Games Theory (Nash Equilibria) in International Conflicts

Abstract

The concept of Nash equilibria was first applied to economics, but later also to ecology. However, Evolutionary stable strategies (EES’s) which are based on the establishment of Nash equilibria, are not as common in nature as often assumed. Here we examine the value of using Nash equilibria for analysing international conflicts and conclude that it seems risky to base decisions on peace or war, economic sanctions or not, etc., on “games” using game theory and specifically Nash equilibria.

Background

I have written a detailed discussion of applications of games theory in evolutionary biology (evolutionary stable strategies or ESS’s), published as an appendix to my book Nonequilibrium Ecology [1] (free online support material), available on the internet. Here, I wish to draw attention to the risks of using games theory (Nash equilibria) for analysing international conflicts.

Definition

A Nash equilibrium is one in which none of a number of players in a game can gain by changing her/his strategy unilaterally [2].

Conditions for a Nash equilibrium strategy

A Nash equilibrium strategy set will be adopted if the following conditions are met (I take these conditions from Wikipedia: Nash equilibrium): 1) players try indeed to maximise their potential payoff; 2) players are flawless in execution; 3) the players are intelligent enough to deduce the solution; 4) everybody knows that all players meet these conditions, including condition 4.

However, often these conditions are not met. 1) The first condition is not met if the quantities a player wishes to maximize are not properly defined; 2) the second condition is not met if players bungle execution of a plan; 3) the third condition is not met if players cannot deduce the correct solution because of its complexity, or if only some players can deduce it; 4) The fourth criterion is not met when players distrust each other and act as if their adversaries behaved “irrationally”.

Consequences of these conditions for the application of Nash equilibria in international conflicts

Because of these limitations, establishments of Nash equilibria are difficult to foresee in international conflicts. It therefore seems risky to base decisions on peace or war, economic sanctions or not, etc., on “games” using game theory and specifically Nash equilibria.

Example Iran

Let us use the example of Iran. Condition 1: the “West” always assumes that Iran does indeed wish to “maximize” its payoff by developing nuclear weapons. This may well be the case, but what is the evidence? The Grand Ayatollah has issued a fatwa forbidding development of such weapons (of course, he might issue a contradictory one tomorrow). Condition 2: execution of war plans has been bungled more often than not in the Middle East (Iraq, Lebanon), and probabilities are high that one against Iran will be bungled also. Condition 3: I think that the assumption of all players being able to deduce the correct outcome of a war against Iran is preposterous. Iran is unlikely to foresee how it would be “punished”, and the US, judging from its performance in Iraq, is unlikely to foresee all the consequences of a war. Condition 4: it is more than obvious that Iran distrusts the US. and vice versa.

The conclusion, then, is that attempts to analyse the present situation in the Middle East and specifically with regard to Iran using Nash equilibria, are not only without hope of success but highly dangerous, in particular also because equilibria in nature including human society are less common than nonequilibria, and because players are almost by definition “irrational”: they are consistently biased as discussed in the following.

General reasons why Nash equilibria are unlikely

There are two important general reasons, in addition to the four specific ones mentioned above, which might make it  difficult to adopt strategies based on Nash equilibria.

1. Equilibria in nature

Nash equilibria, as their name implies, are equilibria, and nonequilibria are more common than equilibria in nature, and this includes mankind. I have pointed out in my account of evolutionarily stable strategies, that ESS’s are not likely when disturbances are frequent and large, that is, under nonequilibrium conditions. I cite:

“it is to be expected that frequent and drastic abiotic and biotic changes in the environment which affect the fitness (reproductive success) of potential contestants in evolutionary “games”, will make it more difficult to establish evolutionary stable strategies, because the establishment of an ESS cannot keep up with the changes. If the development of an ESS takes a long time, even a single strong environmental disruption with long lasting effects may make it impossible for an ESS to develop. An established ESS may be affected by environmental instability for example by reducing population size so much that encounters with possible contestants are radically reduced, facilitating the invasion by mutants which are less fit, on a more or less random basis. Alternatively, a strategy stable under certain conditions may become less stable, permitting establishment of a different ESS. For example, it may well be that in the “war of attrition” mentioned above, the strategy of posturing in an unpredictable way and for a duration depending on the value of the resource, is replaced by one which demands greater aggressiveness, because resources are severely depleted.”

