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  • 5 Game Theory Models in Action: Historical Decisions That Follow Logic

    5 Game Theory Models in Action: Historical Decisions That Follow Logic

    Introduction

    Human Beings are social animals. Since the development of their cognition, humans have developed various kinds of tactics and strategies to survive and evolve at both personal and social levels. Game theory is the science related to strategy, developed in conjunction with mathematical models, to determine the best outcomes with respect to the implemented strategy.

    Although officially, game theory was developed by the Hungarian-American mathematician John von Neumann and the German-American economist Oskar Morgenstern in the 1940s, the various “Games” or strategies had been used by human civilizations throughout history. They had taken important decisions for their survival across different cultures and societies on earth, based on their Nash Equilibria. Now, a Nash Equilibrium is a situation inside a game, in which none of the players can improve their state through strategies, without changing the strategies of other players. Its name comes from its developer, the American mathematician John Nash. In the Nash Equilibrium, all players are basically in their best response state and will remain so until one or more players deviate to other strategies. Many games have been developed and studied among the economic, mathematical, business, and even philosophical circles. Each games create a certain interactive situation, with a certain Nash equilibrium, or equilibria. In this blog, we discuss the five most famous games and strategies, along with one historical example for each, showing how certain geopolitical powers acted and reacted in accordance with their specific Nash Equilibrium. So, let’s begin.

    Chapter 1: Prisoner’s Dilemma

    The Prisoner’s Dilemma is perhaps the most well-known, studied, and discussed game in game theory. It is a paradoxical situation developed, which includes two players, each deciding for their general self-interest without knowing the decision of the other. Let us imagine a situation: The police arrested two different individuals on suspicion of robbery in a building. They are kept in two separate cells such that they cannot interact with each other in any possible way. Now, the police went to the individual suspects and gave the following offer. If both of them confess to doing the robbery, both get 3 years of imprisonment. If neither confesses, they get 1 year of imprisonment. But, if one of them confesses to having robbed together while the other denies, the one who confessed is immediately released by the police, while the one who denied gets 10 years of imprisonment. Let us consider the two suspects, A and B. So, the following situation arises:-


    From the table, let us assess the choices of both A and B. As they cannot contact each other, their individual decisions should be based on assumptions about the other. So, if we consider that B confessed, the best decision A has is also to confess, as 3 years imprisonment is better than 10. Similarly, if B didn’t confess, the best decision for A is still confessing, as he would be released instead of serving 1 year of imprisonment. The situation is the same from B’s side. So, both confess and arrive at the Nash Equilibrium, which is confessing.

    Now, let us consider the Trench War Stalemate on the Western Front during the First World War in 1914. The German and Allied forces clashed in Belgium and France. But after both sides failed to achieve a decisive breakthrough, they dug continuous trenches in the ground to avoid catastrophic losses. After months of a potential stalemate, the options the armies had were to restrain, retreat, or continue bombardment. Although at first glance, restraint sounds like the best option in a stalemate, none of the armies could afford to do so without knowing the motives of the other. If one party had stopped bombarding and attacking, there could have been a possible “10-year prison” situation as mentioned before. Also, they could not run away, as this would lead to an unavoidable defeat. So, even after months and years, the two parties continued their aggression till 1918, in order to maintain the Nash Equilibrium of the Prisoner’s Dilemma game.

    Chapter 2: Game of Chicken

    The Game of Chicken is a very different model from the Prisoner’s Dilemma. In this game, there is not one but two Nash Equilibria. Let us consider a situation in which there are two drivers, A and B, driving their two cars towards each other. They had the pre-made agreement that the one who swerves will be trolled by being labelled as a chicken. Now, if none of them swerves and drives full speed toward each other, they will ultimately crash, resulting in severe injury, if not death. Let us consider the injury or death as 0 (the worst possible outcome), being called a chicken as 1 (the second worst outcome), the opponent as 3 (the highest positive outcome), and both swerve as 2 for each (as they neither won nor lost). So, the situation is as follows:-

    So, even though the safest outcome looks like both swerving, that may lead to humiliation for both. Also, neither of them swerving can lead to serious injury or death. Thus, unlike the Prisoner’s dilemma, the best possible outcome is if both players make the opposite decision from each other, i.e., only one of them swerves. This leads to two Nash Equilibria: either Driver A swerves or Driver B swerves and accepts the humiliation of being called a chicken.

