Nash Smoothing on the Test Bench: HαHα-Essential Equilibria
Abstract
Nash’s [1953] demand game models the second step in a “two-move game” that formalizes his “Negotiation Model”. Nash claimed for any two-person bargaining game (S,d)(S,d) the existence of a unique stable equilibrium of its associated second move demand game that by its payoff vector supports the symmetric Nash solution of that bargaining game.
Nash’s negotiation game is considered the first contribution to the Nash program. Only weaker versions of stability than that claimed by Nash have been formally proven later by other authors. However, Nash’s request for “studying the relative stabilities” of the demand game’s equilibria has never been complied with. By performing that task, we establish analogous stability results for all generalized Nash solutions and thereby disprove Nash’s “unique stability” claim.
Furthermore, we explain the impact of our result on the Nash solution with endogenous variable threats (NBWT) of the two move negotiation game, which is defined as the symmetric Nash solution of that bargaining game (S,d∗)(S,d∗) whose status quo point d∗d∗ is the unique payoff vector of the payoff-equivalent equilibria of the first move threat game.
