Totally Balanced Games and Games of Flow

Ehud Kalai
Ehud Kalai
Department of Managerial Economics and Decision Sciences, J. L. Kellogg Graduate School of Management, Northwestern University, Evanston, Illinois 60201
Search for more papers by this author
,
Eitan Zemel
Eitan Zemel
Department of Managerial Economics and Decision Sciences, J. L. Kellogg Graduate School of Management, Northwestern University, Evanston, Illinois 60201
Search for more papers by this author

Department of Managerial Economics and Decision Sciences, J. L. Kellogg Graduate School of Management, Northwestern University, Evanston, Illinois 60201

Search for more papers by this author

Eitan Zemel

Department of Managerial Economics and Decision Sciences, J. L. Kellogg Graduate School of Management, Northwestern University, Evanston, Illinois 60201

Search for more papers by this author

Published Online:1 Aug 1982https://doi.org/10.1287/moor.7.3.476

Abstract

A class of characteristic function games arising from maximum flow problems is introduced and is shown to coincide with the class of totally balanced games. The proof relies on the max flow-min cut theorem of Ford and Fulkerson and on the observation that the class of totally balanced games is the span of the additive games with the minimum operation.

Cited by
- Sustainable flood management in nonurban-urban watersheds using green-grey infrastructures: A cooperative perspective
  Land Use Policy, Vol. 168
- The pipeline externalities problem
  Journal of Mathematical Economics, Vol. 122
- Approximate Cores of Submodular Cost Set Cover Games
  13 August 2025 | Journal of Optimization Theory and Applications, Vol. 207, No. 3
- Flow Allocation Games
  Nils Bertschinger; ,
  Martin Hoefer; ,
  Daniel Schmand
  22 January 2024 | Mathematics of Operations Research, Vol. 50, No. 1
- Stable source connection and assignment problems as multi-period shortest path problems
  6 May 2024 | International Journal of Game Theory, Vol. 53, No. 3
- Averaged dual solution for linear production games and its characterization
  15 October 2022 | Central European Journal of Operations Research, Vol. 31, No. 2
- A game theoretical approach to emergency logistics planning in natural disasters
  11 May 2021 | Annals of Operations Research, Vol. 324, No. 1-2
- A two-stage linear production planning model with partial cooperation under stochastic demands
  6 November 2022 | Annals of Operations Research, Vol. 320, No. 1
- On the population monotonicity of independent set games
  Operations Research Letters, Vol. 50, No. 5
- Facets of the cone of exact games
  18 February 2022 | Mathematical Methods of Operations Research, Vol. 95, No. 1
- Network disconnection games: A game theoretic approach to checkpoint evaluation in networks
  Discrete Applied Mathematics, Vol. 308
- Computing payoff allocations in the approximate core of linear programming games in a privacy-preserving manner
  Operations Research Letters, Vol. 50, No. 1
- Cooperative reliability allocation in network flow problems considering greenhouse gas emissions: Optical fiber networks structure
  Journal of Cleaner Production, Vol. 326
- A note on weighted multi-glove games
  3 May 2021 | Social Choice and Welfare, Vol. 57, No. 4
- Explicit flow-risk allocation for cooperative maximum flow problems under interval uncertainty
  10 June 2019 | Operational Research, Vol. 21, No. 3
- Efficient distributed solutions for sharing energy resources at the local level: a cooperative game approach
- Decentralized Defence of a (Directed) Network Structure
  15 March 2019 | Defence and Peace Economics, Vol. 31, No. 6
- Allocating costs in set covering problems
  European Journal of Operational Research, Vol. 284, No. 3
- Network strength games: the core and the nucleolus
  9 November 2018 | Mathematical Programming, Vol. 180, No. 1-2
- Market Games and Clubs
  21 August 2020
- Relationship between labeled network games and other cooperative games arising from attributes situations
  Economics Letters, Vol. 185
- Multi-player flow games
  24 August 2019 | Autonomous Agents and Multi-Agent Systems, Vol. 33, No. 6
- Facets of the cone of totally balanced games
  21 May 2019 | Mathematical Methods of Operations Research, Vol. 90, No. 2
