The standard set game of a cooperative game

We show that for every cooperative game a corresponding set game can be defined, called the standard set game. Values for set games can be applied to this standard game and determine allocations for the cooperative game. On the other hand, notions for cooperative games, like the Shapley value, the $\tau-$value or the core can be considered in the context of the standard set games. \u

Retaliatory disagreement point with asymmetric countries. Evidence from European wine sector during enlargement

The vector space model facilitates a very useful representation of the strategic interaction in trade because it is possible to incorporate both symmetric and asymmetric features of the players. This paper characterizes the Nash solution of the non-cooperative international trade game in the orthogonal vector space. We have used the standard properties of the Nash solution to determine if the non-cooperative action-reaction trade policy space should be written in terms of 'import-import' or 'import-export' quotas as strongest punishment. The trade policy space defined by import-export' quotas is not a Nash solution of the non-cooperative game but an improvement in the disagreement set. We show the positive correlation between import and export quotas using data on trade relations between EU-15, Romania, Hungary and Bulgaria for wine sector during 1995-2005. In our model the outcome of the non-cooperative trade is autarky. Retaliation is played when countries restrict their imports to one third of the national optimum.asymmetries, quotas, non-cooperative game, disagreement points,Nash solution

Cooperative Games in Graph Structure

By a cooperative game in coalitional structure or shortly coalitional game we mean the standard cooperative non-transferable utility game described by a set of payoffs for each coalition that is a nonempty subset of the grand coalition of all players.It is well-known that balancedness is a sufficient condition for the nonemptiness of the core of such a cooperative non-transferable utility game.For this result any information on the internal organization of the coalition is neglected.In this paper we generalize the concept of coalitional games and allow for organizational structure within coalitions.For a subset of players any arbitrarily given structural relation represented by a graph is allowed for.We then consider non-transferable utility games in which a possibly empty set of payoff vectors is assigned to any graph on every subset of players.Such a game will be called a cooperative game in graph structure or shortly graph game.A payoff vector lies in the core of the game if there is no graph on a group of players which can make all of its members better off.We define the balanced-core of a graph game as a refinement of the core.To do so, for each graph a power vector is determined that depends on the relative positions of the players within the graph.A collection of graphs will be called balanced if to any graph in the collection a positive weight can be assigned such that the weighted power vectors sum up to the vector of ones.A payoff vector lies in the balanced-core if it lies in the core and the payoff vector is an element of payoff sets of all graphs in some balanced collection of graphs.We prove that any balanced graph game has a nonempty balanced-core and therefore a nonempty core.We conclude by some examples showing the usefulness of the concepts of graph games and balanced-core.In particular these examples show a close relationship between solutions to noncooperative games and balanced-core elements of a well-defined graph game.This places the paper in the Nash research program, looking for a unifying theory in which each approach helps to justify and clarify the other.cooperative games;graphs

Simple Efficient Contracts in Complex Environments

The paper studies a general model of hold-up in a setting encompassing the models of Segal (1999) and Che and Hausch (1999) among others. It is shown that if renegotiation is modelled as an infinite-horizon non-cooperative bargaining game then, with a simple initial contract, an efficient equilibrium will generally exist. The contract gives authority to one party to set the terms of trade and gives the other party a non-expiring option to trade at these terms. The difference from standard results arises because the existing contract ensures that the renegotiation game has multiple equilibria; the multiplicity of continuation equilibria can be used to enforce efficient investment

Mechanism Design with Renegotiation and Costly Messages

The paper studies a general model of hold-up in a setting encompassing the models of Segal (1999) and Che and Hausch (1999) among others. It is shown that if renegotiation is modelled as an infinite-horizon non-cooperative bargaining game then, with a simple initial contract, an efficient equilibrium will generally exist. The contract gives authority to one party to set the terms of trade and gives the other party a non-expiring option to trade at these terms. The difference from standard results arises because the existing contract ensures that the renegotiation game has multiple equilibria; the multiplicity of continuation equilibria can be used to enforce efficient investment

The impact of intermediaries on a negotiation: an approach from game theory

Standard approaches to model interaction networks are limited in their capacity to describe the nuances of real communication. We present a game theoretical framework to quantify the effect of intermediaries on the interaction between agents. Inspired by the seminal work Myerson (1977). on cooperative structures in cooperative games, we set the basis for multidimensional network analysis within game theory. More specifically, an extension of the point-arc game Feltkamp and van den Nouwe51 land (1992). is introduced, generalizing the analysis of cooperative games to multigraphs. An efficient algorithm is proposed for the computation of Shapley value of this game. We prove the validity of our approach by applying it to a intermediaries network model. We are able to recover meaningful results on the dependence of the game outcome on the intermediaries network. This work contributes to the optimal design of networks in economic environments and allows the ranking of players in complex network

