Prospect Theory and the Problem of Strategy: Lessons from Sicily and Dien Bien Phu


Amos Tversky, left, who died in 1996 and Daniel Kahneman, who won a Nobel Prize in 2002 (Sean Gallup/Getty Images/Barbara Tversky)

Prospect theory, as described by Kahneman and Tversky in their 1979 paper “Prospect Theory: An Analysis of Decision under Risk,” challenged traditional paradigms of decision making (expected utility theory) and predictive behavior. In its simplest form, prospect theory suggests actors tend to overvalue losses opposed to gains. The result is they may tend to over-invest in an endeavor involving sunk costs rather than accepting losses and ceasing participation in that endeavor. Similarly, the theory also suggests decision makers will employ approaches that might be characterized as risk averse when allocating resources in pursuit of gains.

While the broader implications are troubling, two specific dimensions of the intersection of strategy and prospect theory—risk aversion and risk acceptance—are particularly interesting, but how both behaviors manifest themselves in the context of military operations varies significantly. In a 1997 paper, “Prospect Theory Goes to War: Loss-Aversion and the Duration of Military Combat,” Thomas Bauer and Ralph Rotte, identified and tested the relationship between both size of forces available for commitment to an offensive—and the losses sustained in the duration of an offensive. A second significant hypothesis tested was whether the total manpower available to a commander increased the likelihood for sustained offensive action. This demonstrates a heuristic form of risk-aversion, derived from the mass committed acting as a guarantor of operational sucessfulness.

They conclude first, that there is a trend suggesting that a commander’s willingness to stop an offensive operation decreases when higher levels of casualties are sustained. That is, commanders tend to demonstrate risk-seeking behavior in offensive operations in the face of losses. That is, commanders tend to overvalue their own losses compared to losses inflicted upon an adversary. Their findings also suggest that offensive operations tend to snowball for that very reason.

Second, that there was an increased likelihood of prolonged combat so long as the offensive actor maintained larger reserves or a larger force. Though this hypothesis is ultimately guided by a fundamentally different rationale, its implementation is intimately linked to the psychological pathway of the first described phenomena. The expansion of force ultimately enables risk-seeking behavior in the failure to accept sunk costs.

Thus, we arrive at the central question at the intersection of prospect theory and strategy. Is strategy a means of avoiding the behavior trap described by theory? In other words, does the absence of good strategy increase the chance of embarking on and continuing a flawed or failing military operation—even in the face of significant losses—or is good strategy a pathway for avoiding such traps altogether?

There is no shortage of incidents throughout history that demonstrate these behavioral dynamics in war. The challenge of balancing ends and means is a central component of all strategic action, yet strategists have often done so poorly and to disastrous effect. To briefly explore the strategic consequences of prospect theory in action, excellent examples include the Athenian’s Sicilian Expedition in the Peloponnesian War and the French experience in Vietnam at the Battle of Dien Bien Phu.

The Sicilian Expedition: Prospect Theory in Practice

In 415 BC, the Greek city state Athens embarked on a daring expedition to shift the balance of the ongoing Peloponnesian War. Over 130 triremes, containing some 5,000 hoplites, set out for the island of Sicily to combat and capture the super-polis Syracuse—then caught in a localized conflict with the Segestans (a rival city-state on the island and partner of Athens). Just two years later, however, the force was decimated—their objectives unachieved, a sizable part of the Athenian navy destroyed, and thousands of hoplites killed or captured. In the view of Thucydides, one of a handful of known sources to have written on the expedition, the consequences for the Athenian war-effort were damning. Athens never fully recovered. Despite continuing the war for another 11 years, Thucydides links the loss of its navy and thousands of hoplites committed to the expedition to Sparta’s eventual victory in 404 BC.

An engraving by Agostino Veneziano, reflecting a Renaissance view of Alcibiades. (Wikimedia)

In the debates leading up to the decision to send the expedition, Athens found itself divided between two poles. One, lead by Alcibiades, the adopted son of the legendary general and statesmen Pericles, favored the operation and the opening of a new front in the war against Sparta. The other was championed by Nicias, one of Athen’s most significant commanders in the early phases of the war, and favored restraint.

During the second set of debates, perhaps paradoxically, Nicias raised the necessity of expanding the expeditionary forces size to ensure its success. Thucydides informs his readers that Nicias’ true motive was to dissuade the Assembly from embarking on the mission, hoping they would see folly in the proposal and the colossal risk of committing an immense force (or any force) to such an expedition. Rather than rejecting the proposal, however, it was embraced. Both Nicias and Alcibiades embarked on the endeavor in 415 BC.

