Sphinx

The Melian Dialogue in Thucydides has been of interest to game theorists since the earliest development of the field; it was discussed on several occasions by John von Neumann, generally accepted founder of this approach, and it appears in the work of a leading game theorist like Thomas Schelling. It’s entirely understandable: the dialogue presents two sides in a high-stakes, zero-sum conflict, pursuing very different strategies with a limited number of possible outcomes, and – if you want to push the boundaries of game theory a bit further, it also offers interesting examples of how each side seeks to anticipate and influence the decision-making of the other, and raises some fundamental questions of rationality. I fully expect to find lots of other examples when I have time to pursue this theme in depth, but for today I want to focus on one case of a game theoretical discussion of the Dialogue, written by the current Greek Finance Minister Yanis Varoufakis (1997; revised version 2014: 262-83). It is in itself an interesting reading of the situation, in relation both to Thucydides and to the normal assumptions of game theory, but there are also some striking implications for the current negotiations between Greece and the EU, especially Germany, which I will consider in the final section.

1. Varoufakis on Thucydides

Varoufakis speaks of Thucydides with familiarity and confidence, and knows him well enough to offer his own translations rather than relying on a standard version. These are generally close to the conventional readings, though with occasional interesting variations. The passages quoted are as follows, in order of their mention:

5.89: On the one hand the principles of justice, encompassed in human reason, hinge on the equal capacity to compel, yet on the other hand, the strong actually do what is possible and the weak suffer what they must.

Varoufakis here echoes (if not follows) Crawley in seeing the weak as ‘suffering’ rather than simply ‘accepting’ what they have to; and is in the tradition of emphasising that the strong ‘do’ what they are able to do rather than, more narrowly, ‘exact’ what they are able to exact. His choice of the phrase ‘encompassed in human reason’ isn’t wholly clear; I feel uncertain whether he wants to emphasise the human element (the idea that, as other translations make clearer, discussions of justice in debased human terms rest on issues of strength and power whereas true, divine justice operates by different rules) or the rational element (which edges into the neo-realist assumption that Thucydides here describes presents lawless anarchy as the true and reasonable state of things, rather than as something to be deplored). Finally, Varoufakis is the only translator I can recall off-hand who seeks to contrast the two parts of the sentence – justice depends on equal power and yet the strong exact and the weak endure – rather than seeing these as consecutive – justice depends on equal power and so the strong exact and the weak endure (i.e. there is no equality and so no justice). His subsequent discussion seems to follow the latter reading – at any rate it emphasises inequalities in power and strategic advantage – and so it’s difficult to see why he has translated the phrase in this way.

5.90: Then in our view (since you force us to base our arguments on self-interest, rather than on what is proper) it is useful that you should not destroy a principle that is to the general good – namely that those who find themselves in the clutches of misfortune should be justly and properly treated, and should be allowed to thrive beyond the limits set by the precise calculation of their power. And this is a principle which does not affect you less, since your own fall would be visited by the most terrible vengeance, watched by the whole world.

The distinctive feature of Varoufakis’ translation here is that he sees the Melians as arguing that those suffering misfortune should be treated justly and as if they have more power than they actually possess – in other words, a calculation about the real state of affairs – whereas other translations read this as a claim that their argument should be treated leniently even if not fully proven – as Mynott puts it, “should have the benefit of the doubt, even if their case is not quite fully demonstrated.” This may or may not be significant; as I suggest below, Varoufakis does seem to conflate the Melians’ arguments and their actual strategic choices, or doesn’t regard the distinction as important, and perhaps this is driven by a sense that (as in game theory generally) what matters is the relative advantage of each player rather than the quality of their arguments.

5.105: We know that you or anybody else with the same power as ours would be acting in precisely the same manner.

The only quibble here is that Varoufakis references this as 5.104.

5.95: No, because we are not injured by your hostility; rather we are worried that, if we were on friendly terms with you, those whom we have already subjugated would regard this as a sign of weakness in us, whereas your hostility is evidence of our power.

