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International Game Theory Review
Journal Prestige (SJR): 0.236  Number of Followers: 0  Hybrid journal (It can contain Open Access articles)ISSN (Print) 0219-1989 - ISSN (Online) 1793-6675 Published by World Scientific  [121 journals]
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- A Differential Game Approach to Investment in Greentech Innovation in a
Duopoly with Network Externality-
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Authors: Shengbiao Ma, Huiquan Li
Abstract: International Game Theory Review, Ahead of Print.
In this paper, we revisit a well-known differential game model to investigate the R&D activity for Greentech innovation in a duopoly market with network externality. In our study, firms carry out independent R&D or Cartel R&D for Greentech innovation which aims to reduce end-of-pipe emission and network externality effects play a role in the R&D activity via the inverse demand functions. Firms are concerned not only with their own profits, but also with the relative profits. At the steady-state equilibrium, the efforts for Greentech innovation under independent R&D are higher than that under Cartel R&D when the degree of altruism is higher than the degree of technological R&D spillover, and the network size under independent R&D is lower than that under Cartel R&D. Moreover, under a given market structure, whether profits under independent R&D are higher than under Cartel R&D depends on the initial network size, which means that at the initial moment firms can decide to undertake independent or Cartel R&D activities based on the initial network size.
Citation: International Game Theory Review
PubDate: 2024-07-31T07:00:00Z
DOI: 10.1142/S0219198924400115
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- Analysis of Depreciation Methods Based on Cooperative Game Theory —
Focusing on the Straight-Line Method-
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Authors: Eiko Arata, Takuhei Shimogawa, Takehiro Inohara
Abstract: International Game Theory Review, Ahead of Print.
This study develops a model to explain why accounting procedures, also known as Generally Accepted Accounting Principles, are “generally accepted”. For this purpose, we focus on depreciation defined as the rational and systematic allocation of the original cost of an asset over the expected useful life of that asset. We investigate what it means to be “rational” using cooperative game theory. We show that cost allocations determined by the straight-line (SL) method, which is conventionally used worldwide, are elements of the core and that the conditions of the core can be rational in practice. Furthermore, we examine the relationship between the SL method and other solution concepts, such as the Shapley value and the nucleolus. Our next step is to clarify the characteristics besides the core selection of the SL method, those of other depreciation methods used in practice, and the logical relations between these characteristics.
Citation: International Game Theory Review
PubDate: 2024-07-31T07:00:00Z
DOI: 10.1142/S0219198924500130
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- Nash Smoothing on the Test Bench: [math]-Essential Equilibria
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Authors: Papatya Duman, Walter Trockel
Abstract: International Game Theory Review, Ahead of Print.
Nash’s [1953] demand game models the second step in a “two-move game” that formalizes his “Negotiation Model”. Nash claimed for any two-person bargaining game [math] the existence of a unique stable equilibrium of its associated second move demand game that by its payoff vector supports the symmetric Nash solution of that bargaining game. Nash’s negotiation game is considered the first contribution to the Nash program. Only weaker versions of stability than that claimed by Nash have been formally proven later by other authors. However, Nash’s request for “studying the relative stabilities” of the demand game’s equilibria has never been complied with. By performing that task, we establish analogous stability results for all generalized Nash solutions and thereby disprove Nash’s “unique stability” claim. Furthermore, we explain the impact of our result on the Nash solution with endogenous variable threats (NBWT) of the two move negotiation game, which is defined as the symmetric Nash solution of that bargaining game [math] whose status quo point [math] is the unique payoff vector of the payoff-equivalent equilibria of the first move threat game.
Citation: International Game Theory Review
PubDate: 2024-07-30T07:00:00Z
DOI: 10.1142/S0219198924500129
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- Matching in Networks: Structure of the Set of Stable Allocations
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Authors: Alejandra Garces, Alejandro Neme, Eliana Pepa Risma
Abstract: International Game Theory Review, Ahead of Print.