The acceptance of Nicias’ proposal by others involved in the planning of the operation demonstrates the danger of strategic decision-making which views reduced risk in increasing the size and strength of a force committed to an inherently risky endeavor. The entire incident, as noted most significantly by Josiah Ober, is a demonstration of the intersection of prospect theory and military strategy.

Roughly a year after landing on the island the progress of the Athenian campaign had stalled. Though they had managed to establish a series of walls surrounding port of Syracuse and defeated the Syracusan army in the field, the arrival of a joint Corinthian-Spartan force led to a dramatic reversal of their fortune.  Nicias wrote to the Athenian Assembly in 414/413 BC:

“Now, however, the whole of Sicily is united against us; a fresh army is expected from the Peloponnese, while our troops on the spot are not sufficient to deal even with the opposition we have at present. The time therefore has come for you to decide to recall us, or else to send another force, both naval and military, as big as the first.”

An Athenian relief army arrived under Demosthenes in 413 BC, finding elements of the original intervention force in disarray. Disease had taken hold in the Athenian camp, for example, affecting Nicias himself. Thucydides writes that Demosthenes proposed a withdrawal from Sicily. Nicias, however, was the legitimate commander of the intervention and refused. Following the arrival of additional Spartan forces that year, a withdrawal was agreed to, but the decision proved to come too late—the Athenian force was trapped and later decimated.

"Destruction of the Athenian Army in Sicily" by Hermann Vogel, showing the final defeat of the Athenian at the river Assinarus. (Eon Images)

The Sicilian example highlights both aforementioned behavioral tendencies of prospect theory.It even offers insights into circumstantial effects on strategic decision making in the case of Nicias. As a commander, he demonstrated a spectrum of military decisions linked to the core assumptions of the theory. For example, Nicias’ initial opposition to the operation, and then subsequently damning it through refusing to withdraw in the face of sunk costs is a classic prediction of prospect theory. It was precisely the mismanagement of means in the expansion of the mission's mandate by Nicias (the expansion of the force during the second set of debates and its subsequent reinforcement) that created the conditions necessary for Athens’ eventual defeat in 413 BC to have the long-term consequences it did.

Dien Bien Phu: Prospect Theory in Practice

In 1954, faced with an ever-elusive enemy, the French command sought to provoke one final battle in the valleys of Dien Bien Phu. The French would airlift a large force behind Vietminh lines to force their withdrawal from critical areas of Laos and southern regions of Vietnam. General Navarre, commander of French forces in Indochina, sought to model the operation on the earlier successful campaign at Na San. Simultaneously the battle would draw the Vietminh into a fight that would bring culmination and a negotiated settlement.

Map of Dien Bien Phu Battlefield (Weapons and Warfare)

Operation Castor, the prelude to battle, began on 20 November 1953, with one of the largest air drop operation since D-Day. As geography inhibited the movements of forces on land, the French committed thousands of soldiers to the fight securing an airfield that would serve as a vital artery in keeping the flow of supply and troops open for the battle to come. Over the course of the four months leading up to the battle of Dien Bien Phu, more than 10,000 soldiers were airlifted into the valley, establishing a series of eight strong points.

By the height of the battle, over 14,000 French troops were committed to Dien Bien Phu. The majority of these forces were quickly hemmed in by superior Vietminh positioning and surprisingly effective use enemy artillery. By mid-April, Vietminh forces were able to capture the majority of the central airfield, which was a necessary artery to French reinforcement and supply. This effectively trapped French forces in the valley. Yet despite the rapid deterioration of conditions on the battlefield the French command carried out attempts to reinforce the positions through the air—committing an additional 4,291 soldiers to the fight. One such attempt on the nights of April 11th and 12th sustained over a 40% casualty rate.

French forces in Laos  also launched another attempt to relieve French forces trapped in Dien Bien Phu on April 30th, just days before the last garrisons would be overrun. Operation Condor, which began in December of 1953 was transformed into a last-ditch effort to list the siege at Dien Bien Phu. It involved an additional 3,000 troops in an unsuccessful attempt to disrupt both VietMinh artillery involved in the battle and supply lines.

By May 3, French defensive lines had collapsed, leaving only a fraction of the original force operational, which finally surrendered on May 7. The Battle of Dien Bien Phu was a military disaster. In just over a month, between March and May of 1954, French forces numbering over ten thousand were decisively defeated—much to the surprise of the French general staff and the world. Defeat had been unthinkable, and it was the very size of the force that had convinced all concerned the operation would be successful...or at least far from catastrophic. Yet it was for this very reason the loss of Dien Bien Phu would force the withdrawal of French forces from Vietnam.

