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In this paper we propose a new instrument, a simultaneous penalization and subsidization, for stabilizing the grand coalition and enabling cooperation among all players of an unbalanced cooperative game. The basic idea is to charge a penalty z from players who leave the grand coalition, and at the same time provide a subsidy [omega] to players who stay in the grand coalition. To formalize this idea, we establish a penalty-subsidy function [omega](z) based on a linear programming model, which allows a decision maker to quantify the trade-off between the levels of penalty and subsidy. By studying function [omega](z), we identify certain properties of the trade-off. To implement the new instrument, we design two algorithms to construct function [omega](z) and its approximation. Both algorithms rely on solving the value of [omega](Z) for any given z, for which we propose two effective solution approaches. We apply the new instrument to a class of machine scheduling games, showing its wide applicability. Funding: The work is partially supported by the Hong Kong Research Grants Council [Grant 16225316], the National Natural Science Foundation of China [Grants 71401149, 71701192, and 71731010], and the Hong Kong Polytechnic University [Grant 1-ZVDS]. Supplemental Material: The e-companion is available at https://doi.org/10.1287/opre.2018.1723. Keywords: cooperative game * grand coalition stability * simultaneous penalization and subsidization * parallel machine scheduling game, 1. Introduction In many decision making problems that involve multiple players, minimizing total cost can be pursued by centralized optimization, which essentially requires all the players to form a grand [...]

We introduce a new noncooperative multilateral bargaining model for networkrestricted environments in which players can bargain only with their neighbors. The main theorem characterizes a condition on network structures for efficient equilibria. If the underlying network is either complete or circular, an efficient stationary subgame perfect equilibrium exists for all discount factors--all the players always try to reach an agreement as soon as practicable, and hence no strategic delay occurs. In any other network, however, an efficient equilibrium is impossible if a discount factor is greater than a certain threshold, as some players strategically delay an agreement. We also provide an example of a Braesslike paradox, in which network improvements decrease social welfare. Supplemental Material: The e-companion is available at https://doi.org/10.1287/opre.2018.1725. Keywords: noncooperative bargaining * coalition formation * cooperation restriction * strategic delay * Braess's paradox, 1. Introduction Bargaining occasionally requires an agreement among three or more players. Sometimes each player can directly cooperate with all the other players, while other times, some players can cooperate [...]

We extend classical force-on-force combat models to study the attrition dynamics of three-way and multilateral war. We introduce a new multilateral combat model--the multiduel--which generalizes the Lanchester models, and we solve it under an objective function that values one's own surviving force minus that of one's enemies. The outcome is stark: either one side is strong enough to destroy all the others combined, or all sides are locked in a stalemate, which results in collective mutual annihilation. The situation in Syria fits this paradigm. Keywords: Lanchester model * multiplayer nonzero-sum game, 1. Introduction Conventional attrition models of armed conflicts (Ancker Jr 1995, Washburn and Kress 2009, Kress 2012) usually feature a duel between two sides (or coalitions thereof) out of which [...]

Game theory is the study of human conflict and cooperation within a competitive situation. Many real conflict problems can be modeled as games. Here we have considered a Multi-Objective Matrix Game model with an additional entropy objective function and fuzzy goals. The said model can be reduced to a generalized regular Max-Min problem and applying fuzzy optimization with entropy disturbance approach for smooth and uniform distribution to solve the said problem. Numerical illustration is included in support of theory. Keywards: Multi-objective Matrix Game; Entropy; Fuzzy Goal., 1. Introduction Game theory deals with situation where there are conflicts of interests between persons. This is game of a strategy that is which strategy a person should adopt for [...]

Dynamic Modeling of Electricity Price Risk Accurate representation of price risk is a crucial element in many short-term decisions in the electricity industry. However, electricity price distributions exhibit a variety [...]

We address a generic price competition model in an industry with an arbitrary number of competitors, each offering all or a subset of a given line of N products. The [...]

We analyze a noncooperative bargaining game with a general coalition structure. In each period an opportunity for a feasible coalition to form arises according to a stochastic process, and a [...]

We study a situation where several independent service providers collaborate by complete pooling of their resources and customer streams into a joint service system. These service providers may represent such [...]

We consider a transportation station, where customers arrive according to a Poisson process. A transportation facility visits the station according to a renewal process and serves at each visit a [...]

A cooperative game with transferable utility is said to be homogeneous of degree one if for any integer m, the value of cloning m times all players at any given [...]

Scrip systems provide a nonmonetary trade economy for exchange of resources. We model a scrip system as a stochastic game and study system design issues on selection rules to match [...]

We study firms that sell multiple substitutable products and customers whose purchase behavior follows a nested logit model, of which the multinomial logit model is a special case. Customers make [...]

Heavy and uncertain traffic conditions exacerbate the commuting experience of millions of people across the globe. When planning important trips, commuters typically add an extra buffer to the expected trip [...]

We provide a review of the types of equilibria typically found in operations management inventory papers and a discussion on when the commonly used stationary infinite-horizon (open-loop) equilibrium may be [...]

We consider cooperative traveling salesman games with nonnegative asymmetric costs satisfying the triangle inequality. We construct a stable cost al-location with budget balance guarantee equal to the Held-Karp integrality gap [...]

We study network flow problems in an uncertain environment from the viewpoint of robust optimization. In contrast to previous work, we consider the case that the network parameters (e.g., capacities) [...]

We study a class of stochastic dynamic games that exhibit strategic complementarities between players; formally, in the games we consider, the payoff of a player has increasing differences between her [...]

This paper considers abstract election games motivated by the United States Electoral College. There are two political parties, and the electoral votes in each state go to the party that [...]

This paper analyzes decentralized assembly systems under asymmetric demand information and sequential contracting. We reveal new insights on the value of contract type (price-only versus complex), demand information (complete versus [...]

We generalize analysis of competition among newsvendors to a setting in which competitors possess asymmetric information about future demand realizations, and this information is limited to knowledge of the support [...]

Many real-world systems operate in a decentralized manner, where individual operators interact with varying degrees of cooperation and self motive. In this paper, we study transportation networks that operate as [...]

During counterinsurgency operations, government forces with superior firepower confront weaker low-signature insurgents. Under what conditions should govern (m)ment (Blue) forces attack insurgent (Red) strongholds? How should the government allocate its [...]

In this paper, we study a make-to-stock manufacturing system where two firms compete through dynamic pricing and inventory control. Our goal is to address competition (in particular a duopoly setting) [...]

In this paper, we study the practice of forecast sharing and supply chain coordination with a game-theoretical model. We find that in a one-shot version of the game, forecasts are [...]

In the traffic assignment problem, first proposed by Wardrop in 1952, commuters select the shortest available path to travel from their origins to their destinations. We study a generalization of [...]

This paper concerns a two-person zero-sum game between an infiltrator and a defender. The infiltrator wants to pass through a channel, while the defender wants to detect the infiltrator by [...]

Evaluation methods for assessing strategic offensive and defensive force structures as well as the impact of nuclear coalitions are presented. Coalitions refer to nuclear weapon states combined with nonnuclear weapon states, determined as integral parts of the total value target inventory which refers to the value attached to civilian and military targets of a nuclear attack in each country. The method was arrived at by using two models representing two scenarios involving coalitions A, B and C. The first model assumed a two-entity, zero-sum formulation given a maximin hypothesis while the second model consisted of a nonzero-sum game formula. The outcome of each game is expressed as percent of surviving value. The number of value targets, offensive and defensive weapons as well as coalition composition determined the outcome of the games.