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Vijay Subramanian
Publication date
2013
fields
Informatics Engineering
and research's language is
English
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We study decentralized markets with the presence of middlemen, modeled by a non-cooperative bargaining game in trading networks. Our goal is to investigate how the network structure of the market and the role of middlemen influence the markets efficiency and fairness. We introduce the concept of limit stationary equilibrium in a general trading network and use it to analyze how competition among middlemen is influenced by the network structure, how endogenous delay emerges in trade and how surplus is shared between producers and consumers.
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We consider bargaining problems which involve two participants, with a nonempty closed, bounded convex bargaining set of points in the real plane representing all realizable bargains. We also assume that there is no definite threat or disagreement point which will provide the default bargain if the players cannot agree on some point in the bargaining set. However, there is a nondeterministic threat: if the players fail to agree on a bargain, one of them will be chosen at random with equal probability, and that chosen player will select any realizable bargain as the solution, subject to a reasonable restriction.
Shapleys impossibility result indicates that the two-person bargaining problem has no non-trivial ordinal solution with the traditional game-theoretic bargaining model. Although the result is no longer true for bargaining problems with more than two agents, none of the well known bargaining solutions are ordinal. Searching for meaningful ordinal solutions, especially for the bilateral bargaining problem, has been a challenging issue in bargaining theory for more than three decades. This paper proposes a logic-based ordinal solution to the bilateral bargaining problem. We argue that if a bargaining problem is modeled in terms of the logical relation of players physical negotiation items, a meaningful bargaining solution can be constructed based on the ordinal structure of bargainers preferences. We represent bargainers demands in propositional logic and bargainers preferences over their demands in total preorder. We show that the solution satisfies most desirable logical properties, such as individual rationality (logical version), consistency, collective rationality as well as a few typical game-theoretic properties, such as weak Pareto optimality and contraction invariance. In addition, if all players demand sets are logically closed, the solution satisfies a fixed-point condition, which says that the outcome of a negotiation is the result of mutual belief revision. Finally, we define various decision problems in relation to our bargaining model and study their computational complexity.
We consider a one-sided assignment market or exchange network with transferable utility and propose a model for the dynamics of bargaining in such a market. Our dynamical model is local, involving iterative updates of offers based on estimated best alternative matches, in the spirit of pairwise Nash bargaining. We establish that when a balanced outcome (a generalization of the pairwise Nash bargaining solution to networks) exists, our dynamics converges rapidly to such an outcome. We extend our results to the cases of (i) general agent capacity constraints, i.e., an agent may be allowed to participate in multiple matches, and (ii) unequal bargaining powers (where we also find a surprising change in rate of convergence).
This paper addresses the paucity of models of matching markets, both one-sided and two-sided, when utility functions of agents are cardinal. The classical Hylland-Zeckhauser scheme cite{hylland}, which is the most prominent such model in economics, can be viewed as corresponding to the linear Fisher model, which is most elementary model in market equilibria. Although HZ is based on the attractive idea of using a pricing mechanism, from the viewpoint of use in applications, it has a serious drawback, namely lack of computational efficiency, due to which solving instances of size even 4 or 5 is difficult. We propose a variety of Nash-bargaining-based models, several of which draw from general equilibrium theory, which has defined a rich collection of market models that generalize the linear Fisher model in order to address more specialized and realistic situations. The Nash bargaining solution satisfies Pareto optimality and symmetry and the allocations it yields are remarkably fair. Furthermore, since the solution is captured via a convex program, it is polynomial time computable. In order to be used in industrial grade applications, we give implementations for these models that are extremely time efficient, solving large instances, with $n = 2000$, in one hour on a PC, even for a two-sided matching market. The idea underlying our work has its origins in Vazirani (2012), which viewed the linear case of the Arrow-Debreu market model as a Nash bargaining game and gave a combinatorial, polynomial time algorithm for finding allocations via this solution concept, rather than the usual approach of using a pricing mechanism.
There has been much work on exhibiting mechanisms that implement various bargaining solutions, in particular, the Kalai-Smorodinsky solution cite{moulin1984implementing} and the Nash Bargaining solution. Another well-known and axiomatically well-studied solution is the lexicographic maxmin solution. However, there is no mechanism known for its implementation. To fill this gap, we construct a mechanism that implements the lexicographic maxmin solution as the unique subgame perfect equilibrium outcome in the n-player setting. As is standard in the literature on implementation of bargaining solutions, we use the assumption that any player can grab the entire surplus. Our mechanism consists of a binary game tree, with each node corresponding to a subgame where the players are allowed to choose between two outcomes. We characterize novel combinatorial properties of the lexicographic maxmin solution which are crucial to the design of our mechanism.
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