    An example of this game is the Kargil War Resolution in 1999. At that time, both India and Pakistan were recent nuclear powers. In May 1999, Pakistani forces and militants illegally occupied high-altitude positions on the Indian Side of the Line of Control (LoC), which is a militarily sensitive region, in the hope of altering the status quo. Indian forces retaliated, and soon the 4th Indo-Pak war, also known as the Kargil war (Kargil being the region), began. India launched strategic, high-altitude operations while avoiding crossing the LoC. Pakistan, on the other hand, faced growing international pressure. Neither force could retreat at first, as it was a matter of pride and honor. For Indians, Kargil was legally part of their motherland, while for Pakistanis, it was their newly occupied territory. Thus, the war continued for two and a half months, until the Pakistani forces retreated. Already hammered and predicting more upcoming devastation, they had to accept defeat. The Indian forces, on the other hand, became victorious and restored the pre-conflict status quo. Thus, both parties attained the Nash Equilibrium of the Game of Chicken.

    Chapter 3: Stag Hunt

    Another interesting game, or model, is the Stag Hunt. It was devised by the French Philosopher, Jean Jacques Rousseau. As per the game, two hunters, A and B, could hunt together a stag, which is a large meal, or could hunt rabbits individually. But hunting together needs trust, as one could always betray the other. Also, hunting a stag alone is very difficult as it is a large beast. Here, we give credit to their accomplishments. If both successfully hunt the stag, we give 10 to each. If they individually hunt rabbits, each gets 2. If one goes for the stag and the other goes for the rabbit, the one hunting the stag is almost certain to fail and gets 0, while the one who goes for the rabbit gets 4, as he is the only successful hunter. Thus, the following matrix describes the situation:-

    From the matrix, we see that neither the hunter will go to hunt the stag alone, resulting in two possible Nash Equilibria: they either hunt the stag together or hunt rabbits individually. Although hunting a stag will give a better outcome, there exists a possibility of betrayal, whereas hunting rabbits gives a lesser outcome but no chance of betrayal, thus resulting in two different kinds of equilibria. The Stag Hunt model thus has two solutions: one based on more profit and the other based on more security.

    A real-life great geopolitical example for this model occurred more than two millennia ago, at the Battle of Salamis in 480 BCE. When Emperor Xerxes (Kshayarshsa in Old Persian) of the Achaemenid (Haxamanesi in Persian) Empire invaded Greece, many Greek states, of different customs and culture, allied under the Athenian general Themistocles. Thus, we see how the Greeks approached a trust-based Stag Hunt equilibrium, thus finally leading to their victory. If they hadn’t allied, it would have been nearly impossible to hunt a stag named Xerxes. 

    Chapter 4: Battle of the Sexes

    Let us suppose a couple where the man wants to watch an action movie together, while the woman wants to watch a romantic movie together. This situation gives rise to a game theory model called the Battle of the Sexes. In this situation, both want to watch the movie of their choice, but together. So, let us give ratings to their satisfaction levels. If both watch different movies, their satisfaction rating is zero, as they feel lonely, not surrounded by their loved ones. But if both watch the same movie, the person whose preferred movie is chosen is more satisfied, getting a satisfaction rating of 2, while the one who compensates for the movie to be with his or her partner gets a satisfaction rating of 1. This results in the following matrix:-

    In this game, we see that to achieve equilibrium, one of them must compensate and achieve a lower level of satisfaction. Thus, the Battle of the Sexes also has two equilibria where one achieves a lower level of satisfaction than the other.

