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 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 be 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, 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 interest 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.