Sunday 25th October 2015 marks the 600th anniversary of the Battle of Agincourt in 1415. It is an interesting battle from the perspective of non-cooperative game theory. It has elements of both imperfect information on how the game is played and incomplete information of player type. The optimal strategy for Henry V or Charles VI depended on what each believed to be the strategy of the other player. In particular, we believe that Henry’s playbook demonstrates a winning strategy with noise the purpose of which is to influence an opponent’s belief system. Noise occurs in a game when an opponent believes that you are going to do X but your real intention is Y. The French believed that the English would retreat. Henry V reinforced that belief. In the early morning of 25th October the English repositioned wooden stakes on the battlefield in full view of the French. Once the French committed resources to an English retreat, Henry V out-manoeuvred the French army by a surprise attack.
The Player’s Type
Some historians argue that the French believed that the English would retreat rather than fight, given the superior numbers in the French army. Also historians can recount that Henry V himself by 1415 had preferred a defensive play. However, we believe that Henry V in 1415 and his trusted advisers, the Duke of York, Lord Camoy and the knight Thomas Erpingham were early practitioners of modern non-cooperative game theory tactics. They were strategic lateral thinkers in the sense that they realised in 1415 that Agincourt was a zero-sum game and that winning was a function of noise. It created uncertainty.
They facilitated the French in their belief that the English would retreat. Henry knew that the French commanders were prepared to wait for nobles and knights to join the attack and crush the retreating English. Although not at the battle due to illness Charles VI believed that the French could defeat Henry V and historians recount how eager the French nobles wanted to fight the English against the advice of the more experienced and superior French knights. On good intelligence, Henry V knew this and allowed the French to continue to believe that they were retreating.
Game Dimension: The Terrain
With a hundred years of war, and a long campaign in France, by 1415, this was a battle that Henry V had to win to solve claims on the French throne and secure the English throne. Henry V was a committed player. In addition, Henry’s knowledge of the field of battle facilitated his strategy. He had marched his army across Northern France as the French had pushed him south and away from the port of Calais. Thomas Erpingham canvassed the terrain and assessed its suitability for cavalry and knights in full plate armour.
Shortly after sunrise Henry knew that he had influenced the French belief system – they prevaricated, they waited for noblemen. Furthermore they believed that Henry believed that the superior French army would defeat the English. So they believed that the English would defend and then retreat. A strip of open land between the woods of Tramecourt and Agincourt was chosen and Henry V deployed his army and made plans to form a battlefield. He initiated the first move according to historians by moving his army forward and re-positioning wooden stakes across the terrain to protect the longbow-men from a French cavalry charge. He was signalling an attack. The French observed this change of tactic but did not advance the cavalry. Historians are puzzled by this.
The Opponent’s Rationality
Choice is rational if it is optimal for some belief that you hold about your opponent’s choice. So it is possible that the belief system of the French, in particular the belief system and choices of Constable Charles d’Albret, the French commander, had been influenced by the English tactics. There are at least three answers to the puzzle from non-cooperative game theory offering some insight into the internal dialogue between the French commanders:
- Credible Threat: The French truly believed in an English defence: when they observed English tactics and manoeuvres in the early morning they had all the hallmarks of a defensive play followed by retreat.
- Reputational Advantage: The French dismissed an attack: they had a reputational advantage in greater numbers and Charles d’Albret believed that Henry V believed that in an attack the French infantry would have out-numbered the English.
- Noise and Uncertainty: Given the significance of 1 and 2 the French behaved like Sisyphus pushing his boulder up the hill – only the boulder grows a little bigger with each delay by the French commanders.
Henry V’s Attack
In the early hours after sunrise the French commanders now believed that the English were retreating. So the French waited. But Henry V believed that the French believed that Henry believed that the French infantry would outnumber them. In retreat Henry V would attack rather than defend the English positions.
The English launched an attack from the flank positions. Surprise entered the game. However, the chosen field of battle was narrow and both English and Welsh archers and longbow-men took the flanks and placed sharp pointed wooden stakes at an angle in front of their archers in order to impale enemy cavalry horses. In addition the battle-field was narrow but recently ploughed land and as it had rained the night before so Henry V knew the significance of a very muddy battlefield.