    A classic example of this model is the imperial court arrangement of the Tokugawa Shogunate in Japan from the 17th to the 19th century. Japan, at that time, had two parallel sources of legitimacy: The Emperor in Kyoto, the sacred, ritualistic, and symbolic authority, and the Shogun in Edo (modern Tokyo), the military, administrative, and real power. In the 1600s, Tokugawa Ieyasu became the Shogun after centuries of chaos. He had 3 choices: if the Shogun dominated, a potential rebellion may arise due to moral illegitimacy; if the Emperor dominated, the chaos resumes,  and the only realistic choice was that both powers cooperate with some sort of compensation. Thus, the imperial court was designed such that the Emperor remained as the ceremonial head, while the Shogun took over the administrative, financial, and military powers. Thus, the Shoguns settled with more satisfaction, while the Emperors settled with a little less but were still satisfied. This system of equilibrium with respect to the Battle of the Sexes continued for more than 250 years till the Meiji restoration in the 1860s. 

    Chapter 5: Zero-Sum Games

    The previous games we explored above were all non-zero-sum games, i.e., when one player wins, the other player doesn’t need to lose. But in zero-sum games, when one player gains something, the other player loses the same amount, so that the total outcomes of the strategy remain zero. For example, in a coin toss, if one side picks heads and the other picks tails, only one side wins, and the other side loses. In zero-sum games, the Nash equilibrium is not about trust, fear, coordination, or compromise, like in the previously mentioned models. The only sensible thing each player can do is to assume that their opponent will try to harm them and thus choose a strategy that limits the damage, even in the worst case. In short, strategies here are individualistic.

    An example of a real-life zero-sum game is the Great Game in Central Asia. In the 19th century,  two expanding powers faced each other in Asia: the British Empire in India and the Russian Empire moving south through Central Asia. The central buffer states between them included Afghanistan, Persia, and the Central Asian Khanates. Both had the ambition of influencing these regions. Their options included a formal alliance, open war, and complete withdrawal, with each resulting in a moral or practical defeat. Thus, both empires chose a fourth option, an option of constant rivalry, with espionage, proxy influence, diplomatic pressure, and local interventions. Thus, both sides chose a zero-sum strategy, and when one got a small win, the other suffered a small loss. They interacted independently based on their individual interests and settled into balance, not through cooperation but through mutual limitation.

    Conclusion

    In this blog, we see how mathematical models dominated human interactions and decision-making, even before they were officially formalized. Game theory, however, is not limited to only human beings, but also affects plants, animals, and even algorithms and AIs. Every decision made by them can be modelled into a game of game theory. So, studying these games, which are numerous in number, can benefit those who want to understand human psychology, business interactions, and geopolitical decisions.

    That’s all for this blog. Hope you find this interesting. Please like, comment, share, and subscribe to my newsletters to be notified of future blogs and updates. Finally, thank you for reading this piece, and wish you all a Happy New Year, 2026.

  • 13 David vs. Goliath Battles: True Stories of Small Forces Stopping Massive Armies

    13 David vs. Goliath Battles: True Stories of Small Forces Stopping Massive Armies

    Introduction

    Wars and Battles are an important part of world history. In most battles, the total strength of the clashing forces generally determines the outcome. In fact, Joseph Stalin, the Soviet Leader, is often allegedly quoted as saying, “Quantity has a quality of its own.” But sometimes in history, a very small group of soldiers was able to stop and sometimes even defeat a large, powerful force. In this blog, we discuss 13 such David vs Goliath instances that happened in the last 1000 years. Ancient battles like Thermopylae, Sphacteria, Alesia, and Watling Street are excluded due to some conflicts about the authenticity of the numbers among some academic historians. Only those battles are included whose numbers are almost confirmed and accepted in the general academia, although the actual number can be a little more than that. So, let’s begin.

    1. The Battle of Vitkov Hill (1420)

    The first battle on our list is the Battle of Vitkov Hill, fought on July 14, 1420. The Holy Roman Empire, led by Emperor Sigismund, launched a crusade to crush the Hussite movement in Bohemia. The force had a strength of 20,000 to 25,000 supported by heavy cavalry, whose primary objective was to capture Prague, along with the reformer Jan Zizka.

    The crusaders attacked through Vitkov Hill, a strategic position that controlled the food supply to Prague. But Zizka, anticipating the attack,  had already fortified the hill with wooden fences and ditches, creating a funnel-like opening for the enemy to enter. The defenders numbered about 60-80 soldiers with a few hundred inexperienced townspeople.