- Beyond the Stand-Alone Core Conditions
  16 November 2019
- Labeled Network Allocation Problems. An Application to Transport Systems
  1 November 2019
- Cooperative Linear Production Planning with Pooling of Resources
  Transactions of the Institute of Systems, Control and Information Engineers, Vol. 31, No. 8
- Values for cooperative games over graphs and games with inadmissible coalitions
  Games and Economic Behavior, Vol. 108
- Games in Coalitional Form
  15 February 2018
- Dynamic linear programming games with risk-averse players
  18 July 2016 | Mathematical Programming, Vol. 163, No. 1-2
- Induced Subgraph Game for Ensemble Selection
  21 February 2017 | International Journal on Artificial Intelligence Tools, Vol. 26, No. 01
- Finding a Nash equilibrium and an optimal sharing policy for multiagent network expansion game
  14 October 2016 | Networks, Vol. 69, No. 1
- Market Games and Clubs
  24 May 2017
- Computing the Shapley Value of Threshold Cardinality Matching Games
  14 October 2017
- Using Computational Intelligence Algorithms to Solve the Coalition Structure Generation Problem in Coalitional Skill Games
  9 November 2016 | Journal of Computer Science and Technology, Vol. 31, No. 6
- DEA production games and Owen allocations
  European Journal of Operational Research, Vol. 252, No. 3
- Efficient Implementation of Collective Extended Producer Responsibility Legislation
  Luyi Gui,
  Atalay Atasu,
  Özlem Ergun,
  L. Beril Toktay
  3 September 2015 | Management Science, Vol. 62, No. 4
- A core-allocation for a network restricted linear production game
  20 January 2016 | Annals of Operations Research, Vol. 238, No. 1-2
- Axiomatic characterizations under players nullification
  Mathematical Social Sciences, Vol. 80
- Efficient algorithms for game-theoretic betweenness centrality
  Artificial Intelligence, Vol. 231
- Finding the nucleoli of large cooperative games
  European Journal of Operational Research, Vol. 248, No. 3
- Nucleolus
  22 April 2016
- Induced Subgraph Game for Ensemble Selection
- Subjective independence and concave expected utility
  Journal of Economic Theory, Vol. 158
- Forms of representation for simple games: Sizes, conversions and equivalences
  Mathematical Social Sciences, Vol. 76
- Stochastic linear programming games with concave preferences
  European Journal of Operational Research, Vol. 243, No. 2
- Nucleolus
  6 June 2015
- Special Transferable Utility Games
- Cooperative maximum-flow problem under uncertainty in logistic networks
  Applied Mathematics and Computation, Vol. 250
- On the Gas Routing via Game Theory
  American Journal of Operations Research, Vol. 05, No. 04
- On $${\alpha }$$ α -roughly weighted games
  12 December 2013 | International Journal of Game Theory, Vol. 43, No. 3
- General Bibliography
  8 August 2014
- Network Design Problems: Fundamental Methods
  8 August 2014
- The complexity of egalitarian mechanisms for linear programming games
  Operations Research Letters, Vol. 42, No. 1
- Cooperative games and multiagent systems
  3 May 2013 | The Knowledge Engineering Review, Vol. 28, No. 4
- COST SHARING IN NETWORKS: SOME OPEN QUESTIONS
  9 June 2013 | International Game Theory Review, Vol. 15, No. 02
- Approximating the least core value and least core of cooperative games with supermodular costs
  Discrete Optimization, Vol. 10, No. 2
- Network Design Problems: Fundamental Methods
  13 February 2013
- Market Games and Clubs
- Computational Aspects of Cooperative Game Theory
  11 March 2022
- Agent Failures in Totally Balanced Games and Convex Games
- Balancedness conditions for exact games
  20 March 2011 | Mathematical Methods of Operations Research, Vol. 74, No. 1
- An average lexicographic value for cooperative games
  European Journal of Operational Research, Vol. 213, No. 1
- Shipper And Carrier Collaboration
  15 February 2011
- Procurement Network Formation: A Cooperative Game Approach
  16 February 2011
- Strategic Network Interdiction
  SSRN Electronic Journal, Vol. 75
- Introduction to the special issue in honor of Ehud Kalai
  Games and Economic Behavior, Vol. 70, No. 1
- Sharing Supermodular Costs
  Andreas S. Schulz,
  Nelson A. Uhan,
  1 July 2010 | Operations Research, Vol. 58, No. 4-part-2
- The bargaining set of a large game
