This post has little to do with religion (aside from the Israel/Palestine debate), but I thought the subject worthy of an article on this blog.
In 2012 Palestinian prisoners being held indefinitely in Israeli jails staged a massive and highly successful hunger strike that compelled the Israeli government and military forces to give into the Palestinians’ demands. This was an incredible achievement, but game theoretical literature on this topic is scant (actually it straight up does not exist). So lately I’ve been developing my own model to explain the prisoners’ and Israel’s actions.
If you’re familiar with game theory and extensive form games, this will make the most sense to you, and I ask for feedback (good or bad) because this is not a fully developed model (I haven’t even gotten to the maths yet). Please note I had to make some inferences about each players’ preferences. These might not reflect reality, but they’re as close as I can assume at this point.
The rudimentarily designed game above is quite long, so I divided it into two parts.
To illustrate this game, assume Player 1 is a suspected Palestinian militant who is being held indefinitely in an Israeli prison without trial. He wants to protest these conditions and force the Israeli government to give him a fair trial. The prisoner is aware of hunger strikes as a tool because he has seen it successfully used in this prison. He is also aware that some hunger strikers die playing this game. He is willing to take that risk and is willing to die if Player 2 (Israel) does not give into his demands. For the purpose of simplicity, I will call the prisoner “He” and the Israeli government “She.”
At the first node, Player 1 decides to go on a hunger strike (HS) or not (~HS). If he plays ~HS then status quo is maintained and the payouts are -10, 10. Here Player 2 gets 10 because she has interest in keeping the prisoner in prison and also has interest in preventing mass media coverage of yet another hunger strike in Israeli prisons. Player 1 gets -10 because he loses any potential media coverage that could draw public attention to his plight. He also must remain in prison without trial.
If he plays HS the game moves on to the next node. At node 2 the Israeli government must decide whether to resist Player 1’s demands (R) or acquiesce and give into those demands (A). If she plays A the payouts are 5, 5. She receives 5 because she has given into Player 1’s demands but also prevented mass media coverage or a mass hunger strike. Player 1 gets 5 because his demands are met but no attention has been brought to his case. He still must go to trial with ineffective, indigent counselor.
If she plays R the game moves on to the next node. At node 3 Player 1 again must decide between HS and ~HS. If he plays ~HS he ends his hunger strike and the game is over. The payouts are now -8, 8. He receives -8 because he is still in prison. His payouts are a little better than if He played ~HS in the first node because now there is media attention about his case. He gets a slightly better lawyer to represent him (even though there’s still no trial). Player 2 receives 8 because she lost some of the payout from the first node but the amount of media attention is small.
If he plays HS the game moves on to the next node. At node 4 Player 2 decides between R and A. If A, the game is over. Player 1 receives a trial and maybe a better lawyer. Payout is 7, 3. Media attention has diminished Player 2’s payout.
At each node the payouts increasingly turn in the prisoner’s favor, alternating between negative values for ~HS and positive values for A. This diminishes the Israeli government’s payouts for each players’ respective plays. This gives Player 1 incentive to continue the game as long as possible. It also gives Player 2 incentive to end the game as soon as possible… just not yet. At most plays of HS, Player 2 can do better by playing R and hoping Player 1 plays ~HS at the next node. This changes as the game nears the point of Player 1’s death. At Player 2’s last point of play she will play A, giving into the hunger striker before Player 1 can play Death.
This game can continue theoretically in perpetuity until Player 1 dies. Although it is unlikely to get this far because Player 2 will acquiesce before this point, the payouts at death are 10, 0. By now massive media coverage is following the strike, bringing discredit to the Israeli government. Other prisoners have started their own hunger strikes in solidarity. This and the fact that Player 1 becomes a martyr give Player 1 his best payout even though he is not alive to enjoy it.
However, at the final node, when Player 1 knows death is imminent but survival is still possible, he can choose ~HS, which will make the payout 0, 2. Mass media coverage has brought a lot of attention to his plight, but he remains in an Israeli prison without trial. Not even his pro bono lawyer can help him now.
In order to solve this game I am using backwards induction to find subgame perfect equilibrium. In sum Player 1 is choosing to die and Player 2 always plays R until the last node she can play.
- Player 1 plays HS (if Player 2 plays A at next node 5 > -10)
- Player 2 plays R (if Player 1 plays ~HS at next node 8 > 5)
- Player 1 plays HS (if Player 2 plays A at next node 7 > -8)
- Player 2 plays R (if Player 1 plays ~HS at next node 4 > 3)
- Player 1 plays HS (if Player 2 plays A at next node 9 > -4)
- Player 2 plays A (no matter what Player 1 does in final node 2 > 1, 2 > 0)
- Player 1 plays HS (and dies) (10 > 1)
Equilibrium <HS, HS, HS, HS (and dies); R, R, A>
Please note that this applies only to the Palestinian Prisoner case, particularly the 2012 mass hunger strike. Some hunger strikes have been less successful for the protestors. For example, in the case of the massive California prison hunger strike in 2013, the vast majority (~99.7%) of the 29,000 protestors gave up their hunger strikes on their own very early in the game. The remaining ~0.3% gave up their hunger strikes when an appeals court threatened to begin force feeding (which is a different game).