GAME THEORY IN POLITICAL SCIENCE

Politics is, at its core, a matter of interaction. Voters respond to candidates, candidates respond to one another, states respond to the moves of other states and legislators respond to the rules under which they bargain. Whenever the outcome for one participant depends on what others choose to do, the situation invites a particular kind of analysis. That analysis is the province of game theory, the mathematical study of strategic decision-making among rational actors whose choices affect each other.

Over the past eight decades, game theory has moved from the margins of mathematics into the centre of political science. It supplies a vocabulary and a set of formal tools for thinking about conflict, cooperation, bargaining and deterrence. This article explains the origins of game theory, sets out its central concepts and surveys the ways in which it has been applied to the study of political life.

What Game Theory Is

A game, in the technical sense used by the discipline, is any situation in which two or more participants each choose a course of action, and in which the result for every participant depends on the combined choices of all of them. The participants are called players. The courses of action available to them are called strategies. The result of any particular combination of strategies is described by a payoff, a numerical representation of how much each player values that result.

The defining feature of a game, as opposed to a simple decision problem, is interdependence. When a person decides whether to carry an umbrella, the outcome depends on the weather, which does not care about the decision. When a person decides whether to enter a price war with a competitor, the outcome depends on what the competitor does, and the competitor is reasoning in the same way about them. Game theory is built for the second kind of situation.

Two broad assumptions underpin most of the field. The first is that players are rational, meaning that each has consistent preferences over outcomes and chooses the strategy that best advances those preferences given what they expect others to do. The second is that the structure of the game, the players, the strategies and the payoffs, is common knowledge, so that each player can reason about how the others will reason. These assumptions are idealisations, and much modern work relaxes them, but they provide the starting point from which the theory is built.

The Origins Of The Discipline

Although isolated results in strategic reasoning appeared earlier, the field acquired its modern foundation in 1944 with the publication of Theory of Games and Economic Behavior by the mathematician John von Neumann and the economist Oskar Morgenstern. Von Neumann had already proved a central result, the minimax theorem, for two-player zero-sum games in 1928. The 1944 book extended these ideas into a general framework and argued that strategic interaction could be treated with the same rigour that mathematics had brought to the physical sciences.

The early development of the field was closely associated with the RAND Corporation, a research institution in the United States of America (hereinafter: USA) founded in the years after the Second World War. Analysts there were drawn to game theory because it offered a formal language for problems of conflict and deterrence that were pressing during the period of tension between the USA and the Union of Soviet Socialist Republics. It was in this setting, in 1950, that the mathematicians Merrill Flood and Melvin Dresher devised the scenario that the mathematician Albert William Tucker would later name and popularise as the prisoner’s dilemma.

The most influential single contribution came from the mathematician John Forbes Nash Junior. In a doctoral dissertation submitted at Princeton University in 1950, and in papers published shortly afterwards, Nash introduced a solution concept that applied to games far more general than the zero-sum cases von Neumann had solved. For this work, Nash was awarded the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel in 1994, sharing it with John Harsanyi and Reinhard Selten.

The Nash Equilibrium

The concept that bears Nash’s name is the single most important tool game theory has given to political science. A Nash equilibrium is a combination of strategies, one for each player, with the property that no player can improve their own payoff by changing strategy alone, while the others keep theirs unchanged. Each player’s choice is a best response to the choices of the others, so that no one has any incentive to deviate.

The power of the idea lies in its generality and its stability. An equilibrium is a configuration that, once reached, tends to hold because any individual who departs from it does worse for themselves. It does not require players to coordinate or to trust one another. It requires only that each act in their own interest, given what the others are doing. This makes it a natural way to describe outcomes that arise from independent, self-interested behaviour, which is precisely the situation that recurs throughout politics.

A Nash equilibrium need not be efficient, fair or desirable. It describes what is stable, not what is good. A great deal of the interest in the concept for political analysis comes from situations in which the stable outcome is one that all participants would prefer to avoid, yet none can escape by acting alone. The clearest illustration of this is the prisoner’s dilemma.

The Prisoner’s Dilemma

The prisoner’s dilemma is the most widely discussed example in the whole of game theory, and it has become a standard reference point well beyond the discipline. In its classic form, two suspects are arrested and held separately. Each is offered the same choice: stay silent or confess and implicate the other. If both stay silent, each receives a light sentence, because the authorities can prove only a minor charge. If one confesses while the other stays silent, the confessor is rewarded with release, and the silent suspect receives the heaviest sentence. If both confess, each receives a moderately heavy sentence.

Examined from the standpoint of either suspect, confessing yields a better personal result, whatever the other does. If the other stays silent, confessing brings release rather than a light sentence. If the other confesses, confessing avoids the heaviest sentence. Confessing is therefore what game theorists call a dominant strategy: it is preferable regardless of the other’s choice. Since both reason identically, both confess, and both end up with the moderately heavy sentence. Yet had both stayed silent, each would have done better.

The unsettling lesson is that the outcome in which both confess is the only Nash equilibrium, and that this stable, individually rational outcome is collectively worse than the available alternative. The pursuit of self-interest by each leads to a result that serves neither well. The dilemma captures, in a single small structure, a problem that appears across politics and economics: the gap between what is rational for the individual and what is best for the group.

