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
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
A 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
See also: Zoo Planet (index)
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