around the world, it will be no mean achievement.