No complaints here.

Varoufakis understands and presents these quotes as the arguments of Athenian and Melians; he interprets Thucydides as an accurate reporter of events, no more. This is Thucydides the old-fashioned historian, rather than the fabricator of the Melian Dialogue – whereas some earlier game theoretical analyses of the passage see Thucydides himself as an analyst of strategy or even a proto-game theorist, making deliberate use of the situation (if not largely inventing it) to explore problems and principles. Varoufakis’ concern (as will be seen below) is with how real people behave in such situations, contrary to some of the expectations of abstract theorising, so it is perhaps natural for him to interpret the passage as a real high-stakes confrontation between opposing sides, rather than a staged debate between Thucydidean sock puppets.

2. The Games

Varoufakis does not actually attempt to ‘game’ the Melian Dialogue; the game that he develops does not attempt to replicate the historical situation or its most likely outcomes, but rather takes it as a starting-point: his experiment finds its origins in “ancient arguments and puzzles”, and the Melian Dialogue “reminds us” that putting forward moralising arguments in a position of weakness is a strategy of last resort. The key question here is why the Melians (in 5.90) abandon instrumental arguments in favour of general moral claims about how those in a position of weakness should be treated (of course, this is presented as an instrumental argument, appealing to the Athenians’ self-interest in up-holding such a principle for the event that they find themselves in such a position of weakness in future, but that appears to be merely a cloak for a basically moral claim).

Game theory is concerned with choices rather than arguments; in the game that Varoufakis constructs, the appeal to moral principle is equated with a co-operative strategy that aims for the outcome that brings the greatest benefit to both parties, rather than a selfish (or ‘cheating’) strategy that aims for personal benefit at the expense of the other. The cooperative strategy produces the only mutually beneficial outcome (in all other scenarios, at least one player ends up with a negative payoff), but it is undermined by the fear that your opponent may anticipate your co-operative choice and cheat to collect the largest possible individual payoff at your expense, and by the temptation to cheat yourself to gain the largest individual pay-off. Why, then, would anyone choose the co-operative strategy (or the Melians’ moral argument) in such a situation? Varoufakis canvasses a number of possibilities from the literature, both instrumental (the subject has misread the situation, or accepts short-term disadvantage in the hope of long-term benefit, or is motivated by natural sympathy to others rather than solely rational self-interest) and non-instrumental (a Kantian moral imperative that trumps rationality and disregards consequences, or an ancient Greek perspective that embeds morality and self-interest in the social order, echoed by writers like Hegel and Habermas), or a hybrid form in which the players come to conceive of themselves as a single decision-making unit, rather than as opponents, and so rationally seek a mutually beneficient outcome.

One striking aspect of Varoufakis’ approach to game theory in this article is that he does not stop at the theoretical level; having constructed the game and proposed some possible explanations of cooperative behaviour, he then got real people to play it to see how they responded to the situation in practice. In this game, there is no instrumental reason for anyone to choose the co-operative strategy – and yet people did; the number of cooperative outcomes declined steadily through successive rounds, but the number of cooperative choices remained steady – as the players in the weaker strategic position cooperated more and more, even as those in the stronger position learnt to cooperate less. This was not the result of getting to know one’s opponent or building up a relationship of trust or suspicion over time, as players faced different opponents in each round. Nor was it a matter of disposition, as the players switched roles in each game; rather, it appears to be a function of situation, so that the ‘rationality’ (in instrumental terms) of a player’s choices depended on whether s/he was playing the weaker or the stronger side. At this point Varoufakis offers a new hypothesis for such behaviour: the argument of the Athenians at 1.105, that anyone in their position would act in exactly the same way; in other words, being in a position of strategic advantage promotes an inclination to cheat and privilege self-interest, whereas – and this is the reading that he emphasises – being in a weaker strategic position leads players to “exhibit a quasi-moral urge to cooperate”.

