Andrew McCurdy
Professor Lorraine Li
Microeconomics 102 (#3917)
12/12/13
Nuclear Negotiations:
Game Theory, International Relations & UN vs. Iran 2013
Background: Since the bloody Iranian revolution in 1979 1 , relations
between the United States and Iran have been tense and often controversial. These
tensions peaked in 2003, when Iran revealed its intentions to build a nuclear
program for electrical power. The US, not believing Iran’s claims of peaceful
intentions, immediately opposed any nuclear development fearing it would lead to
nuclear armament. Ever since, the American-led United Nation Security Council has
pressured Iran to stop. However, Iran continued to develop their nuclear program.
Iran’s refusal sets the stage for a complex game that could decide the fate of
the Middle East and international peace. Understanding this game requires a unique
and comprehensive lens that incorporates the complexities of human behavior and
maintains objective analysis. This lens comes in the form of Game Theory. A branch
of economics, Game Theory is a “formal way of analyzing the interactions among a
group of rational agents who behave strategically” (Dutta 4). Often applied to
numerous disciplines including economics, biology and international relations,
Game Theory attempts to mathematically capture behavior in strategic situations. A
The revolution overthrew the US supported Shah and their government. The US
made active efforts to suppress the uprising, but failed. Further, it was a long time
before the US even recognized the new regime. The US did more to oppose the
revolution than anybody else. This would carry forward into US-Iran relations.
1
game consists of five key elements: rational players2, interaction, strategy, rules
(and/or information set) and payoffs (real or perceived).
Players: In this game, the key players are Iran, Russia, China, Germany,
France, the United Kingdom and the United States3. Together these nations
(excluding Iran) create the so-called “P+1” or all the permanent members of the
United Nations Security Council plus Germany (a moderator). Every player in the
P+1 has nuclear capabilities but Iran4. This in many ways leaves Iran at the mercy of
the others in military and political power.
Each of the players in the P+1 has an invested interest in avoiding a nuclear
capable Iran. In the interest of time and space, this game will include just two
players: the UN (P+1)5 and Iran.
Payoffs: Each player in this scenario has four potential payoffs that are
arbitrarily assigned a value on a 1-4 scale. The worst possible outcome, which
happens to be the UN’s greatest asset, is a US invasion and carries an expected
payoff of -3. Iran’s second worst-case scenario is having no nuclear ability but still in
conflict with the UN thus given an expected payoff of 1. Another scenario is to have
nuclear capabilities but solely for energy production without the ability for
armament (expected payoff = 2). Their second best payoff is to have the nuclear
Rational in this case indicates that each of the players will act in their best interest
and proceed with a strategy that gets them the largest payoff.
3 It should be noted that this is a simplified list of players. A comprehensive study
would include hundreds of players including political factions, individuals and
various interest groups worldwide.
4 While Germany is not a primary weapon holder, the US has weapons stationed in
Germany as part of a weapons sharing agreement. This involves non-American
personnel handling and distributing the bombs in the event of war.
5 This is an assigned name. It should not be held to the same standards of the United
Nations. This is simply a coalition of nations led by the US.
2
capabilities for a bomb but not to have it actually made yet. In the case of war, they
want the ability to make it in an emergency, perhaps in 4-6 months. In this scenario,
the expected payoff equals 3. Finally their absolute best-case scenario would be to
actually make a bomb and wheel it out of the facility for a press conference
(expected payoff = 4).
The expected payoffs for the UN are exactly the opposite of Iran. For each,
strategy Iran achieves, the UN will get exactly the opposite payoff. Thus if Iran
achieves its ideal scenario the UN’s expected payoff will equal -4. And if Iran
achieves its second best scenario, the UN’s expected payoff will equal -3 and so
forth. If Iran achieves its second worst-case scenario, the UN still has an
uncooperative Iran to deal with and thus is given a -16. Finally, if it comes to an
invasion, the UN (mostly the US) suffers equally with Iran (expected payoff = -3).
While Iran will lose its freedom, the UN will lose money and manpower.
