The game theory of political power

Why it exists and how people get it

In the excellent Danish political drama Borgen, Birgitte Nyborg, the leader of a moderate left party, finds herself negotiating a coalition government after the elections. Her initial steps are hesitant, and more seasoned leaders try to convince her to accept a junior role in a government they would control. Bent Sejrø, her political mentor, takes her to the roof of the government building, overlooking Copenhagen, and drives home a crucial lesson:

Look here, damn it! All this could be yours! But power isn’t a cute little puppy that jumps in your lap. You have to grab it and hold onto it, or it will disappear!

Borgen Season 1 Episode 2 “Count to 90”

This political lesson rests on two facts: political power exists—“all this could be yours”—and it is a hard fight to acquire and keep. In this post, I’ll unpack the deep underlying reasons behind these realities.

Why we have leaders

Hobbes’ mistake about the origin of leadership

Why do we have leaders? Why don’t we live in anarchic societies without bosses telling us what to do? A widely influential answer comes from Hobbes’ Leviathan: we need leaders to protect us from each other. Without overarching authority, we would exist in a state of nature, ready to rob and kill one another. As Hobbes put it:

In such condition, there is no place for industry, because the fruit thereof is uncertain: and consequently no culture of the earth; no navigation; no commodious building; no instruments of moving, and removing, such things as require much force; no knowledge of the face of the earth; no account of time; no arts; no letters; no society; and which is worst of all, continual fear, and danger of violent death; and the life of man, solitary, poor, nasty, brutish, and short. - Hobbes (1651)

Hobbes argued that the state’s monopoly on legitimate violence protects people, giving them confidence that they can live their lives without constant fear of harm. His answer has, however, a flaw. He assumes that social order requires a leader—in his case, a monarch. At first glance, this seems reasonable: if there is policing to be done, there must be a police force and, ultimately, a decision-maker at the top. But game theory teaches us that this conclusion is mistaken. Social policing does not necessarily require a leader. Communities can self-police.

One of the key insights from game theory is that social conventions function as equilibria of social games. A small community can establish conventions governing acceptable behaviour without a central authority. These rules are enforced by the group through active monitoring and social pressure, such as gossip. In fact, most rules of social behaviour are not enforced by the state but by the informal mechanisms of community surveillance and sanctioning.

Consider a suburban neighbourhood in 1950s America, where rigid social norms dictated behaviour. It was not the police who ensured that people mowed their lawns, dressed well, spoke properly in public, and refrained from yelling at their neighbours. These behaviours were primarily enforced by the community through social pressure.

Social equilibria do not need leaders; they can persist because everyone enforces them, ensuring others adhere to the rules. Those who deviate face social sanctions.

Anthropologists like Christopher Boehm have described how ancient hunter-gatherer societies often lacked formal leaders. Social order was maintained through constant peer monitoring and sanctions for transgressions like bullying. These sanctions ranged from mockery to ostracism and, in extreme cases, even execution. Similarly, Nobel laureate Elinor Ostrom documented how social norms can emerge as solutions to social problems such as dealing with typical conflicts arising in a community.

The benefits of leadership

The preceding points may suggest that we do not need leaders. Some, like Pierre Clastres (1977), have pointed to the egalitarian lifestyle of hunter-gatherers as evidence that societies can function without hierarchical leadership. But this conclusion is also mistaken. I am sorry to disappoint those inclined toward anarchist or libertarian ideas: there is a strong reason why we need leaders—coordination.

One key insight from game theory is that many problems arise from coordination issues. There are multiple ways cooperation can be beneficial, but which one should be adopted? In stable settings, social conventions can gradually emerge to assign roles and ensure the community functions effectively.

However, conventions take time to form. They are ineffective when new situations arise frequently, and when major decisions need to be made quickly. Without pre-existing conventions, organising collective behaviour in new situations would require deliberations. Constant collective deliberation has a cost: it is slow and time-consuming. If a community faces persistent, unpredictable challenges, the inefficiency of direct democracy can cripple its ability to respond.