Matching models with contracts have been extensively studied in the last years as a generalization of the classical matching theory. Matching in networks is an even more general model in which firms trade goods via bilateral contracts constituting a supply chain. Hatfield and Kominers ([2012] Matching in networks with bilateral contracts, Am. Econ. J., Microecon. 4(1), 176–208, doi:10.1257/mic.4.1.176) showed that a natural substitutability condition characterizes the maximal domain of firm preferences for which the existence of stable allocations is guaranteed in such a model, if the set of all existent contracts is acyclic. Moreover, they asserted that these conditions are sufficient to obtain a suitable lattice structure for the set of all stable allocations. In this paper, we exhibit an inconsistency in the last point through an example, and introduce an additional condition over firm preferences that allows to recover an appropriate lattice structure.
Citation: International Game Theory Review
PubDate: 2024-07-16T07:00:00Z
DOI: 10.1142/S0219198924500105
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- The Game with a “Life-Line” for Simple Harmonic Motions of
Objects-
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Authors: Abdulla Azamov, Bahrom Samatov, Ulmasjon Soyibboev
Abstract: International Game Theory Review, Ahead of Print.
The purpose of this work is to study the pursuit-evasion problem and the “Life-line” game for two objects (called Pursuer and Evader) with simple harmonic motion dynamics of the same type in the Euclidean space. In this case, the objects move by controlled acceleration vectors. The controls of the objects are subject to geometrical constraints. In the pursuit problem, the strategy of parallel pursuit (in brief, the [math]-strategy) is suggested for the Pursuer, and by this strategy a capture condition is achieved. In the evasion problem, a constant control function is offered for the Evader, and an evasion condition is derived. Employing the [math]-strategy we generate an analytic formula for the attainability domain of the Evader (the set of all the meeting points of the objects), and we prove the Petrosjan type theorem describing that the attainability domain is monotonically decreasing with respect to the inclusion in time. In the “Life-line” problem, first, by virtue of the [math]-strategy solvability conditions to the advantage of the Pursuer are achieved and next, in constructing a reachable domain of the Evader by a control function, solvability conditions to the advantage of the Evader are identified. Differential games under harmonic motions are more complex owing to some troubles in determining optimal strategies and in building the meeting domain of objects. Accordingly, such types of games have not been fairly investigated than the simple motion games. From this point of view, studying the pursuit, evasion, and “Life-line” problems for oscillated motions arouses a special interest.
Citation: International Game Theory Review
PubDate: 2024-06-28T07:00:00Z
DOI: 10.1142/S0219198924500099
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- A Note On “A Methodology For Solving Bimatrix Games Under 2-Tuple
Linguistic Environment”-
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Authors: Kirti, Tina Verma, Amit Kumar
Abstract: International Game Theory Review, Ahead of Print.
To the best of authors’ knowledge, only two methods are proposed in the literature to solve 2-tuple linguistic bi-matrix games. In this paper, a 2-tuple linguistic bi-matrix game is considered to show that none of these methods is valid and hence, it is inappropriate to use these methods to solve 2-tuple linguistic bi-matrix games. Also, a new method is proposed to solve 2-tuple linguistic bi-matrix games. Furthermore, the origin of the proposed method as well as its validity is discussed. Finally, the proposed method is illustrated with the help of the considered 2-tuple linguistic bi-matrix game.
Citation: International Game Theory Review
PubDate: 2024-06-27T07:00:00Z
DOI: 10.1142/S0219198924500117
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- Preface: Special Issue on Game Theory and Optimization in Honor of Pierre
Bernhard-
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Authors: Marc Deschamps, Georges Zaccour
Abstract: International Game Theory Review, Ahead of Print.
Citation: International Game Theory Review
PubDate: 2024-05-29T07:00:00Z
DOI: 10.1142/S0219198924020018
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- Ecological Economics and Dynamic Games: A Systematic Literature Review
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Authors: Régis Y. Chenavaz, Stanko Dimitrov, Shoude Li
Abstract: International Game Theory Review, Ahead of Print.