Game Setup: The format in which the game designed, it is considered a
“zero-sum” game. 7 A zero-sum game is defined as a game “in which the payoffs of
the two players add up to zero, no matter what strategy vector is played” (Dutta
139). This type of game has a number of qualities. First, it consists of just two
players. Second, the player’s must be strictly opposed. That is to say that one
Note that the UN and Iran have irreconcilable ideological differences. Thus even an
agreement leaves the UN at a negative outcome. They still have to deal with a
belligerent Iran. Iran, on the other hand, is still an aggressor and can pursue actions
that hurt UN members in the event of achieving their worst-case outcome.
7 In reality, zero-sum games are rare. This technically is not a zero-sum game
because in the event of war, both parties are harmed. Further almost all games
consist of more than two players (including this one). Further, based on long-term
goals and the nature of learning, zero-sum games are often disqualified. But for the
purposes of illustration, the zero-sum game format is exceptionally informative.
6
player’s gain results in an equal amount of loss to the other player (Dixit and
Nalebuff 178). Thus the player’s goal is to minimize his opponent’s maximum payoff
while the other player should try to maximize his own minimum payoff (Dixit and
Nalebuff 178). This quality sets up an unusual characteristic, in zero-sum games “the
minimum of the maximum (mini-max) payoffs equals the maximum of the minimum
(maxi-min) payoffs. Neither player can improve his position, and so these strategies
form an equilibrium of the game” (Dixit and Nalebuff 178).
It happens that this zero-sum game is a particular kind of game called a
prisoner’s dilemma8. The most elementary of all games, the prisoner’s dilemma is
defined by its lack of available information. Neither player knows what the either is
going to do but they do know the position the other player is in. At best they can put
themselves in the other player’s shoes and try to predict the opponent’s strategy.
One of the unique aspects of international negotiations is that neither
country can completely and permanently leave the interaction. Nations do not
disappear. Rather nations are forced to deal with each other in ongoing
relationships. In game theory, this is called a repeated game, where the game
repeats over and over with each interaction. In on-going relationships, the promise
of future rewards and threat of punishment often provides incentives for good
behavior today. In this case, the promise of future payoffs in money, oil or surrender
Technically speaking, prisoner’s dilemmas are not zero-sum games because in one
of the outcomes, both players can gain. In the classical version, it is if neither
prisoner confesses. However, for the purposes of this paper, this will be a zero-sum
game for two reasons. First, the UN’s best possible outcome is to limit its losses.
Second, because of the UN’s (really the US) superior military forces, it has a “trump
card”, which causes Iran to strategize as if it is a zero-sum game, not a simple
prisoner’s dilemma.
8
of hostages (also potentially money or oil or military) encourages both sides to
cooperate and reach a resolution. Likewise, the threat of potential harm, in the form
of Iranian nuclear arsenal or a UN invasion, also encourages cooperation.
There are two other key aspects to a repeated game. The first is that all costs
or benefits that come from the previous games become sunk and should not
influence the next game. That is not to say previous games should not be a
consideration. As such, the second key aspect is that reputation is vital to strategic
development in repeated games.
Strategy: Sadly, it is impossible to know exactly the strategies either party
can employ because there simply is not enough public information about what each
has as its assets. But it is not hard to assume that the most reckless pure strategies
for both are either military force (allowing the other to proceed with any action and
respond with military force) or passivity (allowing the other player to proceed with
any action and not respond). The other option is a security strategy (explained
below). In the event they employ a mixed or pure strategy (other than the security
strategy) their maximum potential payoffs will be higher, and their minimum
potential payoffs will be lower.
The Security Strategy: The UN will have a negative outcome regardless of
Iran’s actions. Thus UN’s objective becomes to minimize Iran’s payoff and Iran’s
objective is to maximize its own minimum payoff (the mini-max/maxi-min theory).
This strategy is known as a security strategy. The security strategy guarantees Iran
its maxi-min payoff and the UN its mini-max payoff. It is always the best strategy in
zero-sum games. Further, because these are rational players, each can assume that
the other will play its best strategy (security strategy) in response to their best
strategy (also the security strategy).
