Bargaining in a non-stationary environment.
The paper studies Rubinstein's alternating offers bargaining game in the following non-stationary setting. Two players \(A\) and \(B\) alternatively bargain at times \(t=s, s+\Delta, s+2\Delta,\ldots\) (\(s\) and \(\Delta>0\) are fixed), and \(\Omega (t) \subset \mathbb R^2\) is the set of possible utility pairs of their payoffs available at time \(t\). The players negotiate according to the following procedure. At times \(s+2n\Delta\) (\(n=0,1,\ldots\)) player \(A\) makes an offer \((u_A,u_B)\) from the set \(\Omega(s+2n\Delta)\), and player \(B\) decides whether to accept or reject it. If he accepts the offer, then the bargaining game ends and players' payoffs are \((u_A,u_B)\), respectively. Analogous situation occurs to player \(B\) at times \(s+(2n+1)\Delta\) (\(n=0,1,\ldots\)). When both players reject their offers at all times, their payoffs are equal to zero. Three standard assumptions are assumed about the Pareto frontiers of the sets \(\Omega (t)\): concavity, shrinking and vanishing, and smoothly evolving. Using this the authors characterize the set equilibria in the limit as \(\Delta \rightarrow 0\). It is shown that then any Markov and non-Markov subgame perfect equilibrium (SPE) converges to the same unique limiting one. This result is illustrated by an interesting example about players' bargaining over a unit size cake. The second essential result in the paper gives sufficient conditions under which Nash's bargaining solution for the game at initial time \(s\) with the disagreement point \((0,0)\), coincides with the unique limiting SPE payoff pair. In the last part of the paper the authors extend the previous results for time-varying inside options and demonstrate the robustness of this approach.
scientific article; zbMATH DE number 1924811
scientific article