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 game consists of five key elements: rational players[2], 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 States[3]. 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 Iran[4]. 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 scenariois having no nuclear ability but still in conflict with the UN thus given an expected payoff of 1. Anotherscenario 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 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 -1[6]. 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 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 dilemma[8]. 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 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). Theother 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 theirbest 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 theUS accepts a nuclear Iran, then the game terminatesand this choice costs a units to the US: (CA = a). On the other hand, if the US denies a nuclear Iran, anddecides upon more sanctions or other actions, then Iran in response may insist on further progress in itsnuclear program with a probability equal to(1-p) or it may accept to leave its programs with a probabilityequal to p. If the US costs for either of these decisionsare 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 Statesis the one, which minimizes its cost (remember the security strategy). So we have thefollowing decision strategy:
Accept
CDCA
Deny
Or
Accept
P(a-b)/(c-b)
Deny
(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:
Accept
C + b ((1 – p)/p)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 Iran
AB
-2, +2
-2, +2
-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]
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 short-term 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.
[1] 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.