  30 January 2009 | Economic Theory, Vol. 43, No. 3
- Some new cooperative coverage facility location games
  14 May 2010
- Computing equilibria: a computational complexity perspective
  27 February 2009 | Economic Theory, Vol. 42, No. 1
- Algorithms for core stability, core largeness, exactness, and extendability of flow games
  7 December 2009 | Frontiers of Mathematics in China, Vol. 5, No. 1
- Games in Coalitional Form
- Systemic Risk Components and Deposit Insurance Premia
  SSRN Electronic Journal, Vol. 348
- On the Core and f-Nucleolus of Flow Games
  Walter Kern,
  Daniël Paulusma,
  2 October 2009 | Mathematics of Operations Research, Vol. 34, No. 4
- Modeling cooperation on a class of distribution problems
  European Journal of Operational Research, Vol. 198, No. 3
- On core stability, vital coalitions, and extendability
  Games and Economic Behavior, Vol. 67, No. 2
- Stable allocations of risk
  Games and Economic Behavior, Vol. 67, No. 1
- Finding nucleolus of flow game
  25 January 2008 | Journal of Combinatorial Optimization, Vol. 18, No. 1
- Minimum cut tree games
- Extended cooperative networks games
  Discrete Applied Mathematics, Vol. 157, No. 4
- Market Games and Clubs
- Market Games and Clubs
- Mechanism design for a multicommodity flow game in service network alliances
  Operations Research Letters, Vol. 36, No. 5
- Totally monotonic games and flow games
  Operations Research Letters, Vol. 36, No. 2
- Nucleolus
- Algorithmic Cooperative Game Theory
- Dual Payoffs, Core and a Collaboration Mechanism Based on Capacity Exchange Prices in Multicommodity Flow Games
- Restricted Core Stability of Flow Games
- Games in Coalitional Form
  21 December 2016
- Cooperative Interval Games Arising from Airport Situations with Interval Data
  SSRN Electronic Journal, Vol. 9
- Balancedness Conditions for Exact Games
  SSRN Electronic Journal, Vol. 28
- Cooperative networks games with elastic demands
  11 October 2007 | RAIRO - Operations Research, Vol. 41, No. 4
- Type monotonic allocation schemes for a class of market games
  10 March 2007 | TOP, Vol. 15, No. 1
- Core Stability of Flow Games
- Algorithms for Core Stability, Core Largeness, Exactness, and Extendability of Flow Games
- A NETWORK IN A SOCIETY CONSISTS OF INDIVIDUALS WITH UTILITY DEPENDING ON THEIR REPUTATION
  Transactions of the Operations Research Society of Japan, Vol. 50, No. 0
- Stable Allocations of Risk
  SSRN Electronic Journal, Vol. 26
- Pairwise solutions and the core of transportation situations
  European Journal of Operational Research, Vol. 175, No. 1
- A game theory approach for solving the transshipment problem: a supply chain management strategy teaching tool
  Supply Chain Management: An International Journal, Vol. 11, No. 4
- Multi-attribute coalitional games
  11 June 2006
- The vector lattice structure of the n-person TU games
  Games and Economic Behavior, Vol. 54, No. 2
- Some Characterizations of Convex Games
- The nucleolus of balanced simple flow networks
  Games and Economic Behavior, Vol. 54, No. 1
- Logistics networks: A game theory application for solving the transshipment problem
  Applied Mathematics and Computation, Vol. 168, No. 2
- Optimal Equilibria in the Non-Cooperative Game Associated with Cost Spanning Tree Problems
  Annals of Operations Research, Vol. 137, No. 1
- A Note On The Owen Set Of Linear
  Theory and Decision, Vol. 56, No. 1-2
- A Note on the Owen Set of Linear Programming Games and Nash Equilibria
- The pairwise egalitarian solution
  European Journal of Operational Research, Vol. 150, No. 1
- Total balancedness condition for Steiner tree games
  Discrete Applied Mathematics, Vol. 127, No. 3
- Strategic behavior and partial cost sharing
  Games and Economic Behavior, Vol. 43, No. 1
- INFORMATION SHARING GAMES
  20 November 2011 | International Game Theory Review, Vol. 05, No. 01
- A Strategic Model of Social and Economic Networks
- Growth of wireless ad hoc networks
- Cost Allocation for a Tree Network with Heterogeneous Customers
  Daniel Granot,
  Jeroen Kuipers,
  Sunil Chopra,
  1 November 2002 | Mathematics of Operations Research, Vol. 27, No. 4
- LINEAR AND INTEGER PROGRAMMING TECHNIQUES FOR COOPERATIVE GAMES
  20 November 2011 | International Journal of Foundations of Computer Science, Vol. 13, No. 05
