Truth and Deception: The Games of Joint Security Area

A tale of separation and friendship on the DMZ.

Park Chan-Wook’s 2000 film Joint Security Area begins with a murder mystery in the demilitarized zone (DMZ) that separates the two Koreas. Two North Korean soldiers are dead and one soldier from both sides is injured as a result of a shooting on the North Korean side of the demarcation line. Both countries stand by their soldier’s depositions despite the conflicting truths of the reports. The North Korean soldier Sgt. Oh Kyeong-pil (Song Kang-ho) claims that Sergeant Lee Soo-Hyuk (the injured South Korean soldier played by Lee Byung-hun) attacked them, while the South claims that the North Korean guards kidnapped Sergeant Lee. In the end it is up to a Swiss military officer from the Neutral Nations Supervisory Commission, Major Sophie E. Jean (Lee Young-ae), to find out what really happened. She is pressured from both nations to declare both depositions true to diffuse a politically volatile situation. Slowly she discovers the truth that the North Korean guards and South Korean guards were friends who were caught in this treasonous act by an inspecting North Korean lieutenant.

She is removed from the case after inciting tensions between the two sides with her adamant quest for the truth. She confronts Sergeant Lee in the end of the film with a choice. He can tell her the truth (about who shot first in the North Korean guardhouse) and she will not leave the incriminating evidence of the friendship for her replacement, or he can refuse and she’ll leave the evidence. By telling the truth he will also protect his friend and fellow South Korean soldier. This is where game theory can be used to show the rational progression of the choices in the film. What follows is heavily dependent on spoilers so do not continue if you want to see this film untainted.

THE GAME MATRIX

Game Key:
(x, y)=(payoff to Lee, payoff to Jean)
[x, y]=[payoff to Lee, payoff to Jean] in Anticipation Game
4=best, 3=next best, 2=next worst, 1=worst
Nash equilibrium in original game underscored
Non-myopic Equilibria (NMEs) in bold italics
Td: Deterrent Threat of Column

The Progression of States to the NME is as follows: III to IV to I to II.

EXPLANATION OF THE PREFERENCES

1. Lee Loses: (1,2): The worst for Sgt. Lee as he has told the truth and is incriminated along with his friend. This is the second worst for Major Jean as she has gone back on her word, but she has learned the truth.
2. Compromise: (3,4): The second best for Sgt. Lee as will not be incriminated, but he has told the secret. The best for Major Jean as she learns the truth, and does not have to incriminate Sgt. Lee.
3. Lee Wins: (4,1): The best for Sgt. Lee as he keeps his secret and is not incriminated for it. The worst for Major Jean as she did not learn the truth nor did she follow through with her threat.
4. Jean Follows Through: (2,3): The next worst for Sgt. Lee as he is incriminated, but he keeps his secret. The next best for Jean because she follows through with her threat, but she does not learn the truth.

EXAMINATION OF THE GAME

The initial state of the game is (4,1) where Sergeant Lee is keeping his secret and Major Jean has yet to incriminate him. This is the state that Sergeant Lee and Major Jean reside in for the entirety of the movie up to Major Jean’s confrontation with Sgt. Lee. Lee remains silent, and the audience learns of the forbidden friendship between the soldiers in a subjective flashback of the other South Korean soldier Private Nam (Kim Tae-woo), as he lies on the pavement after attempting suicide. Major Jean realizes that the soldiers were friends through deductive reasoning but she does not know the whole truth, nor does she know who shot first and started the bloodbath. Finally, through her removal from the case she has threat power. Her knowledge of the incriminating evidence will be left to her replacement. This gives Major Jean deterrent threat power to induce the final outcome of (3,4) because if Sergeant Lee continues to stay at (4,1) she will force a move to (2,3) which is Lee’s second worst outcome.

Major Jean therefore incites the move to the outcome of (2,3) with the threat of the disc. Classical game theory states that this is the Nash equilibrium (both players making the best decision they can taking into account the other’s decision), and the play would not continue, as all other states are inherently unstable. However, and this is the benefit of using Steven Brams’ Theory of Moves, the characters are rational and forward thinking opponents, and Major Jean induced this state hoping that Lee with think through his options and realize that telling the truth (and thereby leaving the dominant strategy of not revealing the truth) will incite a better outcome for himself. Sergeant Lee does indeed leave from the Nash equilibrium and finishes the flashback started by Private Nam and moves to state (1,2) knowing that Major Jean will swiftly movie to (3,4): the games only non-myopic equilibrium (NME from now on). Non-myopic equilibria are equilibria resulting from both players making forward thinking decisions from an initial state of play and deciding to move or not and is can be dependent on who moves first. Theory of Moves shows that this is a rational progression of moves, even with Lee having left his dominant strategy and the Nash equilibrium. Although the game is theoretically cyclical (game play continuing forever), it is not probable in this situation. Once Lee tells Jean the truth he cannot return to not telling her the truth, as the information is already known. Therefore moving power cannot exist within the context of this game. Under these preferences, the moves the players make are indeed rational, and the outcome is the best for both players given the situation.

