What is game theory? Game theory is a way of thinking about strategic interactions between people, which makes it a crucial component of economics, political science, international relations, psychology and a variety of other disciplines that deal with the complexities of human interaction in decision making.

Much of the theory behind game theory as a unique field was established with John von Neumann and his paper On the Theory of Games of Strategy in 1928, and fundamental contributions were later perfected by John Nash (1950), the brains behind the famous Nash equilibrium. This introduction to game theory in public policy is a collection of resources to help students understand the basics of game theory, how it applies to policy making and illustrates some interesting extensions.

We will begin this dossier by looking at the essential theory and classical concepts behind game theory, such as dominant strategies, Nash equilibrium, pure and mixed strategies, repeated games, and zero sum/non-zero sum games. Then, we will dedicate a significant portion to cover the different policy applications of game theory – such as in vaccination, environmental legislation, and even the current trade war between China and the United States. Finally, we will finish the dossier by incorporating the views of other economic schools on game theory to account for the shortcomings of the neoclassical model.

Traditional Game Theory

To offer a brief introduction to game theory and its most fundamental concepts, this video compilation is best watched in the correct order. The first video introduces game theory, using the example of the Prisoner’s Dilemma to explain the concept of dominant strategies. The second video is a direct continuation that teaches how to find the equilibrium when there are no strictly dominant strategies, via iterative deletion of dominated strategies. The third video introduces the well-known concept of Nash equilibrium, while the fourth focuses on sub-game perfect Nash equilibrium.

Another crucial concept in game theory strategies is that of mixed strategies, which happen when a player chooses between two strategies at random to prevent the other player from predicting their move, and that allows us to find at least one Nash equilibrium even without pure strategy equilibria.

William Spaniel illustrates the concept of mixed strategies in the matching pennies game, when there is no pure strategy equilibrium because, knowing what the other player will do, each player would want to change their action in order to get the best outcome possible. A real-life example of this game is the penalty kick in soccer.

Game theory has evolved immensely, especially over the last decades, with more concepts and complex, real-life situations being modeled by academia.

The Evolution of Trust is a game by Nicky Case that guides you through game theory and how and why to build trust in the real world. It also introduces strategies in repeated games, zero sum vs. non-zero sum games, and communication mistakes. Understanding the most basic concepts in game theory, try to predict the strategies that will lead to the best outcome in the game.

See that when a game is played only once, cheating yields a better outcome than cooperating. However, in reality, games are most often repeated; when deviation from an agreement occurs, the player is punished in the future. This leads to the Nash equilibrium action of the game being played indefinitely, which is usually a sub-optimal strategy for all parties involved. If the duration of the game is high, the loss is bigger than the gains from cheating initially.

Public Policy Applications

So how does game theory influence public policy? Through a concept called social dilemmas. A social dilemma is a collective action situation in which the Nash equilibrium results in outcomes below the Pareto optimal, a state in which there is no alternative that would make a player better off without making anyone else worse off (Ingham, 2014). In other words, it can be defined by two properties: “each individual receives a higher payoff for a socially defecting choice than for a socially cooperative choice, no matter what the other individuals do, but all individuals are better off if all cooperate than if all defect” (Dawes & Robyn, 1980).

In this chapter of “The Principles of Social Psychology”, Charles Stangor explains the concepts of public goods and social dilemmas, and how these conflicts influence human interactions, by looking at different types of social dilemmas. He starts by considering the Tragedy of the Commons, which occurs when the short-term self-interest of individuals wins against the, “time delayed”, potential long-term costs of the behavior to the public good being used. The Contributions Dilemma is another type of social dilemma explained, when the short-term costs of a behavior lead individuals to not engage in a specific action and free ride, even though this may prevent the long-term benefits associated with the action if everyone in the group chooses not to contribute. Finally, Stangor also reviews different laboratory games that study social dilemmas, such as the Prisoner’s Dilemma, resource dilemma, and the trucking game.

Public policies, then, are one way to shift the equilibrium of the game from a suboptimal outcome to one that is more beneficial to the group as a whole, when all players behave selfishly.

Real-life examples of sub-optimal equilibria and how different policies can act to change that are abundant, ranging from election systems and government competition to public health and war. Below are resources that exemplify policy applications of game theory.

