WPO, COV and IIA bargaining solutions

The class of bargaining solutions that are defined on the domain of finite sets of alternatives and satisfy Weak Pareto Optimality (WPO), Independence of Irrelevant Alternatives (IIA) and Covariance (COV), is characterized. These solutions select from the set of maximizers of a nonsymmetric Nash product -- i.e., from a nonsymmetric (multi-valued) Nash bargaining solution -- according to a specific decomposition of the indifference curves of this Nash product. We use this characterization in two ways. First, we derive consequences on this domain and on larger domains of compact (non-convex) bargaining problems, and show that most results in the literature are special cases and consequences of our central results -- in particular by adding continuity or symmetry axioms. Second, since the continuity axiom prevents nontrivial selections from the Nash bargaining solutions, we use the Axiom of choice to construct for example non-single-valued discontinuous WPO, IIA and COV bargaining solutions. It is conjectured that, in the case of two-person bargaining problems,the existence of such discontinuous bargaining solutions cannot be shown from the Zermelo-Fraenkel axioms for set theory without using the Axiom of Choice.mathematical economics;

On the computation of stable sets for bimatrix games

In this paper it is shown how to compute stable sets, defined by Mertens (1989), inthe context of bimatrix games only using linear optimization techniques.combinatorics;

Equilibrium plans in constrained environments

In this paper we analyze equilibria in competitive environments under constraints across players'' strategies. This means that the action taken by one player limits the possible choices of the other players. In this context the classical approach, Kakutani''s Fixed Point theorem, does not work. In particular, best replies against a given strategy profile may not be feasible. We extend Kakutani''s Fixed Point theorem to deal with the feasibility issue.Our main motivation to study this problem of co-dependency comes from the field of supply chain planning. A set of buyers is faced with external demand over a planning horizon, and to satisfy this demand they request inputs from a set of suppliers. Both suppliers and buyers face production capacities and the planning is made in a decentralized manner. A well-known coordination scheme for this setting is the upstream approach where the planning of the buyers is used to decide the request to the suppliers. We show the existence of equilibria for two versions of this coordination model. However, we illustrate with an example that the centralized solution is not, in general, an equilibrium, suggesting that regulation may be needed.We also apply our Fixed Point theorem to a production economy, where both supply and demand are upper bounded.operations research and management science;

Where strategic and evolutionary stability depart - a study of minimal diversity games

A minimal diversity game is an n player strategic form game in which each player has m pure strategies at his disposal. The payoff to each player is always 1, unless all players select the same pure strategy, in which case all players receive zero payoff. Such a game has a unique isolated completely mixed Nash equilibrium in which each player plays each strategy with equal probability, and a connected component of Nash equilibria consisting of those strategy profiles in which each player receives payoff 1. The Pareto superior component is shown to be asymptotically stable under a wide class of evolutionary dynamics, while the isolated equilibrium is not. On the other hand, the isolated equilibrium is strategically stable, while the strategic stability of the Pareto efficient component depends on the dimension of the component, and hence on the number of players, and the number of pure strategies.Strategic form games, strategic stability, evolutionary stability

Sequential Auctions with Synergies: The Paradox of Positive Synergies.

In multi-unit (procurement) auctions winning multiple contracts can lead to cost advantages due to synergies. As an example one can think of procurement auctions where construction firms have returns to scale for investments in specialized equipments and workers that are required in large-scale projects. In this paper we analyze the effects of the presence of such synergies on bidding behavior and thus auction outcomes in general. We find that the presence of synergies on the bidders’ side induces more competitive bidding and therefore leads to lower expected payoffs for bidders and higher expected revenues for sellers. Thus, instead of benefiting from the presence of synergies, bidders suffer from it. Moreover it is found that serious bankruptcy problems can occur. In particular the negative welfare consequences caused by these bankruptcy problems are of major importance for auction design when synergies are present. Finally, the presence of synergies leads to a decreasing price trend and can therefore explain the declining price anomaly.industrial organization ;