Sergeant Lee finishes telling the tale in a flashback that continues from where the last left off (the North Korean lieutenant coming through the door). In this sequence we see that Private Nam shot the lieutenant and then turned his gun onto Private Jung (one of the North Korean guards played by Shin Ha-kyun) shooting him in the head. Sergeant Lee shoots him once and then attempts to shoot Sergeant Oh but his gun jams. Private Nam then goes battle crazy and shoots Private Jung many times in the chest, although he is already dead. This version of the events satisfies both Jean and the audience, as we believe that this is the truth, given the perceived preferences of Sergeant Lee. However, Sergeant Lee has deceived us and we were playing a misperceived game. A last revelation comes at the end of the film that while Private Nam did shoot the Lieutenant, Sergeant Lee shot Private Jung, killing his friend and causing tragedy for all soldiers involved. So he has lied to Jean, in reality he was protecting himself as well.

REAL GAME MATRIX AFTER REVELATION

Game Key:
(x, y)=(payoff to Lee, payoff to Jean)
[x, y]=[payoff to Lee, payoff to Jean] in Anticipation Game
4=best, 3=next best, 2=next worst, 1=worst
Nash equilibrium in original game underscored
NMEs in bold italics

Progression of states to NME as follows: III to IV

EXPLANATION OF THE PREFERENCES

Note: Because she has misperceived the game due to Sergeant Lee’s deception Jean’s preferences remain the same while only his change.

1. Lee Loses: (1,2): The worst for Sgt. Lee as he has told the truth and is incriminated along with his friend. This is the second worst for Major Jean as she has gone back on her word, but she has learned the truth.
2. Jean Wins: (2,4): The second worst for Sgt. Lee as will not be incriminated, but he has told the secret that he desperately had tried to keep: the guilt of killing his friend and causing so much tragedy. The best for Major Jean as she learns the truth, and does not have to incriminate Sgt. Lee.
3. Lee Wins: (4,1): The best for Sgt. Lee as he keeps his secret and is not incriminated for it. The worst for Major Jean as she did not learn the truth nor did she follow through with her threat.
4. Jean Follows Through: (3,3): The second best for Sgt. Lee as he is incriminated, but he keeps his secret, presumably able to argue with Jean’s replacement who will most likely be more amiable to both countries desire to diffuse the situation. This is the next best for Jean because she follows through with her threat, but she does not learn the truth.

EXAMINATION OF THE GAME
This is how the game would play out from the initial state of (4,1) if Jean knew the true preferences of Sergeant Lee. Deception is a viable strategy on the part of Lee, as Jean has no reason at this point in the film to not believe this story. She is so invested in finding out the truth that she will believe Lee’s story as long as it has some glimpse of truth in it. She also has no dominant strategy to rely on, and prior communication exists with Jean’s threat of the discs. The first game is the one played out, but in reality (using Lee’s true preferences) this would have been the game. As it stands the result was (4,1) with Lee keeping his secret and Jean not incriminating him.

This state is severely unstable and play does indeed begin again in the film. Jean realizes along with the viewer that Lee may be the real killer of Private Jung, and he has lied to her in his telling of the “truth”. The initial state therefore remains as (4,1) but before Jean could move or even change her preference rankings as a result of the new information, Sergeant Lee commits suicide, and play ends due to an outside force. Theoretically, if play had not ended, Jean would move to (3,3) the game’s only NME as well as the Nash. Sergeant Lee refuses to tell the truth because the guilt for him of other people knowing that he shot his friend far outweighs the consequences of his incrimination. Also most likely the replacement for Major Jean will be quick to resolve the situation, as neither nation is interested in the truth, rather they just want the situation to be over. Therefore, he would not leave from (3,3), effectively ending play here. Again in this game cyclicity is not a factor, as Lee cannot take back the truth once it is told. Major Jean’s threat is no longer valid as the only state she can induce is (3,3) with a deterrent threat, and this is not a state she wants to incite. She has no logical reason to threaten him into not telling the truth within the diegesis of the film.

Because Lee kills himself, I suppose being the cause of one friends death and another’s attempted suicide is too much, play is stopped in a transition between (4,1) and (3,3) as Jean is rushing down the stairs to confront Lee and stop him from killing himself. Either way, even with the deception, the actions of the players can be seen as completely rational, with the exception perhaps of Lee’s suicide. Theory of Moves predicts exactly the motions the characters themselves in this highly complex thriller. When looking at these game matrices it does not seem that complicated at all anymore.

Works Used

Brams, Steven J. Theory of Moves. New York: Cambridge University Press, 1996. Buy it on Amazon.