24 February 2007 – Game theory and the conflict

Earlier this week, I wrote about Peacemaker, a computer game that models diplomacy in the Israeli-Palestinian conflict. That got me thinking about game theory and its possible applications. I did a bit of research and came up with two papers, one by Sukanto Bhattacharya, Florentin Smarandache, and Mohammed Khosknevisan (2004), and the other by Tyler Cowan (2003).

Game theory basically attempts to analyze how people interact with each other when they have to make choices whose outcomes depend on the choices made by other parties. The classic game is the “Prisoner’s Dilemma,” in which two prisoners are interrogated separately, and each is told he can go free if he implicates the other. Both could also remain silent, but must weigh the risk that the other will squeal.

Games may have multiple solutions. In the standard model, each solution is called a “Nash equilibrium,” after Nobel-Prize winning mathematician John Nash, (subject of the movie A Beautiful Mind). A Nash equilibrium is an outcome at which no party, by changing her choice, could improve her welfare. In the Prisoner’s Dilemma, there are two Nash equilibria—one where both stay silent and one where both squeal.

The paper by Bhattacharya et al., entitled “The Israel-Palestine Question – A Case for Application of Neutrosophic Game Theory, argues for the use of “fuzzy” model rather than the standard model of Nash equilibria. This is because “the players”—the Israelis and Palestinians—have goals and strategies that change over time. At times, they are playing “cooperative” games, and at other times “zero-sum” games.

In addition, the authors argue, “the objectives and strategies are often ill-defined, inconsistent and have a lot of interpretational ambiguity.” The parties may signal to each other that they intend to achieve peace, but at the same time do things that seem to directly contradict that goal. Or, conversely, they may launch attacks against each other but signal that they still remain open to a peaceful resolution.

After building some mathematical models of the “neutrosophic evaluative judgment functions” for each side, the authors conclude that these spaces will not intersect, and there will be no possibility for a resolution, if the goal of the Palestinian leadership is to end Israel’s existence as an independent state. However, peace is possible if the primary objectives of the Palestinian leadership can be changed.

The authors conclude: “. . . the aim of the mediator should [be] to make the parties redefine their primary objectives without necessarily feeling that such redefinition itself means a concession.” The authors don’t elaborate much, but I would guess that this would mean getting the Palestinians to commit to Israel’s right to exist in exchange for symbolic Israeli recognition of some other Palestinian claims.

The paper by Tyler Cowen, entitled “A Road Map to Middle Easter Peace? – A Public Choice Perspective,” attempts to evaluate the Bush administration’s “Road Map” to peace. Cowen doesn’t build mathematical models; instead, he refers to basic economic concepts such as the Coase theorem (which states that initial allocations of property rights don’t matter if the parties can bargain freely and costlessly).

The Coase theorem often fails in the real world, and the clearest proof is the fact that countries still go to war, even when they could bargain with each other and save lives and money. Cowen begins by considering several standard explanations for the failure of the Coase theorem, and shows how they do not apply very well to the facts of the Israeli-Palestinian conflict.

One explanation, for example, is that transaction costs are high. But Cowen points out that this cannot be the problem in the Israeli-Palestinian conflict, in which the parties can meet and talk as often as they like. Another explanation is that neither party can write binding contracts. Cowen points out that outside forces, such as the U.S., have been able to enforce other deals, like the peace between Israel and Egypt.

Another typical explanation for the failure of the Coase theorem is that parties might have “infinite compensating variations”—that is, values they are unwilling to trade for peace at any price. Cowen admits that the problem is a real one—especially around issues such as the “right of return”—but that it is probably not the fundamental problem, because there is room for flexibility on both sides.

Cowen then moves to what he considers more likely explanations for the ongoing conflict. One is reputation—that both parties have an incentive to act tough with each other because they anticipate future negotiations, either with each other or with other parties in the region. That means they may each try to hold out for a better deal in the future, rather than settling for a reasonable deal in the present.

Another reason Cowen offers is that there are “nested games”—games within games, conflicts within conflicts. Israeli and Palestinian leaders have to worry about other Arab nations, not just each other. They also have to worry about internal political conflicts. These nested “mini-games,” Cowen writes, “may constrain the actors from settling the larger Israel-Palestinians game.”

Next, Cowen turns to behavioral economics. In many bargains, people “punish cheaters” even when they hurt themselves by doing so, preferring no deal at all to a deal that is less than what they want or expect. The Israeli-Palestinian conflict, he argues, is particularly vulnerable to this problem because each party “believes that the other has violated its rights repeatedly, and thus holds great suspicions.”

Finally, Cowen discusses “meta-rationality,” the ability to have a realistic understanding of one’s own “prospects and abilities.” People often ignore reality when evaluating themselves; for example, most people think they are better drivers than others. This is especially true in the areas of religion and politics, where people think what is good for them is good for the world. This makes agreement difficult.

Cowan summarizes: “The two sides are locked into a long-run bargaining game, which leads them to struggle for power at each step along the way. Nested games and behavioral factors make it difficult for the parties to make the mutual sacrifices required for an agreement. Furthermore neither party is meta-rational about the points of disagreement.

“On top of these problems, the minority that does not want peace at all takes actions to exacerbate adverse behavioral and psychological reactions; we can understand terrorism as an attempt to manipulate such behavioral weaknesses. Periodic retaliations from each side then raise the stakes in the long-run bargaining game, and ratchet up the difficulty of earning subsequent concessions from the other side, thus making peace difficult.”

Cowen looks at the “Road Map” and find that it does, in fact, address all of these problems, and that there is a possibility—however slim—that it will actually work. However, he concludes that there is good reason to be pessimistic, given the deterioration of the situation over time. He quotes Milton Friedman’s optimistic observations on a 1969 trip to the region, which turned out to be completely wrong.

All of this got me thinking that perhaps my proposal for a joint negotiating forum between Israelis and Palestinians was not such a dumb idea after all. A joint forum could partially collapse the nested games into a single game. It could isolate extremists on both sides and prevent them from manipulating the psychological weaknesses of the parties. Other problems would persist, but perhaps less so.