Xenophon, Khalilzad, and the prisoner’s dilemma, a game theory approach to the Afghan peace process

Nicole Valentini
7 min readJul 3, 2021


Game theory can be described as the mathematical study of conflict and strategy among rational players. This interesting discipline has often been used by analysts and researchers to analyze some of the biggest international conflicts and it might still be useful today to provide a different point of view on the peace process in Afghanistan.

In 1944 the mathematician John von Neumann and the economist Oskar Morgenstern published a book that conceived an outstanding mathematical theory of economic and social organization. Their book “Theory of Games and Economic Behaviour” not only revolutionized economics but provided a new field of scientific inquiry that would have since then been used to study the most disparate phenomena: game theory. Modern game theory emerged as a scientific attempt to model and predict the strategic interaction between two or more rational decision-makers. While used in several disciplines, such as mathematics, economy, biology, social and political science, during the 40s and the 50s, game theory has been used by the US army for research purposes.

Universities and research institutes started to be interested in game theory as well. Among them the well-known RAND corporation, a historical think-tank ironically called by Pravda the American “academy of science and death”. In 1954 the RAND corporation published a research study titled “The complete strategist, being a primer on the theory of games of strategy”. It wouldn’t be therefore surprising, if also the RAND senior political scientist in charge to end one of the longest wars in American history, Zalmay Khalilzad, would have at least some notions of game theory. And again, it was two members of the RAND Corporation, Merrill Flood and Melvin Dresher, who in 1950 framed what’s probably one of the most well-known examples of game theory: the prisoner dilemma. In this game, two prisoners accused of a crime are placed in two separate rooms without the possibility to communicate. Both are aware of the consequences of their decision. If both prisoners defect, betraying each other, they will go to jail for two years; if neither confesses, both will go to jail for one year; and if one betrays while the other does not, the defector will be free while the other player will be jailed for 3 years.

The dilemma faced by the prisoners is that whatever the other does, the betrayal will result in a better payoff than cooperation, because the player who betrays will be free, but mutual defection will result in a worse outcome for both the players, who will risk spending two years in prison. Cooperation is irrational, but it yields a better outcome than mutual betrayal.

The prisoners’ dilemma shows how a group whose members pursue rational self-interest may all end up worse off than a group whose members act contrary to rational self-interest, a key concept that should be taken into consideration in every negotiation. A 2020 HRW article about the dispute related to the Taliban demand to free 5000 prisoners before the start of intra-Afghan peace negotiations and the importance of victims’ inclusion, was interestingly titled “Afghanistan’s Prisoner Dilemma. Dispute Over Releases Shows Need to Include Victims’ Groups in Talks”. Even in this Afghan version of the prisoner’s dilemma, cooperation could have resulted in the highest payoff for both the players. The Taliban would have released the captured soldiers, while the government would have released the Taliban detained in its prisons.

The Afghan government and the Taliban though were not the only players involved in the game. The Trump administration in fact pressured the Afghan government to free the Taliban prisoners as the US elections were approaching, and the agreement, rather than opening new glimmers of peace, has resulted in an increase of Taliban attacks, who as claimed by this AAN report have probably “taken advantage of the stronger position which the peace process has left them in”. On April 13, the new Biden administration declared its intention to withdraw the US troops from Afghanistan by Sep. 11. It might come natural starting to believe at this point, the Taliban would feel victorious and ready to take over, yet war can never be a zero-sum game, a game in which one player’s gain is equivalent to another’s loss.

According to the Economics Nobel laureate, cold-war strategist, and Master of Game Theory, Thomas Schelling, war cannot be considered a zero-sum game, because it requires at least a minimum of cooperation or accommodation between the parties. These parties, therefore, are both partners and adversaries. For example, thinking about the cold war, Schelling noticed that both the US and the USSR had an immense joint interest in avoiding a nuclear war. A successful peace process should therefore always consider what could be the joint interest of the parties. As complex as finding what the common interest is probably determining who the parties are.

Who are the players of this war? Is this a war between the Afghan government and the Taliban as it has always been considered by most of the international community? Or is it just a proxy war played by some of Afghanistan’s hostile neighbors? How much do the ethnic, proxy, and international elements of this war weigh on the balance of war? As the Professor of Economics and Sarin Chair in Leadership and Strategy at Berkeley Haas, Steve Tadelis, pointed out:

“The value of our conclusions will be only as good as the sensibility of our assumptions. There is a famous saying in computer science — “Garbage in, garbage out” — meaning that if invalid data are entered into a system, the resulting output will also be invalid”.

In a complex multi-layered conflict such as the Afghan one, where multiple state and non-state actors are involved, it might be difficult to discern the valid information from the wrong ones. Understanding the conflict and the actors’ motivations is vital for the negotiations’ success because as game theory teaches us, what the game is, defines what the players do.

Yet if there is something on which most of the parties agree, it is the necessity to negotiate to avoid the continuation of the conflict. As Schelling pointed out, bargaining avoids or closes war. Wars require limits, and limits require an agreement. But what to do if the parties involved are distrustful? Let us take for example two generals who both agree on the need to end the war, and to prepare for peace. They will do it if they both think that the other will do likewise. Yet, if one general suspects that the other is preparing for war, then his best response may be to prepare for war as well. This problem had already been clearly formulated by Xenophon in the fourth century B.C.

The Greek army was departing Persia and the Persian army was escorting them. The Greek general started to be suspicious fearing that the escortators might want to harm them. For this reason, he called for an interview with his Persian counterpart. His declared intent was “to end the suspicions before they end in open hostility and to openly discuss the issue to put an end to this mutual mistrust.

“I have come to the conviction that misunderstandings of this sort can best be ended by personal contact, and I want to make it clear to you that you have no reason to distrust us.” Sayed the Greek general. Unfortunately, as Xenophon tells, the personal contact so established was used by the Persians to slay the entire leadership of the Greeks. According to Schelling, who mentioned Xenophon’s story in his book “Arms and influence”, the mistake was apparently “in thinking that the only way to take the danger out of distrust is to replace it with trust”. If there has been a mistake in these negotiations has probably been the excessive trust in a group, the Taliban, known to be deceptive and prone to pursue their political goals by using violence rather than diplomacy.

Promises therefore cannot be based on trust, but they should be enforced by agreements, and possibly by one or more neutral external actors who act as referees capable of administering punishments to those who violate the contract to reduce the possible players’ payoffs. At the same time, Peace cannot be considered the passive surrender to the rule of the strongest, of those who rely on violence to achieve their political goals. What the United States and most of the international community tried to pursue through the negotiations with the Taliban was the chance of a decorous exit and a negative peace.

Johan Galtung, the father of peace studies, claimed that there are two kinds of peace, a negative one, that refers to the absence of violence, like for example a ceasefire. And a positive one, which is filled with positive content such as restoration of relationships, the creation of social systems that serve the needs of the whole population, and the constructive resolution of conflict. Afghanistan has shown multiple times in its own history that negative peace cannot work. The future of the peace process will have to start from here.