Wesley Sheker explains how game theory can predict the failure of elections in a first-past-the-post voting system. Choosing a median candidate would lead to an outcome that is better overall, but strategic voting in repeated games (or in new elections, when the voting results of the previous one are known) will make voters on each extreme more satisfied/unsatisfied, while delivering a suboptimal outcome to the majority. This system also develops into a two-party system with committed base voters, more extreme than the median voter, and some swing voters who call the election. Finally, Shekher suggests the Schulze method as a solution to this social dilemma, by altering the voting system to one that selects the optimal winner.

Fiscal competition in decentralized political systems is beneficial in that it “promotes a better match between local policies and the preferences of residents, and creates an environment for experimentation of different policies, with the best outcomes surviving through a mechanism of natural selection.” However, competition between local governments can lead to suboptimal outcomes in terms of the provision of public goods, revenue collection and the redistributive power of government actions.

Varsano looks at fiscal competition in three spheres. First, in the provision of public goods, in which game theory models predict underprovision of merit goods and social policies; Varsano mentions the example of public health services in Rio de Janeiro and neighboring municipalities, and the response from US states to the decentralized welfare policy to avoid becoming a “welfare magnet”. Second, the competition for funds, where subnational governments may attract the wealthy from other jurisdictions by reducing tax rates or providing a package of public goods tailored to their taste. Finally, the competition for business investment through tax exemptions, one of the major fiscal issues in the European Union and among Brazilian states.

Varsano ends the analysis by examining how to reduce the welfare loss without sacrificing the benefits of decentralization, moving the outcome to a position of some cooperation, which may come from several policies – restrictions on beggar-thy-neighbor policies by means of constitutional provision or national laws that bind the decentralized units, a high degree of centralization of taxing powers coupled with transfers to decentralized units, the assignment of tax legislation to the federal government, vertical coordination, intergovernmental transfer mechanisms, harmonization of fiscal policies, among others.

In this article of The Economist, the authors advocate for Pigouvian taxes to account for the negative environmental externalities that arise from a Tragedy of the Commons case of global warming. They use examples such as the Irish tax on plastic bags, a charge on driving in central London, and Finland, Denmark, Chile, Mexico and British Columbia’s carbon taxes. By adjusting players’ payoffs, a tax should encourage people and companies to lower carbon emissions more efficiently and change societal behavior. The end of the article addresses the shortcomings of using Pigouvian taxes to shift the equilibrium of the game.

Professor Michael Finus lays out the assumptions underlying the game theoretical analysis of global environmental problems, and summarizes the difficulties of cooperation on international environmental agreements (IEAs) and how to actually form coalitions for environmental policy between countries. Through a game theoretical analysis, from a global point of view, it would be advisable that governments cooperate, as cooperation is group rational - global emissions are lower than in the Nash equilibrium, which increases global welfare. Although there is an incentive for countries to cooperate on global pollution control, he argues cooperation is difficult because there is no supranational institution at the global level to enforce cooperation. Finally, Finus states that the problem of cooperation can be structured in three respects: individual rationality, free rider incentive and consensus. An effective and successful IEA must take into consideration these three aspects.

In his blog post, Presh Talwalkar explains California’s mandatory vaccination law in terms of game theory and herd immunity. Although it might be rational to not vaccinate if immunization rates are high, and “free ride” on herd immunity, doing so can eventually lead to low levels of vaccination, in which even those vaccinated have a risk of catching the disease thanks to the rest of the group.

John Swift examines the arms race during the Cold War and addresses the motives of both sides for engaging in Mutually Assured Destruction (MAD). MAD quickly became the Nash equilibrium during the Cold War, as nothing could prevent a nuclear attack from the Soviet or American sides, but retaliation from either side could still happen given the technological advances, making both sides suffer. This created a degree of stability by accepting the complete destruction of both if either were to choose an atomic exchange. However, peace campaigners saw MAD as a perpetual threat of war, in which any accident or miscommunication could end the world. Additionally, for the MAD threat to be believable, it required not only ability but also the perception of resolve, which was often played out in proxy wars (think Vietnam and Afghanistan). By the mid-1970s, the risk of nuclear weapons were high.