Hence, a Nash equilibrium today may not be one tomorrow. Who can foresee such changes? Climate change, for example, may have unforeseen consequences for how nations behave: a war of attrition may become more aggressive.

2. Do aggressive instincts in humans prevent the establishment of Nash equilibria?

Nash developed his concept in the context of economics, where rational considerations are more likely than in politics. Do innate agressive instincts perhaps overrule any rational considerations in politics?
The Nobel Prize winner Konrad Lorenz, one of the founders of ethology, the modern study of animal behaviour, advanced the thesis that there are such instincts over 40 years ago [3] [4]. Lorenz describes how intraspecific aggression (an instinct for aggression) in various animal species can have effects that threaten the survival of a species. The same applies to humans. Humans, in their evolutionary history, have acquired aggressive instincts that may have had a survival value at the time, but are dangerous today. Nevertheless, Lorenz is (or pretends to be?) optimistic. He refers to “safety valves” that prevent negative effects due to aggression in various animal species, from which we can learn. A precondition for optimism is that mankind must be modest and realize that we are only part of nature and subject to its laws. (A note for evolutionary biologists: Lorenz bases many of the arguments on group selection, which may not be scientifically sound, but many of his conclusions concerning the survival of species are nevertheless correct).

But even in economics, decisions are by no means always (or even usually) rational, as seen by the present financial meltdown. Reasons are that, as in politics just discussed, human decisions tend to be on the “hawkish” side. The Nobel prize winner Daniel Kahneman (a psychologist and founder of behavioural economics), and Jonathan Renshon have shown just this [5]. According to Kahneman, humans cannot make the  rational calculations required by conventional economics. They rather tend to take mental shortcuts that may lead to erroneous predictions, i.e., they are biased. All biases examined were found to be on the hawkish side.

These hawkish biases are of several kinds, for example:

1) optimism bias: most people believe they are smarter than others ;

2) illusion of control: the amount of control people think they have over outcomes is generally exaggerated;

3) fundamental attribution error: other people’s motives are often misinterpreted; and it is completely ignored that other people may have the same bias towards us;

4) reactive devaluation: something is considered worth less for the only reason that it is offered by the other side.

All these biases vastly increase the likelihood that wrong decisions are made in economics, and even more so in politics. However, not everybody agrees with the view that humans are intrinsically more irrational than rational (see for instance Glimcher 2004 [6]).

Conclusion

We conclude that, because of various biases and the dominance of nonequilibrium over equilibrium conditions in nature and human society, establishments of Nash equilibria are difficult to foresee in international conflicts. It therefore seems risky to base decisions on peace or war, economic sanctions or not, etc., on “games” using game theory and specifically Nash equilibria.

Added by Petr Frish:
Therefore, it would be interesting to extend the theory to include non-equilibrium phenomena, in analogy to the classical Statistical Mechanics of Gibbs, which has been extended to cover approach to an equilibrium.

References

1. Rohde, Klaus (2005). Nonequilibrium Ecology. Cambridge University Press, Cambridge. http://www.cambridge.org/catalogue/catalogue.asp?isbn=9780521674553
2. Nash, John (1950). Equilibrium points in n-person games. Proceedings of the National Academy of Sciences 36: 48-49.
3. Lorenz, Konrad (1963). Das Sogenannte Böse (English translation: On Aggression).
4. Lorenz, Konrad (1988). The Waning of Humaneness (German original 1983).
5. Kahneman, Daniel and Renshon, Jonathan (2007). Why hawks win. Foreign Policy, January/February 2007.
6. Glimcher, P.W. (2004). Decisions, Uncertainty, and the Brain: The Science of Neuroeconomics. The MIT Press.

Copyright Note

This article is based on my earlier posts in Klaus Rohde: Science, Politics and Art.