Ecological and environmental economics are inherently dynamic systems requiring dynamic optimization tools. Understanding the interplay between environmental economics, ecological economics, and dynamic games is crucial. This paper presents a systematic literature review on ecological and environmental economics modeled with dynamic games. To be more specific, this systematic literature review analyzes a dataset of 88 peer-reviewed articles from international journals. This study identifies clusters related to resource management, taxation, and policy. It also reveals niche and motor research themes, such as policy, biological invasions, pollution, taxation, abatement, and efficiency, paving the way for future research avenues. By comprehensively examining the literature, this review provides insights into current and future challenges faced by companies, consumers, regulators, and society. It contributes to a deeper understanding of the complex relationship between ecological and environmental dynamics and the field of dynamic games in economics.
Citation: International Game Theory Review
PubDate: 2024-05-21T07:00:00Z
DOI: 10.1142/S0219198924500087
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- Assessing Available Care Time and Nursing Shortage in a Hospital
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Authors: Romain Biard, Marc Deschamps, Mostapha Diss, Alexis Roussel
Abstract: International Game Theory Review, Ahead of Print.
This paper develops a model to assess the number of nurses needed to ensure both healthy patients and caregivers. We propose a model with random arrivals and exits of patients who may be of a single type (or several), and calculate the average care time they can receive. We show that the mean care time does not depend only on the mean number of patients in the unit. Actually, the probability distribution of the new patients per time step plays a central role. In the Poissonian case, we obtain totally explicit results, prove that the mean care time converges to a constant and give numerical examples. We also propose an analysis of the impact of working conditions on the average time that can be devoted to a patient. Four scenarios are proposed with numerical applications. Our analysis provides insights into current discussions on the introduction of caregiver ratios in hospitals to improve both the quality of care and caregivers’ working conditions.
Citation: International Game Theory Review
PubDate: 2024-05-20T07:00:00Z
DOI: 10.1142/S0219198924400048
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- Effects of Imprecise Cognitive Biases and Free-Riding on the Pricing
Decisions of Dual-Channel Supply Chain Members-
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Authors: Sanchari Ganguly, Pritha Das, Manoranjan Maiti
Abstract: International Game Theory Review, Ahead of Print.
Nowadays, to cater the increasing green customers, firms have switched to green manufacturing. In a dual-channel green supply chain (DCGSC), customers experience products at offline stores and buy them online (free-riding). Often imprecise cognitive biases (“fairness concern” and “overconfidence”) are observed among the supply chain (SC) members. With these facts, this study introduces the free-riding and above cognitive biases in a DCGSC with a manufacturer selling a green product through own online and offline retail channels and examines their effects. A centralized and four decentralized models (for green and nongreen products) are formulated depending upon channel members’ cognitive biases individually and jointly with and without free-riding. The fuzzy objectives and constraints are made deterministic using expectation and possibility measures, respectively. Models are solved and illustrated numerically. The results indicate that free-riding is harmful and beneficial to retailer and manufacturer, respectively. Manufacturer’s overconfidence enhances the retailer’s profit but decreases or increases own profit depending upon the salvage value. Retailer’s fairness concern is catastrophic for manufacturer but beneficial for her. Product greening increases manufacturer’s profit than the carbon tax regulation for lower emissions. In addition to above observations, for maximum profit, management should not go for greening beyond an optimum level.
Citation: International Game Theory Review
PubDate: 2024-05-15T07:00:00Z
DOI: 10.1142/S0219198924500075
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- Swarm Guidance Based on Mean Field Game Concepts
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Authors: Stéphane Le Ménec
Abstract: International Game Theory Review, Ahead of Print.
The concept of swarm comes from the biological world. Drones gather in groups of 100 or even 1000 to fly like a flock of birds, called swarms. Swarm systems satisfy several assumptions such as decentralized controls, local information and simple platforms. Swarm systems have attractive properties such as resilience, scalability, and ease of development and implementation. Swarm techniques can perform simple tasks such as moving in a coordinated direction. The flocking behavior of a group of animals that converge by local interactions toward the same heading is an example of simple consensus for decentralized dynamic systems. However, the notion of decentralized control based on local information suffers from taking into account the overall behavior of the group. For example, in a complex environment, a swarm will adapt to the presence of obstacles and congestion reactively, whereas we would like more anticipatory control. The objective of this paper is to propose a solution based on Mean Field Game (MFG) concepts to integrate macro-level knowledge at the micro-level in decentralized flocking.
