General equilibrium programming

Equilibrium Theory;Algorithm

Tree, web and average web value for cycle-free directed graph games

On the class of cycle-free directed graph games with transferable utility solution concepts, called web values, are introduced axiomatically, each one with respect to some specific choice of a management team of the graph. We provide their explicit formula representation and simple recursive algorithms to calculate them. Additionally the efficiency and stability of web values are studied. Web values may be considered as natural extensions of the tree and sink values as has been defined correspondingly for rooted and sink forest graph games. In case the management team consists of all sources (sinks) in the graph a kind of tree (sink) value is obtained. In general, at a web value each player receives the worth of this player together with his subordinates minus the total worths of these subordinates. It implies that every coalition of players consisting of a player with all his subordinates receives precisely its worth. We also define the average web value as the average of web values over all management teams in the graph. As application the water distribution problem of a river with multiple sources, a delta and possibly islands is considered

Tree-type values for cycle-free directed graph games

For arbitrary cycle-free directed graph games tree-type values are introduced axiomatically and their explicit formula representation is provided. These values may be considered as natural extensions of the tree and sink values as has been defined correspondingly for rooted and sink forest graph games. The main property for the tree value is that every player in the game receives the worth of this player together with his successors minus what these successors receive. It implies that every coalition of players consisting of one of the players with all his successors receives precisely its worth. Additionally their efficiency and stability are studied. Simple recursive algorithms to calculate the values are also provided. The application to the water distribution problem of a river with multiple sources, a delta and possibly islands is considered

Games With Limited Communication Structure

In this paper we consider cooperative transferable utility games with limited communication structure, called graph games. Agents are able to cooperate with each other only if they can communicate directly or indirectly with each other. For the class of acyclic graph games recently the average tree solution has been proposed. It was proven that the average tree solution is a core element if the game exhibits superadditivity. It will be shown that the condition of super-additivity can be relaxed to a weaker condition, which admits for a natural interpretation. Moreover, the concept of subcore is introduced. Under the same condition it is proven that the subcore is a subset of the core and always contains the average tree solution and therefore is a non-empty refinement of the core.

Refinement of solutions to the linear complimentarity problem

Nash equilibrium;game theaory;matrices

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