The French cavalry were more anxious to engage, they were drawn into the battlefield, but as the battle ensued the French cavalry horses were slowed down, their advancing infantry and men at arms could not move forward, knights could not see in their muddied helmets – chaos and disorganisation in a muddy battlefield made it very difficult for French knights to fight in full plate armour. The narrow terrain made it impossible for the French to advance. Once the French army was dragged into the narrow muddy terrain the English archers and knights took victory. The ability of the French knights and cavalry to attack was greatly hampered by the muddy terrain.
So arguably the most significant factor in deciding the outcome was influencing the belief system of the French, allowing them to believe that victory was inevitable, taking them by surprise and then drawing the enemy into battle on to a muddy field. History shows that the Apache may have displayed similar strategic thinking during the early periods of the American Indian wars of 1840-1870 in sporadic games of cavalry quick response posse groups Vs Apache raiding parties. Using solar signalling and Indian scouts and, with a backdrop of a Civil War, cavalry loss in the early years and the Apache gains could be attributed to intelligence gathering on belief systems. Similarly, Cortes, shortly after landing at Tabasco in the Yucatan peninsula in 1519, allegedly burnt all his boats as a signal to the natives observing from the hilltops of his commitment to stay and fight. They cooperated. In a classic betrayal of trust Cortez defeated the natives.
Henry V’s Playbook
In a game against an opponent that outnumbers you in scale and size, your first opening move should be a signalling move to influence the opponent’s belief system. Surprise provides a competitive advantage. The noise – should it be believed as a credible threat in the game – will confuse your opponent, create uncertainty and allow you seize the second win payoff in your subsequent moves. Regardless of what an opponent does influencing the belief system of your opponent is at least as good as not doing so. So do it in any game, independent of player size.
We continue to research the second win and some discussion papers are available at http://www.patrickmcnutt.com/news/masterclass/ for further comment. In our book Decoding Strategy, pp98-99 we discuss a product launch of a gPhone as a signal in 2006 that may have provoked Apple to launch the iPhone2G earlier than planned in 2007. The Apple executives believed the rumours of a rival smartphone so they moved quickly. Early reviews were not favourable and competitors had possesion of a new competing product. The iPhone is less than 10 years old, but it stumbled in 2007-2009, it stumbled in 2013 with iPhone5C and the Android alliance in 2015 provides a formidable threat http://www.patrickmcnutt.com/news/memo-to-ms-ahrendts/.
A more intrinsic threat in the data is the commoditisation of the smartphone and the inevitable demand for lower priced full functionality smartphones in the sub-$100 price ranges. Once the Android alliance, Google and Samsung, commit resources to smart devices, smartphones and tablets, Apple could out-manoeuvre their rivals by a surprise attack. A nano-iPhone, for example, was one of our game theory recommendations in 2012 http://www.patrickmcnutt.com/news/i-lag-or-byte-of-the-apple-2/ and we believe that it continues to be an optimal play for Apple in a time continuum game with noise wherein players exploit the belief systems of an opponent in order to secure a second win.
 Working from the research http://www.patrickmcnutt.com/video/strategic-lateral-thinking/ we could argue that Henry V and his advisers understood that an equilibrium is in a time continuum, requiring good intelligence on player type and intelligence on the game dimension (terrain in this case) and they believed that the French army under Charles VI and his advisers in 1415 were less than fully rational players in the battlefield at Agincourt.
 Shakespeare’s Henry V speaks in Act I Scene II of meeting the Dauphin, a messenger from Charles VI.
 Sisyphus in Greek mythology was condemned to repeat forever the same meaningless task of pushing a boulder up a mountain, only to see it roll down again. Read Albert Camus’s 1942 philosophical essay The Myth of Sisyphus. Also read Ashlee Vance in Bloomberg Business Week edition October 12 2015 in an article on ‘Smartphone Margins’ where rivals to Apple’s iPhone are compared to Sisyphus.