The limitations of direct democracy’s speed of decision, derided by the Monty Python’s The Life of Brian (1979)

As put by game theorist Ken Binmore:

We invest authority in the captain of a ship for [that] reason. Who wants a debate about which crew member should do what in the middle of a storm? - Binmore (2005)

A group that frequently encounters unexpected challenges requiring rapid coordination benefits from appointing a leader to make decisions (Van Vugt, et al. 2008). In other words, there are social gains from leadership: wars are more likely to be won, economic activities are more productive, and protection against external threats is more effectively organised. This is why leaderless societies are virtually nonexistent, and why worker cooperatives rarely operate through continuous direct democracy. These arrangements are simply too inefficient for collective decision-making.¹

Sharing the benefits of leadership

The social benefits of leadership raise a crucial question: how should these benefits be distributed? At one end of the spectrum, a leader could return most of the gains to the community, receiving only minimal rewards in terms of resources and status. This model is common among hunter-gatherer societies, as described by anthropologists like Christopher Boehm and Pierre Clastres.² At the other end, a leader could appropriate all the benefits, using their position to extract resources from the community.³

The figure below illustrates different leadership dynamics. Leadership generates social surplus for the community, but the distribution of this surplus varies. Leaders can either share the benefits widely or use their power to capture it, and even potentially make people worse off.⁴

Consider a small fishing community. Without a leader, its members can sustain themselves, as represented by the blue area in the figure. However, a leader can increase the surplus—for instance, by organising hunts for large sea mammals that require coordination. If the leader primarily serves the community with minimal personal privilege, this resembles the self-effacing leadership seen in many ancient tribes. If the leader accrues greater privileges and access to resources, we move toward more hierarchical scenarios. In extreme cases, where a leader imposes his will and captures the benefits, the community members gain little. If coercion is involved, they may even be worse off than without a leader.

The fight for leadership

The share of surplus allocated to leaders creates an incentive to seek power. In highly egalitarian communities, where leaders' privileges are strictly limited and members resist domination, leadership offers little reward. In such cases, few people volunteer for the role, as seen in hunter-gatherer societies and academic departments.⁵

As the rewards of leadership increase, so does competition for the top position. When leadership grants substantial resources and status, contenders go to great lengths to secure power. In extreme cases, leadership struggles turn into deadly games of thrones. Of the 69 Roman Emperors between 14 CE and 395 CE, 62% died violently (Saleh, 2019). The fight for control of the USSR was similarly ruthless—of 40 Politburo members appointed between 1919 and 1952, only 12 (30%) survived to 1952.⁶

When the prize is ruling large nations, contenders are even willing to eliminate family members who are often the main alternative contenders. For instance, in the Byzantine Empire, blinding or mutilating brothers and sons was common to prevent them from claiming the throne. Later, after conquering Constantinople in 1453, Ottoman Sultan Mehmet II enacted a law of fratricide making it legal to kill one’s brothers upon ascending to the throne. Sultan Mehmed III took this to the extreme in 1595, executing 19 of his brothers to secure his reign.⁷

The coalitional nature of the fight for power

Power is often seen as a comfortable position, conferring status and privilege. In reality, when the stakes are high, not only is the struggle to seize power intense, but holding onto it against all potential challengers is just as difficult. Bent’s advice to Birgitte Nyborg in Borgen captures a crucial truth: winning power requires building a coalition, but keeping it demands maintaining that coalition while preventing rivals from forming counter-alliances. Given the high rewards of leadership, many quietly aspire to seize it, and political intrigue is a constant threat. Treachery and betrayal are not exceptions but routine possibilities. This reality is as old as political power itself

One of the earliest written records reveals these anxieties. In the 7th century BCE, in ancient Assyria, Ashurbanipal, the newly named crown prince and future king, is said to have felt deep concerns about his security:

Is danger to be anticipated from the bearded chiefs, the King’s Companions, his own brother and the brothers of his father, the members of the royal family? He doubts the loyalty of his charioteer and of his chariot attendant, of the night-watch, of his royal messengers and of his body-guard, of the officers in the palace and those on the frontier, of his cellarer and baker. He fears for what he eats and what he drinks, he fears by day and by night; in the city and without, there is danger that a revolt against him will be undertaken. - Olmstead (1875)⁸

These concerns are not confined to ancient history. In the modern world, managers frequently worry—often rightly—about coalitions forming against them. Subordinates can unite in criticism, higher-ups may remove them for poor performance or, paradoxically, for being too competent and, thus, threatening.⁹

Titles—whether Emperor, King, or CEO—mask the underlying reality: leadership depends on sustaining a coalition. A decisive failure, such as military defeat or a high-profile project collapse, can embolden rivals to unite against a leader.

Even totalitarian rulers are not immune. Stalin, despite his absolute grip on the Soviet Union, was consumed by fear of betrayal:

In his last years, however, his lifelong suspiciousness became florid paranoia. He eschewed medical advice, Listening to a veterinarian and treating his hypertension with iodine drops. Stalin feared his own shadow and trusted no-one, even himself. He increasingly withdrew from official functions and he muttered menacingly to his close associates that it was time for another purge.