Citation: International Game Theory Review
PubDate: 2024-04-24T07:00:00Z
DOI: 10.1142/S0219198924400085
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- Criminals Can Be Leaders: An Endogenous Timing Approach to Security Games
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Authors: Eduardo Zúñiga-Leyton
Abstract: International Game Theory Review, Ahead of Print.
Security Games traditionally assume sequential interactions, with the defender acting as the leader and the attacker as the follower. In this paper, we challenge such an assumption by showing that security interactions can also be simultaneous or that even the attacker might be the leader. Specifically, we consider a simple security game framework consisting of two possible targets, one attacker and one defender. Then, we extend that basic interaction using a well-known endogenous timing framework (the Game with Observable Delay) to endogenously obtain the timing of the game as part of the equilibrium outcome. Our results show that, for the same set of general assumptions, the interaction can be simultaneous or sequential (with either the defender or attacker being the leader). Although the simultaneous case could be discarded using payoff dominance, it is impossible to compare the two sequential configurations using the same criterion. The risk dominance criterion also turns out to be helpless in this case. Thus, we argue that considering attackers as leaders in Security Games is a plausible scenario that merits further consideration, not only from a theoretical point of view but also due to its alignment with certain types of real-world crime.
Citation: International Game Theory Review
PubDate: 2024-04-20T07:00:00Z
DOI: 10.1142/S0219198924500063
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- Selfish Grower Behavior Can Group-optimally Eradicate Plant Diseases
Caused by Coinfection-
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Authors: Frank M. Hilker, Lea-Deborah Kolb, Frédéric M. Hamelin
Abstract: International Game Theory Review, Ahead of Print.
Game-theoretic behavioral and epidemiological models suggest that it is impossible to eradicate a disease through voluntary control actions when individuals behave according to their own interests. The simple reason is that free-riding behavior, which is best for self-interest, leads to a control coverage on the group level that is insufficient to eradicate the disease. Here we show that, for diseases that are caused by coinfection, self-interest can actually result in the socially optimal outcome of disease eradication. Our result challenges the conventional wisdom that selfish behavior undermines the group interest; it resolves a social dilemma in the absence of any cooperation, institutional arrangements, or social norms. Our model is motivated by coinfecting plant viruses, common among agricultural crops and natural plants, and the behavioral dynamics of growers to adopt protective action (biological or chemical control). The epidemiological scenario, in which the disease is eradicated by self-interest, is characterized by a positive feedback process in which coinfection enhances infectivity. Similar feedback structures exist for a range of typical epidemiological processes that facilitate disease persistence if prevalence is sufficiently large. The underlying mechanism may therefore be applicable to other diseases.
Citation: International Game Theory Review
PubDate: 2024-04-18T07:00:00Z
DOI: 10.1142/S0219198924400061
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- Reintroducing Time, Money and Constraints: Viability to Bridge the
Economic and Monetary Theories-
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Authors: Jean-Pierre Aubin, Pierre-Cyril Aubin-Frankowski, Vladimir Lozève
Abstract: International Game Theory Review, Ahead of Print.
Why use a viabilistic approach to model economy' Because it is urgent to re-assess the modeling of the business cycle that integrates dynamic money creation and that has at its core the notion of constraints. The purpose of this paper is thus to propose an evolutionary economic model using a mathematical framework derived from set-valued analysis, differential inclusions and viability theory. As this approach is dynamical, the model will not use two concepts on which neo-classical economics are built i.e., (1) the existence of static repeated equilibria, (2) the optimization by an economic agent of a utility function. Furthermore, we will not use any self-organization process or “invisible hand”, as in our viabilist framework the economic viability will be maintained by explicit choices of the economic agents and of the lender of last resort over the budgetary and monetary rules to apply. Indeed, even simple constraints on the second-derivative of the means of payments already induce four-phased business cycles. Coupling these constraints over the creation of means of payment with economic evolutions of prices and commodities through a budgetary constraint allows for a single formalism, tackling jointly the question of the viability of economic and monetary evolutions.
