An approach to transportation network analysis via transferable utility games

We strategically separate different core outcomes. The natural counterparts of a core allocation in a strategic environment are the α-core, the β-core and the strong equilibrium, modified by assuming that utility is transferable in a strategic context as well. Given a core allocation ω of a convex transferable utility (TU) game $$v$$ , we associate a strategic coalition formation game with $$ \left( {v, \omega } \right) $$ in which ω survives, while most other core allocations are eliminated. If the TU game is strictly convex, the core allocations respected by the TU-α-core, the TU-β-core and the TU-strong equilibrium shrink to ω only in the canonical family of coalition formation games associated with $$ \left( {v, \omega } \right) $$ . A mechanism, which strategically separates core outcomes from noncore outcomes for each convex TU game according to the TU-strong equilibrium notion is reported.

Efficient algorithms for game-theoretic betweenness centrality

We consider a sequence of transferable utility (TU) games where, at each time, the characteristic function is a random vector with realizations restricted to some set of values. The first part of the paper contributes to the definition of a robust (coalitional) TU game and the development of a distributed bargaining protocol. We prove the convergence with probability 1 of the bargaining process to a random allocation that lies in the core of the robust game under some mild conditions on the underlying communication graphs. The second part of the paper addresses the more general case where the robust game may have empty core. In this case, with the dynamic game we associate a dynamic average game by averaging over time the sequence of characteristic functions. Then, we consider an accordingly modified bargaining protocol. Assuming that the sequence of characteristic functions is ergodic and the core of the average game has a nonempty relative interior, we show that the modified bargaining protocol converges with probability 1 to a random allocation that lies in the core of the average game.

There is currently much interest in the problem of measuring the centrality of nodes in networks/graphs; such measures have a range of applications, from social network analysis, to chemistry and biology. In this paper we propose the first measure of node centrality that takes into account the community structure of the underlying network. Our measure builds upon the recent literature on game-theoretic centralities, where solution concepts from cooperative game theory are used to reason about importance of nodes in the network. To allow for flexible modelling of community structures, we propose a generalization of the Owen value—a well-known solution concept from cooperative game theory to study games with a priori-given unions of players. As a result we obtain the first measure of centrality that accounts for both the value of an individual node's relationships within the network and the quality of the community this node belongs to.

In this paper we present cooperative games and its fuzzification. A cooperative game (or coalitional game is usually described by a set of players and a characteristics function. In a transferable utility games only one number is attached to each coalition. Cooperative games are useful in considering profit allocation among multiple decision makes who cooperate with each other.

A cooperative game with transferable utilities– or simply a TU-game – describes a situation in which players can obtain certain payoffs by cooperation. A solution concept for these games is a function which assigns to every such a game a distribution of payoffs over the players in the game. Famous solution concepts for TU-games are the Shapley value and the Banzhaf value. Both solution concepts have been axiomatized in various ways.

This work uses the defining principles of the core solution concept to determine not only payoffs but also coalition formation. Given a cooperative transferable utility (TU) game, we propose two noncooperative procedures that in equilibrium deliver a natural and nonempty core extension, the aspiration core, together with the supporting coalitions it implies. As expected, if the cooperative game is balanced, the grand coalition forms. However, if the core is empty, other coalitions arise. Following the aspiration literature, not only partitions but also overlapping coalition configurations are allowed. Our procedures interpret this fact in different ways. The first game allows players to participate with a fraction of their time in more than one coalition, while the second assigns probabilities to the formation of potentially overlapping coalitions. We use the strong Nash and subgame perfect Nash equilibrium concepts.

The family of discounted Shapley values is analyzed for cooperative games in coalitional form. We consider the bargaining protocol of the alternating random proposer introduced in Hart and Mas-Colell (Econometrica 64:357–380, 1996). We demonstrate that the discounted Shapley values arise as the expected payoffs associated with the bargaining equilibria when a time discount factor is considered. In a second model, we replace the time cost with the probability that the game ends without agreements. This model also implements these values in transferable utility games, moreover, the model implements the \(\alpha \)-consistent values in the nontransferable utility setting.

The excessive consumption of coal and petroleum products not only causes potential shortage of energy resources in the foreseeable future, but also creates various negative impacts on the environment, causing growing concerns on reducing the dependency on fossil fuels and diversifying the energy supply. Transportation and electricity production activities are dominant contributors for green-house gas emissions. Recent technology breakthroughs in electric vehicle and renewable generation technologies offer new opportunities to overcome the worldwide dilemma of economic growth and environment protection. The installation of on-road charging and swapping stations will introduce notable interplay between the transportation network and the power distribution network. This chapter aims to provide a comprehensive introduction on the planning, operation, and equilibrium analysis of the interdependent urban transportation and power distribution networks. In particular, the mathematical formulations of the transportation network will be presented; based on which a series of fundamental problems on the interdependent transportation and power distribution infrastructures, including system operation, vulnerability assessment, system expansion planning, and network equilibrium, will be discussed.

Null or Zero Players: The Difference between the Shapley Value and the Egalitarian Solution

A non-negative transferable utility (TU) game is average monotonic if there exists a non-negative vector according to which the relative worth is not decreasing when enlarging the coalition. We generalize this definition to the nontransferable utility (NTU) case. It is shown that an average monotonic NTU game shares several properties with an average monotonic TU game. In particular it has a special core element and there exists a population monotonic allocation scheme. We show that an NTU bankruptcy game is average monotonic with respect to the claims vector.

Intuitive Solutions in Game Representations: The Shapley Value Revisited

This paper presents a new way to fairly distribute welfare gains derived from trade in exchange economies. The imposed fairness condition is based on the balanced marginal contributions condition satisfied by the Shapley value in transferable utility games. The solution is defined for cardinal finite exchange economies. Then, we point out that solutions for ordinal economies can be created by mapping finite ordinal exchange economies onto cardinal economies and then applying the original solution.

Centrality and power in social networks: a game theoretic approach

Group centralization of network indices