The structure becomes richer when the interaction is repeated rather than played only once. In a repeated prisoner’s dilemma, players meet again and again, and the prospect of future encounters changes the calculation. A strategy of conditional cooperation, in which a player cooperates so long as the other does and retaliates against defection, can sustain mutual cooperation over time. The study of such repeated games has been central to understanding how cooperation can emerge among self-interested actors without any external authority to enforce it.

Applications In Political Science

The migration of game theory into political science gathered pace from the 1960s onwards, and it has since reshaped several subfields. Its applications fall into a number of recognisable areas.

The first is international relations. Interactions between states are a natural subject for strategic analysis, because there is no overarching authority to enforce agreements, and each state must anticipate the responses of others. The dynamics of deterrence, the logic of an arms race and the difficulty of sustaining disarmament have all been examined through game-theoretic models. The economist Thomas Schelling, who shared the Sveriges Riksbank Prize in 2005, was especially influential in applying strategic reasoning to conflict and bargaining, showing how commitments, threats and the manipulation of risk shape the behaviour of adversaries.

The second is the study of collective action. Many political problems take the form in which a group would benefit from cooperation, yet each individual has an incentive to let others bear the cost. The provision of public goods, participation in voting and the maintenance of shared resources all share this structure. The prisoner’s dilemma and its relatives give a precise account of why such cooperation is difficult to achieve and of the conditions, such as repeated interaction or enforceable rules, under which it can be sustained.

The third is the analysis of voting, elections and legislatures. Game theory and the closely related field of social choice theory examine how the rules by which votes are aggregated affect outcomes, how candidates position themselves to attract support and how legislators form coalitions to pass measures. The political scientist William Harrison Riker was a leading figure in bringing formal modelling into the study of these questions, an approach that became known as positive political theory. Models of this kind help explain phenomena such as the tendency of two-party competition to drive candidates towards the centre and the instability that can arise when many options are decided by majority rule.

The fourth is bargaining and coalition formation. The construction of governing coalitions, the negotiation of treaties and the distribution of portfolios among parties can all be represented as games in which players bargain over how to divide a benefit. Game theory provides predictions about which coalitions are likely to form and how the spoils are likely to be shared, drawing on the relative bargaining strength of the participants.

Cooperative And Non-Cooperative Approaches

Game theory is conventionally divided into two branches, and the distinction is useful for understanding its political applications. Non-cooperative game theory, which includes the prisoner’s dilemma and the Nash equilibrium, takes the individual player as the unit of analysis and asks what each will do when binding agreements cannot be assumed. It is well-suited to situations of conflict and to settings, such as relations between states, in which no authority can enforce promises.

Cooperative game theory, by contrast, takes groups of players, or coalitions, as the unit of analysis and asks how the gains from cooperation might be divided when binding agreements are possible. It is well-suited to the study of coalition formation and to questions about the fair or stable distribution of a shared benefit. Concepts developed within this branch, such as measures of voting power, have been applied to assess how much influence different members of a legislature or a council actually wield, as distinct from the formal weight of their votes.

The Limits Of The Method

The reach of game theory in political science is broad, but its limits are as important to understand as its strengths. The models rest on assumptions about rationality and about shared knowledge of the situation that real political actors do not always satisfy. People have incomplete information, hold mistaken beliefs, are influenced by emotion and identity and do not always pursue their interests consistently. A model is a simplification, and the value of any particular model depends on whether the features it leaves out are ones that matter for the question being asked.

Game theory has responded to these concerns rather than ignored them. The development of games of incomplete information, in which players are uncertain about one another’s payoffs, was a major advance associated with John Harsanyi. The growth of behavioural and experimental work has tested the predictions of the theory against how people actually behave, often revealing systematic departures from the idealised model. The field today is less a claim that politics is a clean mathematical contest than a disciplined way of reasoning about strategic situations, one that makes its assumptions explicit and traces their consequences.

The strength of the approach is precisely this discipline. By forcing an analyst to state who the players are, what choices they face and how they value the outcomes, game theory turns vague intuitions about political behaviour into clear, testable claims. Even when a model’s predictions fail, the manner of the failure is informative, because it shows which of the stated assumptions was doing the work. This is why the method has endured, and why it continues to be taught as a foundation of the modern study of politics. As a public lecture delivered at the London School of Economics and Political Science by Professor Bernhard von Stengel in February 2020 described it, game theory is the science of interaction, and interaction is what politics is made of.

Conclusion

Game theory entered political science as an import from mathematics and economics, and it has become one of the standard languages in which political behaviour is described and explained. Its central concepts, the strategy, the payoff, the Nash equilibrium and the prisoner’s dilemma, provide a way of thinking about situations in which the choices of separate actors are bound together. Its applications run from the deterrence calculations of states to the coalition arithmetic of parliaments, and its limits remind those who use it that a model is a tool rather than a portrait. What game theory offers political science is not certainty about how politics will unfold, but a rigorous way of asking why rational actors, each pursuing their own ends, arrive at the outcomes they do.

This is also the case with many other tools in political science that are available to politicians. Mostly, such tools do not directly produce an outcome or a final decision, but are geared to improve scenario-building and facilitate decision-making. For example, the political cube is a tool to categorise political actors to develop a better understanding of how to interact with them. Therefore, it is important that political actors, such as citizens, professionals and, first and foremost, politicians, are well-equipped with the knowledge of such concepts and tools. We at Essydo Politics aim for a better political understanding in society to enhance progress through politics.