Most coups emerge from fractures within the ruling coalition. Civilian uprisings rarely succeed unless they coincide with elite defections, particularly within the military (Singh, 2014).

Why democracies are more stable

The selectorate and the winning coalition

In The Logic of Political Survival (2003), political scientists Bueno de Mesquita, Smith, Siverson, and Morrow developed a compelling framework to explain the stability of different political regimes—monarchies, dictatorships, democracies—using two key concepts: the selectorate and the winning coalition.

The selectorate consists of those who have a say in choosing the leader. Its size varies widely: in 1199, King John of England was chosen by a group of 236 barons, while in the Soviet Union, the General Secretary was selected by the Politburo, a body of 10 to 25 members. In modern democracies, the selectorate includes all adult citizens who vote in elections.

The winning coalition is the group, within the selectorate, whose support a leader needs to stay in power. Bueno de Mesquita et al. (2003) put it succinctly:

Every leader answers to some group that retains her in power: her winning coalition. This group controls the essential features that constitute political power in the system. […] If the leader loses the loyalty of a sufficient number of members of the winning coalition, a challenger can remove and replace her in office. - Bueno de Mesquita et al. (2003)

The size of the winning coalition and the prize of leadership

Leaders must keep their coalition satisfied—this is their primary concern. In Ancient Rome, emperors depended on the army, particularly the Praetorian Guard, for survival. Emperor Lucius Septimius Severus famously advised his sons.¹⁰

Do not disagree with each other, enrich the soldiers, despise everyone else. - Septimius Severus

A key feature of any regime is the size of its winning coalition relative to the broader population.¹¹ When the coalition is small, the leader does not need to appeal to a large segment of society. In 1199, once John had secured enough barons and their knights, he had little reason to care about the peasants toiling in the fields.

The smaller the winning coalition, the more benefits its members can extract as a result. A leader who needs only a handful of supporters can distribute wealth and privileges among them while keeping a larger share of the surplus for himself. This concentration of power raises the stakes: the greater the prize, the more ruthless the competition to obtain it.

This dynamic explains why power transitions in non-democratic regimes are often violent. When leaders rely on a small coalition, the prize of leadership, and the prizes for the leader’s followers are larger. In contrast, since democratic leaders must cater to a broad coalition, the benefits of power are more widely distributed. The lower stakes of democratic leadership make peaceful transitions more likely.¹²

Democracies are based on broad and changing coalitions

Democracy is often idealised as rule by an informed public engaging in rational debate. In contrast, the coalition-based perspective suggests that democracy functions because politicians must secure support from large, shifting groups of voters. The need for broad coalitions ensures that leadership benefits a wide cross-section of society. Moreover, as coalitions change over time, many individuals will eventually find themselves on the winning side.

Political scientist William Riker (1982) emphasised this game-theoretic insight, arguing one key aspect of democratic regimes is that they prevent any single majority from holding power indefinitely:

Liberal democracy almost guarantees some circulation of leadership so that great power is usually fleeting and no vested interest lasts forever. - Riker (1982)

Leaders and their political power exist because they serve a purpose—not, as Hobbes suggested, to prevent chaos, but to facilitate collective decision-making with minimal delay. This function creates a social surplus. Whether this surplus is returned to society or captured for private gain depends largely on the structure of the coalition supporting the leader. Across all forms of leadership, from ancient Rome to modern boardrooms, leaders are acutely aware of potential challengers. This compels them to cater to the interests of their winning coalition.

This perspective offers a pragmatic justification for democracy, distinct from idealised notions of civic participation. Democracies function well for the whole population because their large and fluid coalitions ensure that alternating leaders consider the preferences of most social groups, which have a strong chance of being part of a winning coalition at some point.

This post is part of a series on the psychology and game theory of coalitions. In the next post I’ll discuss why democratic institutions are not guaranteed.

References

Boehm, C. (1999). Hierarchy in the Forest: The Evolution of Egalitarian Behavior. Cambridge, MA: Harvard University Press.

Bueno de Mesquita, B., Smith, A., Siverson, R. M., & Morrow, J. D. (2003). The Logic of Political Survival. Cambridge, MA: MIT Press.

Clastres, P. (1977). Society Against the State: Essays in Political Anthropology. Urizen Books.

Ekinci, E. B. (2018). Fratricide in Ottoman Law. Belleten, 82(295), 1013–1046.

