Judicial precedent as a dynamic rationale for axiomatic bargaining theory

Axiomatic bargaining theory (e.g., Nash's theorem) is static. We attempt to provide a dynamic justification for the theory. Suppose a judge or arbitrator must allocate utility in an (infinite) sequence of two‐person problems; at each date, the judge is presented with a utility possibility set in ℝ + 2 . He/she must choose an allocation in the set, constrained only by Nash's axioms, in the sense that a penalty is paid if and only if a utility allocation is chosen at date T that is inconsistent, according to one of the axioms, with a utility allocation chosen at some earlier date. Penalties are discounted with t and the judge chooses any allocation, at a given date, that minimizes the penalty he/she pays at that date. Under what conditions will the judge's chosen allocations converge to the Nash allocation over time? We answer this question for three canonical axiomatic bargaining solutions—Nash, Kalai–Smorodinsky, and “egalitarian”—and generalize the analysis to a broad class of axiomatic models.