Tit-for-tat stability requires both players to believe the other will reciprocate

Evidence

Cooperation is conditional on the belief that the other party is not a sucker (is not disposed to grant trust blindly), but also on the belief that he will be well disposed towards us if we make the right move. Thus tit for tat can be an equilibrium only if both players believe the other will abide by it, otherwise other equilibria are just as possible and selfconfirming. — Diego Gambetta, Trust - Making and Breaking Cooperative…, 2814

Categorization

• DEFINE: Clarifies that conditional cooperation rests on paired beliefs about the other’s disposition, not merely on strategy choice.
• XREF: Belief-based equilibrium maps to Luhmann: familiarity/trust as cognitive expectations about others’ behavior — beliefs doing the structuring work. — connects to: Repeat players resolve disputes outside courts to preserve ongoing relationships — G. Alan Tarr, Judicial Process and Judicial…, 1115