    When the crusaders entered through the funnel-shaped path, the Hussites showered arrows upon them from their crossbows. The arrows decimated the ranks of the aggressors, leading to a crushing defeat of the Holy Roman army.

    2. Battle of Okehazma (1560)

    During the Sengoku period of Japan, there lived the powerful warlord Imagawa Yoshimoto, who dreamt of overthrowing the rival clans. So, on June 12, 1560, he marched with an army of 20,000-25,000 towards the city of Kyoto. On the defending side stood the Daimyo of Kyoto, Oda Nobunaga, with a troop of about 2,000-3,000.

    Yoshimoto’s forces captured the surrounding areas outside Kyoto and encamped at the village of Okehazama for the night. When the soldiers were celebrating their success with sake, Nobunaga used dummies and flags to mislead the scouts and used the cover of a sudden thunderstorm that appeared to approach the enemy camp.

    When they finally reached the enemy camp, they suddenly attacked with deception and killed everyone, including Yoshimoto. The Battle of Okehazama transformed Oda Nobunaga from a provincial daimyo to a rising power in the whole of Japan.

    3. Battle of Haengju (1593)

    The Battle of Haengju was fought during the Japanese invasion of Korea in 1593. At the beginning of the invasion, Japan completely overpowered Korea. Koreans were now desperate to defend their capital, Hanseong (modern Seoul). At Haengju, General Gwon Yul stationed himself at a hilltop fortress along with 2,300 defenders, most of whom were civilians. On February 12, a group of 20,000-30,000 elite Japanese soldiers, including several veteran samurai, approached the hilltop to reach Hanseong. The Koreans used hwacha, multi-arrowed rocket launchers, along with fire arrows, spears, and boiling water to unleash hell upon the Japanese forces from above. The Japanese fought back, but the slope became a deciding factor in the battle. After eight hours of constant fighting, the Japanese finally retreated, and the battle became a turning point in the war, proving that the poorly equipped Koreans can resist and defeat the Japanese army with proper strategy and knowledge of the terrain.

    4. Battle of Pavankhind (1660)

    The battle occurred during the intense conflict between the Maratha Empire and the Bijapur Sultanate in India. The Maratha Emperor Chhatrapati Shivaji Maharaj was encircled by the formidable Bijapur General Siddi Masud at Panhala Fort. On July 13, 1660, the Marathas devised a daring night escape plan towards the fort of Vishalgad. But between the two forts stood the narrow mountain pass of Pawankhind. To ensure the emperor’s safe passage, the Maratha commander Baji Prabhu Deshpande volunteered to hold the mountain pass with 300-600 Maratha soldiers. The plan was simply suicidal, to delay thousands of Bijapuri forces long enough for the emperor to reach Vishalgad.

    Baji Prabhu and his men formed a tight defensive line, completely blocking the narrow pass. They used swords, spears, and matchlock guns to hold off 5,000-10,000 Bijapuri soldiers. Baji Prabhu and his men continued to fight despite sustaining severe injuries. Only after the distant sound of cannon fire signaled the empire’s arrival was the mission completed. Baji Prabhu and his men were killed, but only after completing their mission, which led to the Sultanate’s downfall in the future.

    5. Battle of Shiroyama (1877)

    The Battle of Shiroyama, fought on September 24, 1877, marked the end of the Satsuma Rebellion and the last stand of the samurai. Saigo Takamori and around 300-500 remnant samurai, who were once a force of thousands strong, took position on Shiroyama hill. They faced the modernized Imperial Japanese Army numbering 20,000 soldiers, equipped with rifles, artillery, and naval support.

    The Imperial Army surrounded the samurai on the hill, building trenches, and attacked using dynamites and mortars. The battle continued till dawn, when Saigo and others suddenly charged downhill with swords and spears and temporarily broke the imperial line, demonstrating extraordinary valor and discipline. They kept fighting till the last of the samurai was killed. Although this is an example of a lost battle, Shiroyama became a symbol of loyalty, martial honor, and the feudal transition from feudal Japan to the modern era.