Actions were taken to ease tensions and try to move the equilibrium away from MAD, such as a hotline, a Partial Test Ban Treaty, and the Non Proliferation Treaty. Nonetheless, Swift states that the development of new weapons and the technological advancement of defense systems over the years led to a level of risk and spending on MAD well above the logical, and tries to address why.

This paper considers the implications of a trade war between the United States and China in a game theory perspective. Without the WTO and trade agreements that force them to cooperate, both player’s best response is to impose tariffs, resulting in a Nash Equilibrium (NE) of (TT), both in a strategic and extensive form game. It also takes into account the political and economic motivations for each country to impose tariffs or allow free trade.

Game theory has given us a framework for understanding the complexities of human behavior and the possibility for cooperation. However, the root of the theory stems from neoclassical economics and its three axioms: methodological individualism (socioeconomic explanations are sought at the individual level), methodological instrumentalism (all behavior is as a means for maximizing preference-satisfaction), and methodological equilibration (agents’ instrumental behavior is coordinated so that aggregate behavior reaches an equilibrium) (Arnsperger & Varoufakis, 2006). These assumptions are questioned or rejected by other economic perspectives, which alters their understanding of game theory as a field. Nevertheless, the framework is still useful.

Behavioral Economics and Game Theory

For Herbert Gintis, “the most fundamental failure of game theory is its lack of a theory of when and how rational agents share mental construct; when actors do not share beliefs on how the game will be played, then Nash equilibria are unlikely to result” (Hodgson, 2014). Behavioral game theory is the study of game theory through a behavioral economics perspective; it “incorporates behavioral data from experimental and behavioral economics, as well as psychology” to explain factors that influence real-world decisions, as “modern game theory is often in conflict with the behavior of actual decision makers” (Thrasher, 2011).

In this chapter of The Blackwell Handbook of Judgement and Decision Making, Simon Gächter explains behavioral game theory (BGT) as a tool to make game theory more powerful in the analysis of strategic situations. Gächter reviews experimental findings on classic games, and discusses how negative reciprocity, positive reciprocity, altruism and attributions affect the outcome of games. From the literature review, he finds that, in games of cooperation, people cooperate much more than is compatible with the prediction in the Prisoner's’ Dilemma; that, in coordination games, without communication players end up playing the risk-dominant instead of the payoff-dominant equilibrium; that unfair offers are likely to be rejected almost everywhere, regardless of positive monetary payoffs or in one-shot games without any future interaction; that many, even under complete anonymity, are willing to share their wealth with others; and that the attribution of motivations behind a decision matter for the evaluation of outcomes. For greater benefit, the focus of the reading should be from the section Measuring social preferences with simple games, until the end of the section Attributions.

Given the empirical findings that show people’s apparent willingness to pay to achieve fairness or to punish unfair behavior in games, behavioral game theorists have focused on developing models that account for and incorporate these results in game theory.

This paper by Sarah Bonau examines how game theory’s predictions change with the assumption of bounded rationality, in which assumptions are simplified and heuristics are widely used. The assumptions of bounded rationality has been found to be more consistent with real-life scenarios, and when applied to game theory can help design more effective mechanisms for coordination. Bonau outlines different models that predict behavior in real-life games, such as the cognitive hierarchy model, the quantal response equilibrium (QRE), the Experience Weighted Attraction Learning (EWA), sophistication, and social preference models.

Institutional Economics and Game Theory

From an institutional economics perspective, direct interactions and social institutions are primary drivers of human behavior as it relates to the economy. People adhere to new trends due to herd behavior, because others do it before them; the new fashion ceases to serve as a symbol for status, though, after too many follow it, which turns out to be a social dilemma (Elsner et al., 2014). This issue of negative unintended consequences - as it relates to institutions - has been more prominent after the latest financial crisis, and also depends on asymmetric information due to lack of transparency and highly bounded rationality, which traditional game theory does not account for.

What conditions and institutional settings promote cooperative behavior in situations where individuals have an incentive not to cooperate, and how this has evolved to form the basis for the complex societal structures we observe today are central questions for institutional economics. Fleiß and Palan investigate the question of “how societal coordination can arise endogenously as in response to economic coordination problems”, and look at the evolution of institutions in a context of social dilemma situations. Through experiments, they find that direct power over the decisions of others plays an important role when it comes to the success of collective action in such situations, and that people are overwhelmingly willing to pay to be part of an institution with enforced cooperation when faced with a social dilemma situation. The authors also make a comparison between their experimental setting and that of a country deciding whether or not to give up the freedom to autonomously decide on its laws and regulations in return for the benefits from greater cooperation within the EU institutions, which is an example of how institutional economics and game theory play out in real life policy scenarios.