The game was modified to test this hypothesis further. Game 2 removed any temptation for the weaker player to ‘cheat’ if they anticipated a cooperative strategy from the other, whereas the stronger players were given an incentive to choose an aggressive strategy; Game 3 returned some strategic advantage to the weaker player, giving the stronger player an incentive to cooperate while suggesting that the number of cooperative outcomes might fall, since the weaker players were in a less weak position than previously. In these games (including a repeat of Game 1), players were also asked to indicate their expectation of their opponent’s choice. In each case, the stronger players were more inclined to cheat (choose an aggressive move even when expecting their opponent to be cooperative) than the weaker players; more strikingly, the weaker players became more inclined to cooperate, even when the stronger players became less cooperative over time – and even when they expected their opponent to be uncooperative. Such ‘sacrificial cooperation’ is incomprehensible in conventional thinking; “it never makes sense to cooperate against an uncooperative opponent”, whether on instrumental grounds or according to a Kantian categorical imperative, and yet time and again the players with strategic disadvantage chose such a course of action. Essentially, the experimental subjects generated a social convention in which those in positions of advantage make use of it whereas those in positions of weakness develop a tendency towards moral rhetoric, actions – and expectations.

In other words, the Athenians were right, and discussions of moral motivation need to include reference to Thucydides’ account of the Melian Dialogue. Of course, the Melians’ arguments fail because the Athenians’ goals aimed at ruthlessness rather than magnanimity, testifying to “the impotence of abstract morality against the logic of imperialism”. The experimental findings do not show that moral rhetoric and action is irrelevant – certainly it is not reducible to sophisticated expediency – but they show that choices are shaped by situation, raising serious doubts about whether the Athenians could ever have been swayed by such arguments, and confirming their dismissive attitude towards the Melian claims as merely a sign of weakness. The one cause for optimism is that a moral disposition is not intrinsic (contra Nietzsche’s claim for natural differences between the weak and the strong) but depends on social location, “in which case all that is needed to undo it is a re-designed social context”. That the Melians’ speech has resonated through history, Varoufakis argues, supports such a hope.

3. Negotiations and Compromises

Does it? It’s impossible to quantify such a claim, but my impression of the reception of Thucydides is that the Athenian’ argument for the rights of the stronger has resonated rather more than the arguments of their opponents – of course, this may simply reflect the tendency for the greatest admirers of Thucydides to be in positions of relative advantage in the first place, so already inclined to accept such a view.

This is not a solely academic issue, given Varoufakis’ critical role in current negotiations about Greek bailouts and, potentially, the future of the Euro. The relevance of his expertise in game theory has already been remarked upon in this context; for example, in a profile on Bloomberg.com by Carol Matlack, citing the economist James K. Galbraith:

What’s more, Varoufakis’s academic specialty is game theory, the study of strategic decision-making in situations where people with differing interests try to maximize their gains and minimize their losses. Varoufakis knows as much about this subject “as anyone on the planet,” Galbraith says. “He will be thinking more than a few steps ahead” in any interactions with the troika.

It’s worth emphasising – as Varoufakis himself has done – how far his approach actually diverges from conventional game theory, seeking to question its assumptions and open up questions of indeterminacy (discussed extensively in his 2014 collection of essays). If he is thinking several steps ahead, it is not in the belief that the choices of his negotiating partners are fully rational or that the range of possible outcomes is limited and predictable.

Because I spent many years during my previous life as an academic researching game theory, some commentators rushed to presume that as Greece’s new finance minister I was busily devising bluffs, stratagems and outside options, struggling to improve upon a weak hand. …The trouble with game theory, as I used to tell my students, is that it takes for granted the players’ motives.(‘No time for games in Europe’, New York Times 17/2/2015)

This might to some extent be a bluff, as Henry Farrell implied in a blog for the Washington Post: Varoufakis knows that it can sometimes be rational to appear irrational, including proclaiming a Kantian categorical imperative to do what is right regardless of the consequences for Greece and the rest of Europe – but that only works if everyone takes it at face value.