Cooperative Games in Graph Structure

By a cooperative game in coalitional structure or shortly coalitional game we mean the standard cooperative non-transferable utility game described by a set of payoffs for each coalition that is a nonempty subset of the grand coalition of all players. It is well-known that balancedness is a sufficient condition for the nonemptiness of the core of such a cooperative non-transferable utility game. For this result any information on the internal organization of the coalition is neglected.In this paper we generalize the concept of coalitional games and allow for organizational structure within coalitions. For a subset of players any arbitrarily given structural relation represented by a graph is allowed for. We then consider non-transferable utility games in which a possibly empty set of payoff vectors is assigned to any graph on every subset of players. Such a game will be called a cooperative game in graph structure or shortly graph game. A payoff vector lies in the core of the game if there is no graph on a group of players which can make all of its members better off.We define the balanced-core of a graph game as a refinement of the core. To do so, for each graph a power vector is determined that depends on the relative positions of the players within the graph. A collection of graphs will be called balanced if to any graph in the collection a positive weight can be assigned such that the weighted power vectors sum up to the vector of ones. A payoff vector lies in the balanced-core if it lies in the core and the payoff vector is an element of payoff sets of all graphs in some balanced collection of graphs. We prove that any balanced graph game has a nonempty balanced-core and therefore a nonempty core. We conclude by some examples showing the usefulness of the concepts of graph games and balanced-core. In particular these examples show a close relationship between solutions to noncooperative games and balanced-core elements of a well-defined graph game. This places the paper in the Nash research program, looking for a unifying theory in which each approach helps to justify and clarify the other.microeconomics ;

Cooperative games in graph structure

By a cooperative game in coalitional structure or shortly coalitional game we mean the standard cooperative non-transferable utility game described by a set of payoffs for each coalition that is a nonempty subset of the grand coalition of all players.It is well-known that balancedness is a sufficient condition for the nonemptiness of the core of such a cooperative non-transferable utility game.For this result any information on the internal organization of the coalition is neglected.In this paper we generalize the concept of coalitional games and allow for organizational structure within coalitions.For a subset of players any arbitrarily given structural relation represented by a graph is allowed for.We then consider non-transferable utility games in which a possibly empty set of payoff vectors is assigned to any graph on every subset of players.Such a game will be called a cooperative game in graph structure or shortly graph game.A payoff vector lies in the core of the game if there is no graph on a group of players which can make all of its members better off.We define the balanced-core of a graph game as a refinement of the core.To do so, for each graph a power vector is determined that depends on the relative positions of the players within the graph.A collection of graphs will be called balanced if to any graph in the collection a positive weight can be assigned such that the weighted power vectors sum up to the vector of ones.A payoff vector lies in the balanced-core if it lies in the core and the payoff vector is an element of payoff sets of all graphs in some balanced collection of graphs.We prove that any balanced graph game has a nonempty balanced-core and therefore a nonempty core.We conclude by some examples showing the usefulness of the concepts of graph games and balanced-core.In particular these examples show a close relationship between solutions to noncooperative games and balanced-core elements of a well-defined graph game.This places the paper in the Nash research program, looking for a unifying theory in which each approach helps to justify and clarify the other

Spectrum Sharing Games of Infrastructure-Based Cognitive Radio Networks

The IEEE 802.22 standard is the first proposed standard for the cognitive radio networks in which a set of base stations (BSs) make opportunistic spectrum access to provide wireless access to the customer-premise equipments (CPE) within their cells in wireless regional area networks (WRAN). The channel assignment and power control must be carried out in BSs and CPEs, such that no excessive interference is caused to the users of the primary network. We use a game-theoretic model to analyze the non- cooperative behavior of the secondary users in IEEE 802.22 networks. We first show the existence of Nash equilibrium in a 2-cell non-cooperative game model, where the players (BSs) want to increase their coverage range. Then we extend our game to an N-player non-cooperative game where the players aim at maximizing the number of subscribers (i.e., CPEs). We conclude that the non- cooperative behavior of the players might result in a small number of supported CPEs and this can be solved by cooperative techniques, such as the Nash bargaining solution. Numerical results show that our proposed Nash bargaining solution can significantly increase the efficiency of the opportunistic spectrum allocation