Elinor Ostrom rejects the mainstream notion that privatization is the only way to protect common-pool resources by developing eight design principles through which institutions effectively self-regulate to avoid the Tragedy of the Commons: clearly defined boundaries; proportional equivalence between benefits and costs; collective choice arrangements; monitoring; graduated sanctions; fast and fair conflict resolution; local autonomy; appropriate relations with other tiers of rule-making authority (Wilson, 2016). In the absence of these principles, a top-down approach for cooperation might be necessary. What this means for policies in practice can be seen with the institutional shift that occurred in Ireland after the implementation of their plastic bag tax.

Rosenthal looks again at the plastic bag tax implemented in Ireland, mentioned in The Economist article, but from an institutional perspective. Within just weeks of the introduction of the tax, there was a 94% drop in plastic bag use, and they became socially unacceptable. This institutional shift was possible because there were no domestic plastic bag makers and the environment ministry enforced a strict policy: it is illegal for shopkeepers to take on the cost of the bags, and if they merely switched from plastic to paper bags the latter would also be taxed. The cloth bag fad could have something to do with Ireland’s young, flexible population that has proved a good testing ground for innovation in public policies.

Feminist Economics and Game Theory

Feminist economics focuses on the interdependencies of gender relations and the economy, which has been largely ignored by game theorists, as the players studied in games rarely have a defined gender . This means that issues concerning sex and/or gender in strategic interactions for decision-making have been invisible or, worse, “prone to the sociobiological interpretations that fit easily with the premise of methodological individualism” (Schwartz-Shea, 2002). Schwartz-Shea (2002) reported game-theoretic experiments focused on sex/gender, with the goal of expanding the level of analyses beyond the individual and incorporating the role of gender. Feminist theory was used to design a game relevant to questions of gender equality and to understand the different reactions of men and women to asymmetric games. For the top scorers in the game, there was no sex-of-player effects – both men and women cooperated at similar rates; however, findings for the bottom-scoring men and women were inconsistent with formal game theory, with 63% of women choosing to cooperate versus only 40.7%.

Another result that challenged traditional game theory was observed in Balliet et al (2011) when seeking to answer whether women are more cooperative than men – it depends on several factors, including gender of the partner and duration of interaction.

Although research on game theory through a feminist perspective is still scarce, results from psychology and gender studies can also help inform policies aimed at solving social dilemmas: policies might work for differently for different genders, and this needs to be taken into account when crafting them.

Conclusion

Game theory provides us with an exceptional tool to analyze strategic interactions between people, when the decision of one player to act is a best response to another player’s predicted action. This is very useful when considering social dilemmas, situations in which the choice that benefits each individual ultimately harms the collective. Public policies are one way to shift the equilibrium to one in which the majority will have the best outcome. However, in order to apply the right policies, it is important to consider game theoretic models aside from the traditional. Behavioral economics, institutional economics and feminist economics rely on empirical results to understand game theory through a different lens, one which should be adopted by policy-makers if society is to be truly benefited.

Resources

The Economics Detective. (2013). Game Theory [Video]. Retrieved from https://www.youtube.com/playlist?list=PL_o20EJtc-0hsQ8JEDMVV9XEVVK2JAOed

Spaniel, W. (2012). Mixed Strategy Nash Equilibrium and Matching Pennies [Video]. Retrieved from https://www.youtube.com/watch?v=fvEQujUcPv4

Case, N. (2017). The Evolution of Trust. Retrieved from https://ncase.me/trust/

Ingham, S. (2014). Pareto-optimality. Retrieved from https://www.britannica.com/topic/Pareto-optimality

Dawes, R. (1980). Social Dilemmas. Annual Review Of Psychology, 31(1), 169-193. doi: 10.1146/annurev.ps.31.020180.001125

Stangor, C. (2014). Principles of Social Psychology (1st ed., pp. 517-524).