Varoufakis is caught in a dilemma where the only way that he can bargain effectively is by convincing people that he isn’t actually bargaining, but instead is stating ethical principles that he is prepared to stick to no matter what. Which means, conversely, that if he is just stating his sincere bottom line, people may mistakenly think that he is bluffing, and call him on it. Which is why he is writing this op-ed (although it will probably not solve the problem, since it is exactly the kind of op-ed that a canny bargainer inspired by Thomas Schelling’s take on game theory would be inclined to write).

This does suggest that it may be worthwhile exploring examples of Varoufakis’ activities in the field of game theory for possible insights into his understanding of the situation – which might indeed be more widely applicable. After all, the analogy between the Melian Dialogue and the current stand-off between Greece and Germany has already been noted, albeit in a crude form that claims the German attitude is a straightforward echo of Athenian ‘might is right’ claims (see previous posts on this blog).

The basic situation is one of strategic imbalance, in which the weaker player will lose, to a greater or lesser degree, unless the stronger player chooses a cooperative strategy. It is striking how far the Greek negotiating moves have tended to echo those discussed in Varoufakis’ article: the introduction of moral arguments (the impact of austerity on the Greek people, the issue of WWII reparations, accusations of neo-imperialism), attempts at bringing external pressure (or the fear of loss of reputation) to bear on the Germans from other European states, attempts at shifting the terms of the discussion to a cooperative search for mutually beneficial outcomes rather than a zero-sum game – alternating with warnings about the dire possibility of a mutually destructive outcome if the principles of European solidarity and justice for the weaker from the stronger are abandoned. However, the efficacy of the latter argument is strictly limited; there is, in such a situation, no sense in cooperating with an uncooperative opponent, so the weaker side (which needs its opponents to adopt a cooperative strategy more than they need it to) cannot appear too uncompromising.

Varoufakis’ analysis indicates that the only hope for the Melians and those in similar positions is a shift in their opponents’ motivation from the purely instrumental, to adopt a cooperative approach despite their clear strategic advantage. The experimental data shows that this can happen, and one might detect such a possibility in the Germans’ genuine adherence to principles of European solidarity – but it is alarmingly close to a reliance on mere hope, danger’s comforter (as the Athenians note in a passage that Varoufakis doesn’t mention, 5.103). The best chance for the Melians in fact seems to lie in the possibility of their opponents feeling uncertain about the degree of their strategic advantage – not whether or not the Melians are weaker than them, but how far a mutually destructive outcome would damage them (the claim that Athens would turn all other neutral sides against themselves echoing Greek claims about the potential collapse of the Eurozone; the Athenian argument that it’s better to show strength to keep allies in line paralleling the need for Germany to discourage other PIIGs from similar insurrection).

One problem that the Melians/Greeks face is that their very recourse to moralising arguments can, according to Varoufakis’ analysis, be interpreted as a sign of weakness, and so not only dismissed but taken by their opponents as confirmation of the strength of their position, hence making it less likely that they will adopt a cooperative strategy – one might label this the Melian Dilemma. Still more alarming is the fact that his experimental data shows how those in the weaker position are inclined to adopt cooperative strategies even when they do not expect this to be reciprocated. Various commentators expressed surprise, at the conclusion of the last round of negotiations, that the Greeks had apparently given in, dropped most of their demands and accepted almost all the conditions demanded by the other side, without much of a fight. Varoufakis’ analysis suggests that this was entirely predictable: in practice still more than in theory, the strong exact what they can, and the weak have to endure it. This is not a cheerful conclusion.

Varoufakis, Y. (1997) ‘Moral rhetoric in the face of strategic weakness: experimental clues for an ancient puzzle’, Erkenntnis 46: 87-110

Varoufakis, Y. (2014) Economic Indeterminacy: a personal encounter with the economists’ peculiar nemesis, London & New York: Routledge