The Games Begin: While the center of this essay is the game that each player
entered in late November 2013, it is important to recapitulate the games leading up
to the grand-finally. When the games begin, in 2003, the UN and Iran have poor
relations. Iranians inherently dislike the UN. The dislike goes beyond religious and
ideological reasons. They know for instance that US and European nations provided
Saddam Hussein with poison gas materials during the Iran-Iraq war leading to the
horrific deaths of millions of Iranians (Filkins). Further, the United States recently
betrayed Iranian officials (Filkins). Fearing invasion, Iran had tried to cooperate
with the US after 9/11. Several key officials stuck their necks in Iran to try and aid
the US. However, just a few weeks into the relationship, President Bush labeled Iran
as one of the “Axis of Evil”, destroying the reputation of the Iranian officials and the
promise of partnership with it (Filkins). Soon after this diplomatic collapse, Iran lost
its fear of invasion and actively started supplying and even fighting with Iraqi rebels
against American soldiers (Filkins). The one nation that has any kind of positive
relationship with Iran is Russia, with whom they are on speaking terms.
In light of the nature of these previous attitudes and interactions, the players
are each assigned a current value. Iran starts at a +1 because of its active resistance
to America and the UN. Meanwhile, the UN begins at a -1 because it has to deal with
the thorn in its side that is Iran.
Over the course of the next few interactions between the UN and Iran, Iran
progresses positively and the UN negatively. The reason for the continual disconnect
can be found politically but also in Mohammad Ali Mousavi’s fascinating paper using
basic game theory to explore US-Iranian relations. Mousavi describes the game in a
game tree where at each interval the US or Iran must to either accept or deny the
demands from the other party. If either chooses to accept the other’s demands, the
game ends. But if they continue to deny, then the game continues:
(Mousavi 128)
This leads him to find that for each individual game:
“If the US accepts a nuclear Iran, then the game terminates and this
choice costs a units to the US: (CA = a). On the other hand, if the US
denies a nuclear Iran, and decides upon more sanctions or other
actions, then Iran in response may insist on further progress in its
nuclear program with a probability equal to (1-p) or it may accept to
leave its programs with a probability equal to p. If the US costs for
either of these decisions are c and b respectfully, then the average
cost to the US is equal to: CD = p x c + (1 – p) x b… No doubt the best
decision for the United States is the one, which minimizes its cost
(remember the security strategy). So we have the following decision
strategy:
Accept
>
P
CA
CD
Accept
>
(a-b)/(c-b)
<
Deny
<
Deny
Or
(Mousavi 130)
This becomes more interesting as the game turns into a repeated game. If the US
demands Iran accept its terms and terminate its programs, then the game continues
until Iran accepts to suspend the programs. The result looks like this:
CD = c + b ((1 – p)/p)
So the decision is as follows:
C + b ((1 – p)/p)
Accept
>
a
<
Deny
(Mousavi 131)
To put this in plain English, this equation suggests that at each single step of the
game, it is wiser to refuse the other player’s conditions. However, it is better for
both players to accept the other’s terms as the final result.
This equation also explains with this repeated game has lasted a decade.
When the player looks at the momentary costs and benefits, they find that it is more
beneficial to continue the game to the next step than it is to end it. However, an
intelligent player will realize that continuing the game for an extended period may
not turn out favorably. Therefore, this becomes a classic long-term vs. short-term
decision for each party. The short term offers the promise of higher rewards while
the long-term threatens greater punishment.
This explains how the players arrived at the table in November of 2013 still
without a deal. Each player chose to continue the games at each interval until now.
Once again facing a prisoner’s dilemma. The outcome matrix looks like this:
(Mousavi 138)
By November of 2013, Iran has already reached a payoff of +2 in the games and the
UN a -2. With this in mind, let’s take a look at what the outcome matrix looks like
using the payoffs established earlier in the paper:
United Nations
a
b
A
-2, +2
-2, +2
Iran
B
-3, +3
-3, + 3 or -3, -3
With the game matrix set, let’s take a look at each player’s options. There are five
most likely outcomes (the fifth is the trump card: military invasion from the UN/US).
