Non-cooperative Support for the Asymmetric Nash Bargaining solution

Our work contributes to the game-theoretic analysis of bargaining by providing additional non-cooperative support to the well-known Nash bargaining solution. In particular, in the present paper we study a model of non-cooperative multilateral bargaining with a very general proposer selection protocol and set of feasible payoffs. In each period of the bargaining game, one out of n players is recognized as the proposer according to an irreducible Markov process. The proposer offers a particular element of the convex set of feasible payoffs. If all players accept the offer, it is implemented. If a player rejects the offer, with some probability the negotiations break down and with the remaining probability the next period starts. We show that subgame perfect equilibria in stationary strategies exist and we fuly characterize the set of such equilibria. Our main result is that in the limit, as the exogenous risk of breakdown goes to zero, stationary subgame perfect equilibrium payoffs converge to the weighted Nash bargaining solution with the stationary distribution of the Markov proposer selection process as the weight vector.operations research and management science;

Tracing Microalloy Precipitation in Nb-Ti HSLA Steel during Austenite Conditioning

The microalloying with niobium (Nb) and titanium (Ti) is standardly applied in low carbon steel high-strength low-alloy (HSLA) steels and enables austenite conditioning during thermo-mechanical controlled processing (TMCP), which results in pronounced grain refinement in the finished steel. In that respect, it is important to better understand the precipitation kinetics as well as the precipitation sequence in a typical Nb-Ti-microalloyed steel. Various characterization methods were utilized in this study for tracing microalloy precipitation after simulating different austenite TMCP conditions in a Gleeble thermo-mechanical simulator. Atom probe tomography (APT), scanning transmission electron microscopy in a focused ion beam equipped scanning electron microscope (STEM-on-FIB), and electrical resistivity measurements provided complementary information on the precipitation status and were correlated with each other. It was demonstrated that accurate electrical resistivity measurements of the bulk steel could monitor the general consumption of solute microalloys (Nb) during hot working and were further complemented by APT measurements of the steel matrix. Precipitates that had formed during cooling or isothermal holding could be distinguished from strain-induced precipitates by corroborating STEM measurements with APT results, because APT specifically allowed obtaining detailed information about the chemical composition of precipitates as well as the elemental distribution. The current paper highlights the complementarity of these methods and shows first results within the framework of a larger study on strain-induced precipitation

Optimal value commitment in bilateral bargaining

We study the role of commitment as a source of strategic power in a non-cooperative bargaining game. Two impatient players bargain about the division of a shrinking surplus under a standard bargaining protocol in discrete time with constant recognition probabilities. Before bargaining, a player can commit to some part of the surplus. This commitment remains binding until the surplus has shrunk below the amount that the player is committed to. Intuitively, one cannot remain committed to something which has become impossible. The model offers insight on the relative importance of proposal power and commitment for the bargaining outcome. In a version of the game where both players may simultaneously choose their commitments, the equal split emerges from within a range of equilibrium divisions as a focal point which is robust to changes in the model parameters. © 2012

Negotiating with frictions

We consider bilateral non-cooperative bargaining on the division of a surplus. Compared to the canonical bargaining game in the tradition of Rubinstein, we introduce additional sources of friction into the bargaining process: Implementation of an agreement and consumption of the surplus can only begin at discrete points in time, such as the first day of a month, quarter, or year. Bargaining rounds are of non-trivial length, so that counter-others may be made without triggering costly delay. Communication between players is noisy: When players make others, they are uncertain about the time it takes for the other to arrive. We analyze delays and payoffs in the unique stationary equilibrium of the game. Frictions tend to make the bargaining process less efficient, but lead to a fairer surplus allocation. We establish conditions under which the equilibrium outcome converges to that in a canonical bargaining model as frictions become small