The Computation of a Coincidence of Two Mappings

algorithm;general equilibrium

On the Connectedness of Coincidences and Zero Points of Mappings

inequality;variation;general equilibrium;algorithm

A Discrete Multivariate Mean Value Theorem with Applications

AMS classifications: 47H10; 54H25; 55M20; 90C33; 91B50Discrete set;mean value theorem;fixed point;algorithm;equilibrium;complementarity

An Efficient Multi-Item Dynamic Auction with Budget Constrained Bidders

An auctioneer wishes to sell several heterogeneous indivisible items to a group of potential bidders. Each bidder has valuations over the items but faces a budget constraint and may therefore not be able to pay up to his valuations. In such markets, a competitive equilibrium typically fails to exist. We develop a dynamic auction and prove that the auction always finds a core allocation in finitely many rounds. The core allocation consists of an assignment of the items and its associated supporting price vector.Dynamic auction;budget constraint;core

A Model of Partnership Formation

This paper presents a model of partnership formation. A set of agents wants to conduct some business or other activities. Agents may act alone or seek a partner for cooperation and need in the latter case to consider with whom to cooperate and how to share the profit in a collaborative and competitive environment. We pro- vide necessary and su±cient conditions under which an equilibrium can be attained. In equilibrium, the partner formation and the payoff distribution are endogenously determined. Every agent realizes his full potential and has no incentive to deviate from either staying independent or from the endogenously determined partner and payoff. The partnership formation problem contains the classical assignment market problem as a special case.Partnership formation;equilibrium;indivisibility;assignment market

A Dynamic Auction for Differentiated Items under Price Rigidities

A number of heterogeneous items are to be sold to several bidders. Each bidder demands at most one item. The price of each item is not completely flexible and is restricted to some admissible interval. In such a market economy with price rigidities, a Walrasian equilibrium usually fails to exist. To facilitate the allocation of items to the bidders, we propose an ascending auction with rationing that yields a constrained Walrasian equilibrium outcome. The auctioneer starts with the lower bound price vector that specifies the lowest admissible price for each item, and each bidder responds with a set of items demanded at those prices. The auctioneer adjusts prices upwards for a minimal set of over-demanded items and chooses randomly a winning bidder for any item if the item is demanded by several bidders and its price has reached its highest admissible price. We prove that the auction finds a constrained Walrasian equilibrium outcome in a finite number of steps.Ascending auction;multi-item auction;constrained equilibrium;price rigidities;rationing

A simplicial algorithm for testing the integral properties of polytopes:A revision

Given an arbitrary polytope P in the n-dimensional Euclidean space R n , the question is to determine whether P contains an integral point or not. We propose a simplicial algorithm to answer this question based on a specifc integer labeling rule and a specific triangulation of R n . Starting from an arbitrary integral point ofR n , the algorithm terminates within a finite number of steps with either an integral point in P or proving there is no integral point inP. One prominent feature of the algorithm is that the structure of the algorithm is very simple and itcanbeeasily implemented on a computer. Moreover, the algorithm is computationally very simple, exible and stable.