- NTU PERT games
  Operations Research Letters, Vol. 30, No. 2
- Core capacity of wireless ad hoc networks
- Operations research games: A survey
  Top, Vol. 9, No. 2
- Sharing Nonconvex Costs
  Journal of Global Optimization, Vol. 20, No. 3-4
- Tarification par des jeux Coopératifs avec Demandes Élastiques
  15 August 2002 | RAIRO - Operations Research, Vol. 35, No. 3
- Membership for Core of LP Games and Other Games
  31 July 2001
- Linear Transformation of Products: Games and Economies
  Journal of Optimization Theory and Applications, Vol. 105, No. 3
- Monotonic Allocation Schemes In Clan Games
  SSRN Electronic Journal, Vol. 36
- Cones Of Games Arising From Market Entry Problems
  SSRN Electronic Journal, Vol. 26
- Information Sharing Games
  SSRN Electronic Journal, Vol. 28
- Cost allocation in the Chinese postman problem
  European Journal of Operational Research, Vol. 118, No. 1
- Algorithmic Aspects of the Core of Combinatorial Optimization Games
  Xiaotie Deng,
  Toshihide Ibaraki,
  Hiroshi Nagamochi,
  1 August 1999 | Mathematics of Operations Research, Vol. 24, No. 3
- Cooperative Games and Fuzzy Cooperative Games Arising from Mathematical Programming Problems
  Journal of Japan Society for Fuzzy Theory and Systems, Vol. 11, No. 5
- Combinatorial Optimization and Coalition Games
- On the game-theoretic structure of public-good economies
  International Journal of Game Theory, Vol. 26, No. 4
- On a Market for Coalitions with Indivisible Agents and Lotteries
  Journal of Economic Theory, Vol. 77, No. 1
- On the concavity of delivery games
  European Journal of Operational Research, Vol. 99, No. 2
- Cores and related solution concepts for multi-choice games
  ZOR Zeitschrift f�r Operations Research Mathematical Methods of Operations Research, Vol. 41, No. 3
- Chapter 9 Network models in economics
- On the Reduced Game of Some Linear Production Games
- Monotonic games are spanning network games
  International Journal of Game Theory, Vol. 21, No. 4
- Compromise values in cooperative game theory
  Top, Vol. 1, No. 1
- Cooperation in one machine scheduling
  ZOR - Methods and Models of Operations Research, Vol. 38, No. 2
- A Survey of Cost and Revenue Allocation Problems
- Cooperative games arising from network flow problems
  European Journal of Operational Research, Vol. 51, No. 3
- On the core of network synthesis games
  Mathematical Programming, Vol. 50, No. 1-3
- A Survey of Consistency Properties in Cooperative Game Theory
  SIAM Review, Vol. 33, No. 1
- On cost allocation in communication networks
  11 October 2006 | Networks, Vol. 20, No. 2
- Monotonicity of the core and value in dynamic cooperative games
  International Journal of Game Theory, Vol. 19, No. 1
- On totally balanced games arising from cooperation in fair division
  Games and Economic Behavior, Vol. 2, No. 1
- On balanced games and games with committee control
  OR Spektrum, Vol. 11, No. 2
- Communication and its cost in graph-restricted games
  Theory and Decision, Vol. 25, No. 3
- Decomposition of games with non-empty core into veto-controlled simple games
  1 June 1987 | Operations-Research-Spektrum, Vol. 9, No. 2
- A Mazur-Orlicz type theorem for submodular set functions
  Journal of Mathematical Analysis and Applications, Vol. 120, No. 2
- Market equilibrium in a multistage commodity network
  Automatica, Vol. 21, No. 5
- Totally balanced games arising from controlled programming problems
  Mathematical Programming, Vol. 29, No. 3
- Permutation games: Another class of totally balanced games
  OR Spektrum, Vol. 6, No. 2

cover image Mathematics of Operations Research

Volume 7, Issue 3

August 1982

Pages 319-478

Article Information

Metrics

Information

Published Online:August 01, 1982

Cite as

Ehud Kalai, Eitan Zemel, (1982) Totally Balanced Games and Games of Flow. Mathematics of Operations Research 7(3):476-478.

https://doi.org/10.1287/moor.7.3.476

Keywords

PDF download

Available Issues

Available Issues

Available Issues

Available Issues

Available Issues

Available Issues

Available Issues

Totally Balanced Games and Games of Flow

Abstract

Volume 7, Issue 3

Article Information

Metrics

Information

Cite as

Keywords

Sign Up for INFORMS Publications Updates and News