Game theory
Chapter 3 - Experiential Growth Method®
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Welcome to the Game theory page
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Game theory is the science of the (sub)optimal decision-making of independent and competing actors (individuals or groups) in a strategic setting.
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Core ideas
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If we want to explain the regularities of social interactions, it is helpful to have strategic models that predict that people will adopt regular patterns of behaviour. Game theorists are, for that reason, interested in equilibrium: a situation where no player is interested in unilaterally deviating and changing their behaviour.
The notion of the core is similar in spirit to the notion of equilibrium, but it allows groups of players—instead of just one—to deviate together.
The fact that no coalition is likely stable in voting games can seem disappointing at first sight, but it is likely a blessing for the democratic process. It means that any group has the potential to become part of a winning coalition. No segment of society is forever under the tyranny of a permanent majority, promoting widespread acceptance of democratic conflict resolution. If you lose today, you know that you might win tomorrow. Robert Dahl, known for his work on democracy, emphasised the importance of the instability of a majority for the democratic process to work.
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Deep dive
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Agency
Groups as persons
There is strong evidence that groups exhibit the same behaviour as individuals.
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| Robert J. Aumann lecture - Collectives as Individuals |
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| In many applications of Game Theory, a player is a collective such as a household, team, political party, country or the like. Usually, this is understood as an idealization. In games where, say, countries are modeled as players, the "real" players are the individual citizens, with their individual goals and individual decisions and individual free will. It's only because this "true" game is too big and unwieldy to analyze that, it is held, game theorists model players as they do. Here, we advance the thesis that it *IS* really that way: that in large part, collectives are like individual people, and may be thought of as such. And, perhaps, not only in Game Theory. |
| https://mediatheque.lindau-nobel.org/recordings/33966/robert-aumann |
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| Onni Hirvone - Groups as Persons? A Suggestion for a Hegelian Turn - Journal of Social Ontology - 2017 |
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| If groups have goals, desires, and purposes in the social world, it is likely that they will face questions of normative significance. List and Pettit state that “there is no principled reason” why groups should not be able to make judgments on normatively significant matters. Finally, they make a case for groups ensuring that one or more of their members perform in a relevant manner. Thus, the fact that every act of a group is realized by an individual agent who is in control of her own actions does not present a problem for taking the group to also be in control of its actions. “The members have responsibility as enactors of the corporate deed so far as they could have refused to play that part and didn’t. The group agent as a whole has responsibility as the source of that deed” |
| https://www.degruyter.com/document/doi/10.1515/jso-2016-0019/html |
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Businesses as agents
Businesses often have several strategic choices that affect their ability to realise economic gain. Game theory is beneficial for modelling competing behaviours between economic agents. For example, businesses may face dilemmas such as retiring existing products and developing new ones or employing new marketing strategies. Businesses can often choose their opponent as well. Some focus on external forces and compete against other market participants. Others set internal goals and strive to be better than their previous versions. Whether external or internal, companies always compete for resources, attempt to hire the best candidates away from rivals and dissuade customers from choosing competing goods.
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Interaction
Zero sum
A direct conflict between multiple parties striving for the same outcome is often called a zero-sum game, meaning that the collective net benefit received is equal to the net benefit lost.
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Non-zero sum
A non-zero-sum game is one in which all participants can win or lose at the same time. Instead of competing and attempting to win at the expense of the other, both parties benefit.
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The Nash equilibrium
The Nash equilibrium suggests that in a prisoner's dilemma, both players will make the move that is best for them individually but worse for them collectively.
The prisoner's dilemma is the most well-known example. Consider the example of two criminals arrested for a crime. Prosecutors have no hard evidence to convict them. However, to gain a confession, officials remove the prisoners from their solitary cells and question each in separate chambers. Neither prisoner has the means to communicate with the other. Officials present four deals, often displayed as a 2 x 2 box.
- If both confess, they will each receive a three-year prison sentence.
- If Prisoner 1 confesses but Prisoner 2 does not, Prisoner 1 will get one year and Prisoner 2 will get five years.
- If Prisoner 2 confesses but Prisoner 1 does not, Prisoner 1 will get five years, and Prisoner 2 will get one year.
- If neither confesses, each will serve two years in prison.
The most favourable strategy is not to confess. However, neither is aware of the other's strategy and without certainty that one will not confess, both will likely confess and receive a three-year prison sentence.
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Coalitional game theory
How it works.
Consider a simple example of weighted voting games. Imagine that Alice, Bob, and Carol must agree on how to divide a dollar. They need a majority—any two agreeing on a division—to implement the decision. For instance, they could decide to split the dollar equally: 1/3, 1/3, 1/3. However, this “grand coalition” is unstable.
- Alice might suggest to Bob that they instead propose a division of 1/2 and 1/2 for themselves, excluding Carol.
- If Bob agrees, all seems well until Carol, facing the prospect of nothing, intervenes.
- She could tell Bob, “You get 50% of the dollar under the deal with Alice. What if we arrange 60% for you and 40% for me? We would both be better off.”
- Bob, tempted by a better payoff, might switch allegiance.
- Yet, before the new agreement is finalised, Alice - now set to receive nothing - could approach Carol with an even more attractive offer.
- In an instant, Bob is ousted, and a new negotiation cycle begins.
This endless renegotiation cycle demonstrates that no coalition in such a setting can be entirely stable if members are constantly tempted to defect for a better deal.
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In weighted voting games, players with different weights (for example, social groups of different sizes or political groups with varying numbers in Parliament) aim to form a winning majority. A central question in these games is how stable coalitions can be. Can a political coalition form and remain the same over time?
The stronger the expectations among the members of a political minority that they will enter tomorrow's majority, the more acceptable majority rule will be to them. The less they feel a need for such unique guarantees as a minority veto, the more likely they will see these as impediments to their future prospects as participants in a majority government.