Sheker, W. (2018). Disastrous Elections: Predicted by Game Theory. Retrieved from https://pennpoliticalreview.org/2018/01/disastrous-elections-predicted-by-game-theory/

Varsano, R., Guimarães Ferreira, S., & Afonso, J. (2002). Fiscal Competition: A Bird's Eye View. IPEA. Retrieved from http://www.ipea.gov.br/portal/images/stories/PDFs/TDs/ingles/dp_114.pdf?fbclid=IwAR2NIeRJ0qlV-pkvRYN5vKxrJmH2lKmzBRz3BDWZOOfOz1v1fyUSuu7jNuQ

Pigouvian taxes. (2018). Retrieved from https://www.economist.com/economics-brief/2017/08/19/pigouvian-taxes

Talwalkar, P. (2015). How Mandatory School Vaccinations Solve A Social Dilemma. Retrieved from https://mindyourdecisions.com/blog/2015/07/21/how-mandatory-school-vaccinations-solve-a-social-dilemma-game-theory-tuesdays/#more-16268

Swift, J. (2009). The Soviet-American Arms Race. Retrieved from https://www.historytoday.com/john-swift/soviet-american-arms-race

MccGwire, J. (2017). A Game Theory Analysis of Donald Trump’s Proposed Tariff on Chinese Exports. Student Economic Review, 31. Retrieved from https://www.tcd.ie/Economics/assets/pdf/SER/2017/9trump.pdf

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Hodgson, G. (2013). Herbert Gintis: The bounds of reason: Game theory and the unification of the behavioral sciences. Journal Of Bioeconomics, 16(3), 311-315. doi: 10.1007/s10818-013-9164-6

Bonau, S. (2017). A Case for Behavioural Game Theory. Journal Of Game Theory, 6(1), 7-14. doi: 10.5923/j.jgt.20170601.02

Gächter, S. (2004). Behavioral Game Theory. In D. Koehler & N. Harvey, Blackwell Handbook of Judgment and Decision Making. Blackwell Publishing. Retrieved from http://people.ict.usc.edu/~gratch/CSCI534/Readings/Behavioral%20Game%20Theory.pdf

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Elsner, W., Heinrich, T., Schwardt, H., & Gräbner, C. (2014). Special Issue: Aspects of Game Theory and Institutional Economics. Games, 5(3), 188-190. doi: 10.3390/g5030188

Fleiß, J., & Palan, S. (2013). Of Coordinators and Dictators: A Public Goods Experiment. Games, 4(4), 584-607. doi: 10.3390/g4040584

Sloan Wilson, D. (2016). The Tragedy of the Commons: How Elinor Ostrom Solved One of Life's Greatest Dilemmas - Evonomics. Retrieved from http://evonomics.com/tragedy-of-the-commons-elinor-ostrom/

Rosenthal, E. (2008). By 'bagging it,' Ireland rids itself of a plastic nuisance. Retrieved from https://www.nytimes.com/2008/01/31/world/europe/31iht-bags.4.9650382.html?mtrref=www.thebalance.com

Schwartz-Shea, P. (2002). Theorizing Gender for Experimental Game Theory: Experiments with “Sex Status” and “Merit Status” in an Asymmetric Game. Sex Roles, 47(7/8). Retrieved from https://link-springer-com.ccl.idm.oclc.org/content/pdf/10.1023%2FA%3A1021474929976.pdf

Balliet, D., Li, N., Macfarlan, S., & Van Vugt, M. (2011). Sex differences in cooperation: A meta-analytic review of social dilemmas. Psychological Bulletin, 137(6), 881-909. doi: 10.1037/a0025354

Arnsperger, C., & Varoufakis, Y. (2006). What is neoclassical economics? The three axioms responsible for its theoretical oeuvre, practical irrelevance and, thus, discursive power. Panoeconomicus, 53(1), 5-18. doi: 10.2298/pan0601005a

Finus, M. (2002). Game theory and international environmental cooperation: any practical application?. In M. Finus, C. Böhringer & C. Vogt, Controlling Global Warming: Perspectives from Economics, Game Theory, and Public Choice. Cheltenham: Edward Elgar Publishing Ltd. Retrieved from https://www.researchgate.net/publication/237357514_Game_Theory_and_International_Environmental_Cooperation_Any_Practical_Application