    6. Battle of Rorke’s Bridge

    On January 22, 1879, in the Anglo-Zulu War, the British received a catastrophic defeat at the hands of the Zulu army in Isandlwana. The Zulu forces of 3,000-4,000 warriors, in high spirits after victory, approached the small British station of Rorke’s Drift, which served as a supply depot and field hospital.

    The station was being defended by around 150 soldiers, led by Lieutenants John Chard and Gonville Bromhead, who fortified the station using mealie bags, biscuit boxes, and makeshift barricades.

    The Zulus attacked with wave after wave with spears and shields, while the British used rifles. The battle was intense, and several times the Zulus successfully infiltrated the station, leading to the British soldiers hiding inside the hospital. The British continued their firing from the hospital. Despite being lower in numbers, their advanced weaponry helped them defend the post till dawn, after which the Zulus retreated, acknowledging the difficulty of taking the position. The British group became legendary, earning 11 Victoria Crosses – the most ever awarded in a single action.

    7. Battle of Saragarhi (1897)

    Saragarhi was a tiny fort in the western frontiers of British India (now Pakistan). The fort, though small, acted as a communication link between Fort Lockhart and Fort Gulistan. The area conflicted with the Afghan tribes of Afridi and Orakzai, who often attacked the two larger forts.

    On 12 September 1897, 10,000-12,000 tribes suddenly launched an attack on the tiny fort, aiming to cut the contact between the two larger forts. At that time, Saragarhi had only 21 Sikh soldiers, including Havildar Ishar Singh. The 21 soldiers repelled thousands of Afghans for hours, killing hundreds of them, as the attackers came wave after wave. The 21 soldiers fell one by one, but not before the British-Indian enforcement arrived to properly defend the region. All 21 soldiers were posthumously awarded the Indian Order of Merit, then the highest gallantry award available to native Indians.

    8. Battle of Tolvajarvi (1939)

    The Battle of Tolvajarvi, fought on 12 December 1939, during the Winter War, was Finland’s first major victory against the Soviet Union. The Soviets had launched a large-scale invasion, hoping to quickly conquer Finland, but in the dense forest and frozen lakes near Tolvajarvi, things unfolded differently.

    When about 20,000 Soviet soldiers approached the frozen lake, Finnish Colonel Paavo Talvela planned a counterattack with only 4,500 soldiers with him. Their ski troops attacked the Soviets using the snowy terrain while the aggressors were in open sight near the lakes Hirvajarvi and Tolvajarvi. The Finnish units used grenades, submachine guns, and rapid flanking movements to completely overpower the larger army. Their attack created havoc among the Soviet ranks, forcing them to retreat. 

    Tolvajarvi boosted Finnish morale and proved that small, mobile (skis in this case) units could defeat larger forces by just exploiting terrain and initiative.

    9. Battle of Kohima (1944)

    The Battle of Kohima, nicknamed “Stalingrad of the East”, was fought from April to June  1944 in North-East India. The Imperial Japanese Army of around 15,000 soldiers finally reached British India after conquering Southeast Asia. When they reached Kohima, a major town (now a city), they were stopped by 1,500 soldiers. The Japanese, after their long campaign from Japan, had used up most of their rations and supplies. They were also tired after fighting for months. The defenders, on the other hand, were well rested and fully equipped. The defenders successfully resisted the larger Japanese army till the British 2nd Division arrived, launching a counterattack and marking the end of the Japanese campaign across Southeast Asia.

    10. Battle of Jodotville (1961)

    The Battle of Jodotville or the Siege of Jodotville is one of the most overlooked defensive battles in the history of mankind. In September 1961, during the Congo Crisis, 155 Irish UN peacekeepers of “A” Company, 35th Battalion, were sent to the mining town of Jodotville to protect civilians. On 13 September, more than 3,000 Katangese gendarmes, supported by European mercenaries and heavy weapons, launched a surprise attack. The Irish troop, led by Commandant Pat Quinlan, defended their stand for five days straight. Mortars, machine guns, and sniper rifles were used by the aggressors, yet the Irish defended with exceptional discipline, strategic positioning, and precise marksmanship. Hundreds of Katangese fighters were killed or wounded. But with supplies exhausted and reinforcements unable to break through, Quinlan made the difficult decision to surrender to avoid needless loss of life. His men were later released unharmed, but their heroic stand was ignored and criticized for decades, and it was only in the 21st century that they were formally honored.