French troops seeking cover in trenches. (Wikiwand)

The French defeat at Dien Bien Phu was catastrophic, bringing about the collapse of the French government and the withdrawal of French forces from Indochina. Ultimately French forces in the battle suffered over 11,000 personnel captured and thousands killed and wounded.

Prospect theory can be applied to an analysis of the operation on two planes—the first in risk-averse behavior. General Navarre’s commitment of close to 10% of French forces in Indochina to the battle was done to mitigate risk, not to stoke it. Second, risk-seeking behavior is observable in sustained efforts to reinforce French forces in the Dien Bien Phu valley despite a number of indicators the battle was a losing proposition.


Consideration of both the Sicilian Expedition and Dien Bien Phu raise the troubling prospect that both campaigns, rather than being devoid of strategy, were guided and ultimately damned by it. In both cases, France and Athens sought to achieve a decisive tactical victory that they might parlay a political victory but the pursuit of these objectives led to a perversion of the means necessary to achieve them—as well as an unwillingness to recognize when those objectives were no longer achievable.

The paradox of their strategic thinking lies in the use of forces. Both Athens and France sought to minimize risk by increasing the strength of forces committed. Defeat at both Syracuse and Dien Bien Phu was an outcome in the views of their planners diminished significantly by strength of the force committed. However, in both cases it was precisely the amount of strength committed that necessitated continued support in the face of increasing losses. In retrospect, the French experience in Vietnam succumbed to a folly similar to that of their Athenian counterparts from two thousand years earlier. Both operations sought to mitigate risk through vast force commitments—and later took on increasingly risky measures to compensate for sunk costs.

The planners of Dien Bien Phu and the Sicilian expedition inseparably linked the fate of the operations with the larger campaign. The ultimate lessons learned from both experiences is that political forces can serve as an exacerbating factor. The inability or unwillingness to recognize defeat and its implications resulted in both greater material losses and amplified the strategic consequences for inevitable failures. Strategy is a human endeavor, and prospect theory offers unique insights into another dimension of the human face of war, providing a framework for examination of paradoxical decision making and human error in strategy and tactics.

Gabriel White is a Masters Candidate at American University's School of International Service in Washington D.C.

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Header Image: French parachutists watch comrades being dropped over Dien Bien Phu. (Getty)


[1] Thucydides History of the Peloponnesian War, NY: Penguin Books, 1972, Thuc. Book 7, page. 412

[2] Ibid.,  page. 536

[3] Robert B. Strassler, The Landmark Thucydides, New York: Free Press, 1996, page. 366

[4] Thucydides History of the Peloponnesian War, Thuc. Book 6, Page. 416

[5] Thucydides History of the Peloponnesian War, Thuc. Book 7, page. 478

[6] Ibid., page. 486

[7] Ibid., page. 503

[8] Ibid., page. 508

[9] Turnbull, Patrick, “The Battle of Dien Bien Phu, 1954,” History Today, London, 29.4, April 1, 1979, page. 233

[10] Ibid., page. 238

[11] Turnbull, “The Battle of Dien Bien Phu, 1954,” page 233

[12] Hupe, Bruce H. “The Generalship of General Henri E. Navarre During the Battle of Dien Bien Phu,” U.S. Army Command and General Staff College, Fort Leavenworth, 1994, page 36

[13] Turnbull, “The Battle of Dien Bien Phu, 1954,” page. 238

[14] Hall, Bernard, “Battle of Dien Bien Phu,” HistoryNet, June 12, 2006, Accessible.

[15] Hupe,“The Generalship of General Henri E. Navarre During the Battle of Dien Bien Phu,” page 36

[16] Turnbull, “The Battle of Dien Bien Phu, 1954,” page 238

[17] Shrader, Charles R. A War of Logistics: Parachutes and Porters in Indochina, 1945-1954, The University of Kentucky Press, 2015, pages 331-332

[18] Waite, James, The End of the First Indochina War: A Global History,” Routledge, 2012, page 46

[19] Hall, “Battle of Dien Bien Phu,” HistoryNet, June 12, 2006, Accessible.

[20] Waite, James, The End of the First Indochina War: A Global History, Routledge, 2012, page 144

[21] Hall, “Battle of Dien Bien Phu,” HistoryNet, June 12, 2006, Accessible.

[22] United States Central, I. A. (1954). “Indochina military picture NSC Briefing April 29.”