This matrix actual covers two possible decisions from each player.9
Because of how the high likelihood is of these outcomes, it is possible to keep it to a
four-quadrant matrix. I initially tried to create a matrix that covered all the possible
options (with sixteen potential outcomes), but it proved too complicated.
9
In quadrant-I (strategies a, A), the UN and Iran agree to a treaty that allows
Iran to keep its civilian nuclear power (+2) but agrees to stop attempting to
weaponize it leaving the UN with a -2 outcome. Agreement from both sides ends the
conflict.
In quadrant-II (strategies a, B), the UN accepts that Iran has nuclear weapon
capabilities though is still months away. In this event, the game continues. Iran will
now face the decision of whether to go for a +4 and try to wheel out a nuclear bomb
and the UN has to hope that Iran will stop production for the conflict to end.
In quadrant-III (strategies b, A), neither party agrees to a treaty but Iran does
not continue to pursue further nuclear armament for fear of invasion from the UN.
This leaves Iran at a +2 and the UN at a -2.
In quadrant-IV (strategies b, B), Iran attempts to wheel out the nuclear bomb
but the UN refuses to allow that to happen and leads an invasion that brings Iran to
its knees. The result is a -3 for the UN because war costs money and lives.
Meanwhile, Iran loses its independence and faces the same future Iraq did after the
Iraq war. While this would be catastrophic for Iran (-3), it is not as bad as the UN
launching a nuclear missile at Iran (-4). Regardless, this outcome will also bring an
end to the conflict.
Strategic Analysis: With the potential out comes clear, let’s take a look at the
strategies each can pursue. For Iran, the strategies are either to agree to sanction
from the UN or not. Strategy A is their security strategy in which they stop pursuing
nuclear weapons. It attempts to secure their gains thus far with a civilian nuclear
power plant. Iran’s strategy B is a high risk, high reward plan. In taking this strategy,
they hope that the UN continues to only at the short-term payoffs and not the long
term costs. Iran cannot be sure where the UN has internally drawn the line for what
will require military intervention. If the UN has indeed, drawn that line here, Iran
faces war and destruction.
For the UN, all strategies but one leads to higher costs. Though the shortterm view may offer less cost, the long-term cost will in the end be worse. The UN
should have the line drawn at this game at the latest. Looking at the outcome matrix,
the UN’s best option becomes clear. For the UN, strategy a strictly dominates
strategy b. Regardless of Iran’s decision, strategy a offers the possibility of a higher
reward or lower loss depending on how you look at it. Further, the UN should
employ one of Game Theory’s primary principles: put yourself in your opponent’s
shoes. If they look closely they will realize that Iran’s security strategy is strategy A,
meaning that the chance of achieving their best-case scenario is actually quite high.
Now looking at the game as a whole, the most likely outcome of the game is
quadrant-I. In this event, the UN cuts its losses and Iran secures its gains. While this
may not be the best outcome for Iran, it should be happy that it got this far.
However, for the UN, this is the best possible outcome.
These were the strategies and choices the UN and Iran had at they sat down
on November 23, 2013. And at 3 a.m. they reached an accord. The agreement is
designed to halt Iran’s nuclear program. In return for Iran’s agreement, the UN
offered six to seven billion dollars in sanctions relief (Gordon 1). This agreement
ends the decade long games. And it played out just as the outcome matrix suggested
and in the end both players chose their best strategies.
Work Cited
Dixit, Avinash and Nalebuff, Barry. Thinking Strategically: The Competitive Edge in
Business, Politics, and Everyday Life. New York, NY: Norton & Company, 1991.
Print.
Dutta, Prajit. Strategies and Games: Theory and Practice. Boston, MA: Massachusetts
Institute of Technology, 1999. Print.
Filkins, Dexter. Interview with Terry Gross. Fresh Air: Meet the Iranian Commander
Pulling Strings in Syria’s War. NPR, 2013. MP3.
Gordon, Michael. “Accord Reached With Iran to Halt Nuclear Program.” New York
Times 23 November 2013. Print.
Mousavi, Mohammad Ali. Iran-US Nuclear Standoff: A Game Theory Approach.
Iranian Review of Foreign Affairs. Vol1. No1. Spring 2010.