Tuesday, 15 July 2025

The Frozen Game

 

The Frozen Game: Nash Equilibrium, Collective Trauma, and the Stagnation of Societies


Abstract

This essay examines how pessimistic expectations shaped by trauma and betrayal can trap entire societies in harmful equilibria, drawing from game theory (particularly Nash Equilibrium), sociology, and psychology. It argues that when people anticipate exploitation or punishment for vulnerability, they adapt strategies of self-protection that become collectively self-defeating. This dynamic explains why societies that long for transformation may remain locked in mistrust, inequality, or authoritarianism. Using historical and contemporary examples, it explores the interplay between learned helplessness, social capital, and strategic expectations. Finally, it considers whether cultural change, trust-building institutions, or transformative leadership can break the cycle.


Introduction: The Game We Cannot Win

At the heart of social cooperation lies a question: "What do I believe you will do — and what do I believe you believe I will do?"
Game theory formalizes this as Nash Equilibrium: a state where no individual can benefit by unilaterally changing strategy, given what others are expected to do (Nash, 1950). But equilibrium need not be positive. Societies scarred by betrayal, fear, or historical trauma may arrive at pessimistic equilibria where mistrust dominates: "If I open up, I will be hurt. If I act honestly, I will be exploited." Even when everyone wishes for change, the fear of being the “first to move” keeps the system frozen.

This paper explores why trauma-borne expectations harden into equilibrium, how this affects social and political life, and what — if anything — might allow societies to transcend these frozen games.


1. Expectations, Strategy, and Nash Equilibrium

Nash Equilibrium arises when each actor chooses a strategy they believe is best, given their beliefs about others’ strategies. It need not be the most socially optimal outcome; rather, it is simply the most stable, given expectations.

Classic examples include:

  • The Prisoner’s Dilemma: both prisoners defect out of fear the other will defect, even though mutual cooperation would benefit both (Axelrod, 1984).

  • Stag Hunt: hunters must choose between hunting stag (requiring cooperation) or hare (which is safe alone). Fear that others might defect leads many to choose the hare — a safer but poorer outcome.

Game theory shows that beliefs about others’ actions shape choices as much as the payoffs themselves.


2. Trauma and the Pessimistic Equilibrium

In societies marked by historical trauma — colonization, oppression, systemic corruption, or betrayal by institutions — expectations become systematically pessimistic. Studies in psychology and sociology show how:

  • Learned helplessness (Seligman, 1975): repeated negative outcomes teach individuals not to try, even when conditions improve.

  • Low social trust (Putnam, 2000): when citizens doubt that others (or institutions) will act fairly, cooperation declines.

  • Transgenerational trauma (Volkan, 2001): collective memories of betrayal or violence shape shared narratives and behaviors.

These shape expectations: “If I act honestly, others will exploit me.” The result is a negative Nash Equilibrium: everyone keeps acting defensively because everyone expects everyone else to do the same.


3. Historical and Contemporary Examples

a) Post-Communist Transitions

In the 1990s, many post-Soviet societies hoped for democracy and civic cooperation. Yet decades of surveillance and betrayal (e.g., neighbors denouncing neighbors to secret police) created entrenched mistrust (Howard, 2003). As a result, many societies saw persistent low civic participation and acceptance of corrupt elites: mistrust became self-reinforcing.

b) Corruption and Everyday Life

In countries with systemic corruption, individuals often assume others will cheat or bribe (Ledeneva, 1998). Even if most wish for honesty, few risk being the “only honest one” — a classic coordination failure.

c) Communities Marked by Violence

Research on communities exposed to prolonged violence shows reduced interpersonal trust, higher fear of strangers, and lower willingness to engage in collective action (Bauer et al., 2016). The anticipation of harm becomes a rational, if self-limiting, adaptation.


4. Cross-Fertilising Psychology and Game Theory

Psychological trauma conditions expectations about others, directly shaping strategic behavior. Game theory shows how these expectations can stabilize harmful equilibria.

  • Pessimistic equilibrium is not irrational: It is often a realistic adaptation to past experiences.

  • Even mutual desire for change is insufficient: Change requires changing shared beliefs about each other’s likely actions.

  • The fear of being betrayed again outweighs hope: Especially in groups with deep historical memory of betrayal.


5. Breaking the Cycle: Pathways Beyond the Frozen Game

a) Trust-Building Institutions

Stable, transparent institutions can gradually rebuild expectations that honesty will be reciprocated and protected (Rothstein & Stolle, 2008).

b) Transformative Leadership

Leaders who signal credible commitment to change — often through costly, risky actions — can shift expectations (North et al., 2009).

c) Small-Scale Cooperation

Local successes can seed wider change. When communities experience direct, repeated success in cooperation, new equilibria emerge (Ostrom, 1990).

d) Collective Narratives and Healing

Truth and reconciliation processes, public apologies, and cultural work can shift collective narratives from betrayal to possibility (Minow, 1998).


Conclusion: Beyond the Frozen Game

Trauma shapes not just memories, but expectations about others — and thus, the strategies people choose. Even when everyone desires change, fear of exploitation can trap societies in a pessimistic Nash Equilibrium. Yet these equilibria are not immutable laws: through trust-building, institutional reform, and cultural transformation, new expectations can take hold.

Ultimately, change begins when enough people come to believe: “If I open up, perhaps others will too.” The task is to make that hope credible — so the frozen game can finally move.


Annotated Bibliography

"Non-Cooperative Games" — John Nash (1950)
Foundational work defining Nash Equilibrium.

"The Evolution of Cooperation" — Robert Axelrod (1984)
Explores how cooperation can emerge among self-interested agents.

"Learned Helplessness" — Martin Seligman (1975)
Classic psychological research showing how repeated negative outcomes erode motivation.

"Bowling Alone: The Collapse and Revival of American Community" — Robert Putnam (2000)
Examines declining social capital and trust in modern societies.

"Transgenerational Transmission and Chosen Trauma" — Vamik Volkan (2001)
Explores how large-group identity and trauma are passed across generations.

"The Weakness of Civil Society in Post-Communist Europe" — Marc Morjé Howard (2003)
Analyzes low civic engagement after communism.

"How Russia Really Works: Informal Practices in the 1990s" — Alena Ledeneva (1998)
Describes everyday corruption and its impact on social trust.

"Can War Foster Cooperation?" — Michal Bauer et al. (2016)
Empirical study on how violence affects trust and prosocial behavior.

"Creating Political Trust: How Institutions Matter" — Bo Rothstein & Dietlind Stolle (2008)
Explores institutional design as a tool to rebuild trust.

"Violence and Social Orders" — Douglass North, John Wallis, Barry Weingast (2009)
Analyzes how elites and institutions shape expectations and political order.

"Between Vengeance and Forgiveness" — Martha Minow (1998)
Examines truth commissions and the role of narrative in post-conflict healing.

"Governing the Commons" — Elinor Ostrom (1990)
Shows how local institutions can foster cooperation and shift collective strategies.



See also: Zoo Planet (index)


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