The possibility for each social group to be part of a coalition also gives them bargaining power in the political process. The instability of majority coalitions means that every group can claim a slice of the pie generated by society.
On the other hand, when coalitions are formed along rigid cultural, ethnic, or religious lines, they tend to be less open to change. This rigidity can lead to long-term minority status for some groups, fostering persistent distrust in democratic institutions and resistance to the growth of state authority. This leads to limited state capacity—the ability to enforce laws, maintain order, implement policies, and deliver public services.
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Human behaviour drivers
Dividing resources
When dividing resources, there is a human tendency for people who own the resources to give slightly less than what is accepted as fair by the receiver of the resources..
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Dictator game
This is a simple game in which player A (the dictator) must decide how to split a cash prize with player B, who has no input into player A’s decision. On average dictators go for a 70̥/30 percent split.
| Christoph Engel - Dictator Games: A Meta Study - 2010 |
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| If one calculates the grand mean from all reported or constructed means, dictators on average give 28.35 % of the pie. |
| https://homepage.coll.mpg.de/pdf_dat/2010_07online.pdf |
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Ultimatum game
In the ultimatum game, player A is given money, part of which has to be given to player B, who can accept or reject the amount given. The catch is that if the second player rejects the amount offered, both A and B get nothing. So, when does player B experience the gift as fair?
The key result of ultimatum experiments is that most proposers offer between 40% and 50% of the endowed amount, and that this split is almost always accepted by responders. When the proposal falls to 20% of the endowment it is rejected about half of the time, and rejection rates increase as the proposal falls to 10% and lower.
| Ryuta Aoki - The neural bases for valuing social equality - Neuroscience Research - 2015 |
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| Humans show remarkable preferences for fairness and social equality. This behavioral characteristic appears as inequality aversion, which has been intensively studied in a wide range of disciplines such as psychology and economics (Adams, 1965, Camerer, 2003, Fehr and Schmidt, 1999).
Equality of outcome is obviously a huge concern in our social life, with examples such as wages that equally-contributing employees receive from employers or praises that equally-achieving students receive from teachers. Vast empirical studies have shown that people care strongly about equality of outcomes among individuals. Likewise, equality of opportunity is also a common issue in contemporary societies. A key feature of equality of opportunity is that it concerns processes that determine outcomes, and does not ensure equality of outcome. To illustrate this, consider an example of voting for political candidates. Equal opportunity in this case means that everyone has the right to vote for their favorite candidate, without being excluded from voting by unfair criteria such as gender, race, religion or beliefs. Obviously, this equal opportunity does not ensure equal outcome: not all voters can get their preferred outcome (i.e., the candidate for whom they voted is selected). Inequality of opportunity due to voting restrictions produces strong feelings of unfairness in those who are restricted, while inequality of outcome in the voting results is unlikely to cause feelings of unfairness (although it may cause feelings of disappointment), as long as the voting process is fair. |
| https://www.sciencedirect.com/science/article/abs/pii/S0168010214002909 |
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Do-gooder derogation
The term "do-gooder" refers to a person who deviates from the majority regarding behaviour because of their morality. One possible reason for do-gooder derogation is 'anticipated moral reproach'. This describes a threat to one's moral standing and sense of self-worth. Research suggests that since people are susceptible to criticism or challenges to their morals, they are more likely to put down the source of this 'threat'. As an example, in research regarding non-vegetarians' attitudes towards vegetarians, non-vegetarians tended to harbour more hostile feelings towards vegetarians when they believed that the vegetarians saw themselves as morally superior. However, not all vegetarians choose to do so because of moral reasons.
People value morality in themselves and others. They want to be moral and good individuals, associate themselves with others who share their values, and belong to moral groups. As an ironic consequence of the importance of morality, people sometimes respond negatively to morally motivated deviants and dislike others who overtly display ethical behaviour.
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| Alain Schläpfe - The social benefits of “anti-social” punishment - Evolution and Human Behavior - 2025 |
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| Punishment of defectors is believed to be a key factor in sustaining cooperation among unrelated individuals. However, several studies have shown that humans also frequently punish those that act cooperatively, a phenomenon termed anti-social punishment. This study shows that punishment of cooperators can be a positive factor in sustaining cooperation rates when used by conditional cooperators against those who cooperate unconditionally. This suggests that judging whether a punitive act is beneficial or detrimental to cooperation is more complex than previously thought. |
| https://www.sciencedirect.com/science/article/abs/pii/S1090513825000042 |
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Cooperation on different levels
| Eric Schnell - Indirect reciprocity undermines indirect reciprocity destabilizing large-scale cooperation - PNAS - 2024 |
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| Previous models suggest that indirect reciprocity (reputation) can stabilize large-scale human cooperation. The logic behind these models and experiments is that a strategy in which individuals conditionally aid others based on their reputation for engaging in costly cooperative behavior serves as a punishment that incentivizes large-scale cooperation without the second-order free-rider problem.
However, these models and experiments fail to account for individuals belonging to multiple groups with reputations that can be in conflict. Here, we extend these models such that individuals belong to a smaller, “local” group embedded within a larger, “global” group. This introduces competing strategies for conditionally aiding others based on their cooperative behavior in the local or global group. Our analyses reveal that the reputation for cooperation in the smaller local group can undermine cooperation in the larger global group, even when the theoretical maximum payoffs are higher in the larger global group. This model reveals that indirect reciprocity alone is insufficient for stabilizing large-scale human cooperation because cooperation at one scale can be considered defection at another. These results deepen the puzzle of large-scale human cooperation. |
| https://www.pnas.org/doi/full/10.1073/pnas.2322072121 |
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