Hachinski, V. (1999). Stalin’s last years: Delusions or dementia? European Journal of Neurology, 6(2), 129–132.

Hobbes, T. (1651). Leviathan, or the Matter, Forme, and Power of a Commonwealth Ecclesiasticall and Civil. London: Andrew Crooke.

Olmstead, A. T. (1923) History of Assyria. New York: Charles Scribner’s Sons.

Przeworski, A., Alvarez, M.E., Cheibub, J.A. and Limongi, F. (2000) Democracy and Development: Political Institutions and Well-being in the World, 1950–1990. Cambridge: Cambridge University Press.

Riker, W. H. (1982). Liberalism Against Populism. San Francisco: Freeman.

Saleh, J. H. (2019). Statistical reliability analysis for a most dangerous occupation: Roman emperor. Palgrave Communications, 5, Article 155.

Singh, N. (2014). Seizing Power: The Strategic Logic of Military Coups. Baltimore: Johns Hopkins University Press.

Van Vugt, M., Hogan, R. and Kaiser, R.B., (2008). Leadership, followership, and evolution: some lessons from the past. American psychologist, 63(3), p.182.

1. Hierarchy does not require leadership to provide benefits. In any community, ambitious individuals may attempt to dominate others through strength and coalition-building. While they may succeed temporarily, such arrangements are unstable due to the flexibility of coalitions. Any leader who extracts more from society than they contribute risks being overthrown by those who would benefit from their removal. Even in monarchies, where much of the population is disenfranchised, extreme exploitation often leads to revolt.

Leadership is more likely to endure when it provides clear benefits to the community. If these benefits are widely shared, there is less incentive to challenge the existing order. As Boehm (1999) notes:

2

A respected band leader would go out of his way to avoid prominence, giving away virtually everything he came to possess. […] the foraging band’s leader was a mere primus inter pares, a first among equals. - Boehm (1999)

3. The paradox of leadership is that power, once entrusted, can be misused. It resembles a household buying a gun for protection—whoever holds it may later turn it against the family.

4. This figure is a simplification. In fact, the size of the social surplus credibly depends on the type of leadership, with leadership capture typically leading to less efficient institutions (e.g., corruption).

5. In some societies, leadership is actively avoided. Boehm (1999) describes the reluctance of men in the Busama of New Guinea to take on leadership roles, a pattern seen across many cultures.

6. The deadly stakes of power struggles extended even to… the papacy. In 1294, Pope Celestine V resigned under pressure from his successor, Boniface VIII, who then had him imprisoned and sentenced to death—likely to prevent a rival faction from rallying around him (Bueno de Mesquita et al., 2003).

7. From an evolutionary perspective, killing family members for power may seem counterintuitive. However, Hamilton’s rule for inclusive fitness suggests that if the rewards are high enough, eliminating a brother could be offset by producing more offspring. While kinship provides natural allies in ruling, history shows that many leaders have found the prize of leadership great enough to justify eliminating even close relatives.

8. Cited in Bueno de Mesquita et al. (2003).

9. The OpenAI coup of November 2023 offers a striking illustration of the coalitional nature of leadership. Initially, a faction within OpenAI’s board ousted CEO Sam Altman, citing a lack of transparency. This move, however, triggered internal upheaval, leading to a counter-coalition. President Greg Brockman resigned in protest, key researchers followed, and over 700 of OpenAI’s 770 employees signed an open letter demanding Altman’s reinstatement. Investors, including Microsoft, applied pressure, and within five days, Altman was restored as CEO while the board was reshaped.

10. Bueno de Mesquita and colleagues focus on the selectorate—the subset of the population involved in leadership selection—rather than the broader disenfranchised population. This focus is strategic: the selectorate determines leadership stability. However, when considering the overall well-being of a nation’s residents, it is useful to analyse the winning coalition in relation to the entire population.

Note for political scientists: This discussion integrates the selectorate theory with the broader concept of leadership as a high-stakes prize, an approach that is outside Bueno de Mesquita et al.'s theory.

11. Cited in The Logic of Political Survival, chap 2.

12. Bueno de Mesquita et al. (2003) argue that regimes with small winning coalitions tend to be stable because coalition members fear losing their privileged status. A new leader would likely rely on a different small coalition, making defection risky.

They define stability by the length of the leader tenure. Here I consider the stability of the overall regime. Democracies are more stable in the sense that institutional rules remain consistent across leadership transitions, ensuring orderly succession. In contrast, autocratic regimes are more prone to violent upheaval and institutional change (Przeworski et al., 2000).