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Introduction to Learning in Games
Published in Hamidou Tembine, Distributed Strategic Learning for Wireless Engineers, 2018
Cooperative game theory is concerned primarily with coalitions, that is, groups of players, who coordinate their actions and pool their payoffs. Consequently, one of the problems here is how to divide the payoff among the members of the formed coalition. The basis of this theory was laid by John von Neumann & Oskar Morgenstern [120] with coalitional games in characteristic function form, known also as transferable utility games (TU-games). The theory has been extended to non-transferable utility games (NTU-games). Robust cooperative games are cooperative games under uncertainties.
Introduction
Published in James K. Peterson, Basic Analysis III, 2020
Part Six: Topics in Applied Modeling We want to finish with a non standard application of these ideas to game theory. Chapter 15 discusses bounded charges on rings and fields of subsets.Chapter 16 is an introduction to games of transferable utility. In our discussion, we even have to look at a Riemann Integral extension, so great fun!
Game Theory
Published in Erchin Serpedin, Thomas Chen, Dinesh Rajan, Mathematical Foundations for SIGNAL PROCESSING, COMMUNICATIONS, AND NETWORKING, 2012
Erik G. Larsson, Eduard Jorswiec
We shall first assume that there is no mechanism that allows the players to pay one another compensation for choosing a specific strategy. Such side payments lead to the theory of transferable utility and is briefly treated in Section 19.5.2.
Cooperative differential games with continuous updating using Hamilton–Jacobi–Bellman equation
Published in Optimization Methods and Software, 2021
Ovanes Petrosian, Anna Tur, Zeyang Wang, Hongwei Gao
In the cooperative differential game model with transferable utility there are two problems: Determining a strategy set for players which maximizes the sum of payoffs or determines strategies corresponding to the cooperative behaviour. These strategies are called optimal and the corresponding trajectory is called the cooperative trajectory and denoted by .Determining an allocation rule for players' maximum joint payoff corresponding to optimal strategies and determining optimal trajectory . This involves, namely, determining the cooperative solution as a subset of the imputation set.
A multi-objective optimisation model for train scheduling in an open-access railway market
Published in Transportation Planning and Technology, 2021
Shahin Shakibaei, Pelin Alpkokin, John A. Black
The IP may also be interested in stimulating communications between private train service operators (PTSO) to improve the quality of services and increase profits. However, the major obstacle to this approach is the PTSOs’ resistance to reveal their information and to cooperate. On the other hand, it is impossible to reach a comprehensive and overall improvement to the network in absence of partial cooperation among the PTSOs themselves and the IP. Within this context, we have applied a philosophy similar to that of the Non-Transferable Utility (NTU) Coalition (Cooperative) game. It is theoretically possible to proclaim that the maximal utility improvement may be reached using transferable utility settings that require large information exchanges and sharing the utility amongst PTSOs. However, application of the transferable-utility game may not reflect the case in real-world situations.
Harsanyi power solutions for cooperative games on voting structures
Published in International Journal of General Systems, 2019
Encarnación Algaba, Sylvain Béal, Eric Rémila, Philippe Solal
Let be the universe of potential agents and let a finite set of n agents. Each subset S of N is called a coalition and N is often called the grand coalition. A cooperative transferable utility (TU)-game is a pair where and is a coalition function such that . For each coalition , describes the worth of S when its members cooperate. Denote by G the set of all TU-games. The subgame of a TU-game with respect to an agent set is the TU-game where for each , .