Shapley-like values for interval bankruptcy games

In this paper interval bankruptcy games arising from bankruptcy situations with interval claims are introduced. For this class of cooperative games two (marginal-based) Shapley-like values are considered and the relation between them is studied.

Share Opportunity Sets and Cooperative Games

In many share problems there is a priori given a natural set of possible divisions to solve the sharing problem.Cooperative games related to such share sets are introduced, which may be helpful in solving share problems.Relations between properties of share sets and properties of games are investigated.The average lexicographic value for share sets and for cooperative games is studied.cooperative games;bankruptcy games;average lexicographic value;opportunity sets

A Geometric Characterisation of the Compromise Value

In this paper, we characterise the compromise value of a game as the barycentre of the edges of its core cover.For this, we introduce the value, which extends the adjusted proportional rule for bankruptcy situations and coincides with the compromise value on a large class of games.geometry;games;bankruptcy;core

A Composite Run-to-the-Bank Rule for Multi-Issue Allocation Situations

In this paper, we propose a new extension of the run-to-the-bank rule for bankruptcy situations to the class of multi-issue allocation situations.We show that this rule always yields a core element and that it satisfies self-duality. We characterise our rule by means of a new consistency property, issue-consistency.allocation;bankruptcy;cooperative games;consistency

Multi-Issue Allocation Games

This paper introduces a new class of transferable-utility games, called multi-issue allocation games.These games arise from various allocation situations and are based on the concepts underlying the bankruptcy model, as introduced by O'Neill (1982).In this model, a perfectly divisible good (estate) has to be divided amongst a given set of agents, each of whom has some claim on the estate.Contrary to the standard bankruptcy model, the current model deals with situations in which the agents' claims are multi-dimensional, where the dimensions correspond to various issues.It is shown that the class of multi-issue allocation games coincides with the class of (nonnegative) exact games.The run-to-the-bank rule is introduced as a solution for multi-issue allocation situations and turns out to be Shapley value of the corresponding game.Finally, this run-to-the-bank rule is characterised by means of a consistency property.game theory;allocation games

An Algorithm for the Nucleolus of Airport Profit Problems

Airport profit games are a generalization of airport cost games as well as of bankruptcy games.In this paper we present a simple algorithm to compute the nucleolus of airport profit games.In addition we prove that there exists an unique consistent allocation rule in airport profit problems, and it coincides with the nucleolus of the associated TU game.algorithm;airports;profit;allocation;games

Implementing with veto players: a simple non cooperative game

The paper adapts a non cooperative game presented by Dagan, Serrano and Volij (1997) for bankruptcy problems to the context of TU veto balanced games. We investigate the relationship between the Nash outcomes of a noncooperative game and solution concepts of cooperative games such as the nucleolus, kernel and the egalitarian core.

A Stroll with Alexia

This paper revisits the Alexia value, a recent solution concept for cooperative transferable utility games. We introduce the dual Alexia value and show that it coincides with the Alexia value for several classes of games. We demonstrate the importance of the notion of compromise stability for characterizing the Alexia value.Alexia value;dual Alexia value;compromise stability;bankruptcy

A Game Theoretical Approach to Sharing Penalties and Rewards in Projects

This paper analyzes situations in which a project consisting of several activities is not realized according to plan. If the project is expedited, a reward arises. Analogously, a penalty arises if the project is delayed. This paper considers the case of arbitrary monotonic reward and penalty functions on the total expedition and delay, respectively. Attention is focused on how to divide the total reward (penalty) among the activities: the core of a corresponding cooperative project game determines a set of stable allocations of the total reward (penalty). In the definition of project games, surplus (cost) sharing mechanisms are used to take into account the specific characteristics of the reward (penalty) function at hand. It turns outs that project games are related to bankruptcy and taxation games. This relation allows us to establish the nonemptiness of the core of project games.Project planning;delay;expedition;cost sharing mechanism;surplus sharing mechanism;bankruptcy problems;taxation problems;cooperative game;core

Investment Complementarities, Coordination Failure and Systemic Bankruptcy

I argue that systemic bankruptcy of firms can originate from coordination failure in an economy with investment complementarities. This new explanation about the origin of systemic bankruptcy promotes better understanding of how financial fragility arises, and provides theoretical guidance for central banks to establish an "early warning system" to prevent the occurrence of financial crises. In a global game setup, investment decisions of firms are studied in the presence of uncertainty and investment complementarities. Uncertainty is twofold here: first, firms are uncertain about economic fundamentals; second, firms are also uncertain about other firms' investment decisions. I demonstrate that even small uncertainty about economic fundamentals can be magnified through the uncertainty about other firms' investment decisions and can lead to coordination failure, which may be manifested as systemic bankruptcy. Moreover, my model reveals that systemic bankruptcy tends to arise when economic fundamentals are in the middle range where coordination matters. High financial leverage of firms greatly increases the severity of systemic bankruptcy. Optimistic beliefs of firms and banks can alleviate coordination failure, but can also increase the severity of systemic bankruptcy once it happens.Systemic Bankruptcy, Financial Crises, Global Games