    11. Battle of Rezang La (1962)

    During the Sino-Indian War of 1962, the Chinese Army tried to capture Ladakh, situated in Northern India. When around 3,000 Chinese troops reached the 16,000-foot-high altitude of Ladakh, they were met by Major Shaitan Singh and his troop of 123 soldiers of Charlie Company, 13 Kumaon Regiment. Major Shaitan Singh positioned his troop into three separate platoons guarding the mountain pass of Rezang La, which led straight to Chushul,  a critical Indian airstrip. When the Chinese launched a pre-dawn attack, the Indians were near-frozen and fighting with limited ammunition. Yet they hold their ground. The battle soon turned into a close-quarter combat, where soldiers used bayonets, grenades, and even stones. Despite being outnumbered over 10 to 1, the Kumaonis inflicted staggering casualties. They fought till their last bullet and their last breath, successfully defending the mountain pass. 

    When their bodies were discovered months later, 114 of the 123 were found frozen dead at their post, mostly in their firing positions. Rezang La remains one of the greatest David vs Goliath stands carved into the snow and stone of the Himalayas.

    12. Battle of Long Tan (1966)

    The Battle of Long Tan, fought on 18 August 1966, during the Vietnam War, is one of the most remarkable defensive victories ever achieved by a small modern infantry company.

    In the rubber plantations of Long Tan, 108 Australian and New Zealand soldiers of Delta Company, 6th Battalion, were unexpectedly attacked by an enormous Viet Cong and North Vietnamese force of 1,500-2,500 troops.

    The engagement began with Viet Cong mortars hammering the Australian base at Nui Dat. The Delta Company was sent to locate the attackers, but soon they were themselves ambushed. Heavy monsoon rain, thick rubber trees, and knee-deep mud made fighting almost impossible for the foreign troop. Despite being outnumbered around 15 to 1, the Australians formed a tight defensive perimeter and held their ground with disciplined fire, coordinated maneuvering, and continuous communication. As ammunition dwindled, relief came in the form of armored personnel carriers from Nui Dat, which helped break through the Viet Cong attack, leaving thousands of casualties in the process. The Viet Cong force retreated, leading to the victory of the Australian and New Zealand forces.

    13. Battle of Longewala (1971)

    The Battle of Longewala was fought on 4-5 December 1971, during the Indo-Pakistan War. At a lonely desert post in Rajasthan, just 120 soldiers of the 23rd Battalion, Punjab Regiment were posted, supported by a single jeep-mounted recoilless rifle. On the night of 4th December, 2,000-3,000 Pakistani soldiers, along with 45-60 tanks, and hundreds of vehicles.

    Pakistan planned to capture Longewala quickly and push deep into Indian territory before sunrise. But the Indians, led by Major Kuldip Singh Chandpuri, refused to abandon their post. They created fortified trenches and prepared to fight even though they had no anti-tank weapons.

    When Pakistan’s armored columns advanced, the desert became their enemy as soft sand bogged down the tanks, and their headlights revealed their positions. Throughout the night, the defenders used precise rifle fire, machine guns, and their lone recoilless rifle to destroy advancing vehicles one by one. 

    At dawn, the Indian Air Force arrived, destroying the trapped armored tanks. The Mirage and the Hunter aircraft annihilated the Pakistani ranks, leading to a major victory at the western front of the war.

    Longewala stands as an example where a smaller infantry halted and later defeated a larger mechanized force.

    Conclusion

    Thus, we saw that battles are not always won by numbers. From Vitkov Hill to Longewala, history has produced many Davids who fought and sometimes defeated Goliaths, even when every statistic was against them. 

    That’s all for this blog. Hope you enjoyed it. Please like, comment, and share if you feel so. Thank you all for reading this blog.

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