Citation: International Game Theory Review
PubDate: 2024-04-10T07:00:00Z
DOI: 10.1142/S0219198924400012
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- Differential Games with Additive Payoffs
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Authors: Leon Petrosyan, Anna Tur
Abstract: International Game Theory Review, Ahead of Print.
Differential games with additive payoffs are considered. A new approach to constructing the characteristic function for such games is defined. Properties of optimality principles such as the core and the Shapley value constructed by applying the new characteristic function are studied. The solutions obtained are demonstrated by means of an example.
Citation: International Game Theory Review
PubDate: 2024-04-10T07:00:00Z
DOI: 10.1142/S0219198924400103
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- Maximum Principle for Mean Field Type Control Problems with General
Volatility Functions-
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Authors: Alain Bensoussan, Ziyu Huang, Sheung Chi Phillip Yam
Abstract: International Game Theory Review, Ahead of Print.
In this paper, we study the maximum principle of mean field type control problems when the volatility function depends on the state and its measure and also the control, by using our recently developed method in [Bensoussan, A., Huang, Z. and Yam, S. C. P. [2023] Control theory on Wasserstein space: A new approach to optimality conditions, Ann. Math. Sci. Appl.; Bensoussan, A., Tai, H. M. and Yam, S. C. P. [2023] Mean field type control problems, some Hilbert-space-valued FBSDEs, and related equations, preprint (2023), arXiv:2305.04019; Bensoussan, A. and Yam, S. C. P. [2019] Control problem on space of random variables and master equation, ESAIM Control Optim. Calc. Var. 25, 10]. Our method is to embed the mean field type control problem into a Hilbert space to bypass the evolution in the Wasserstein space. We here give a necessary condition and a sufficient condition for these control problems in Hilbert spaces, and we also derive a system of forward–backward stochastic differential equations.
Citation: International Game Theory Review
PubDate: 2024-04-09T07:00:00Z
DOI: 10.1142/S0219198924400036
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- On Construction of Subgame Perfect Nash Equilibria in Stackelberg Games
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Authors: Francesco Caruso, Maria Carmela Ceparano, Jacqueline Morgan
Abstract: International Game Theory Review, Ahead of Print.
Identifying a Subgame Perfect Nash Equilibrium (SPNE) of a two-player Stackelberg game could be not a manageable task, especially when the players have a continuum of actions and the follower’s best reply correspondence is not single-valued. Aim of the paper is to investigate the issue of construction of SPNEs in Stackelberg games by exploiting perturbations of both the action sets and the payoff functions of the leader and the follower. To achieve the goal, since the limit of SPNEs of perturbed games is not necessarily an SPNE of the original game even for classical perturbations, we prove under nonrestrictive convergence conditions how to produce an SPNE starting from a sequence of SPNEs of general perturbed games. This result allows to describe a procedure to find SPNEs that can accommodate various types of perturbations. More precisely, under mild assumptions on the data of the original game, we show that a large class of perturbed games (including, for example, perturbation approaches relying on the Tikhonov and entropic regularizations or motivated by altruistic and antagonistic behaviors) satisfies the convergence conditions for constructing an SPNE. The specific SPNE selections associated to such a class, together with their possible behavioral interpretations, are discussed and an illustrative example is provided.
Citation: International Game Theory Review
PubDate: 2024-03-28T07:00:00Z
DOI: 10.1142/S021919892440005X
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- A Note on Zero-Sum Two-Person Undiscounted One Player Control Semi-Markov
Games-
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Authors: Prasenjit Mondal
Abstract: International Game Theory Review, Ahead of Print.
Zero-sum two-person finite undiscounted (limiting ratio average) semi-Markov games are considered where both the transition probabilities and the transition times are controlled by a fixed player in all states. We prove that, if such a game is unichain, the value and optimal stationary strategies of the players can be obtained from an optimal solution of the linear programming algorithm for the associated one player control stochastic game using a data transformation method. An example is provided for such class of games.
Citation: International Game Theory Review
PubDate: 2024-03-28T07:00:00Z
DOI: 10.1142/S0219198924500051
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- Inducement of Desired Behavior via Soft Policies
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Authors: Tamer Başar
Abstract: International Game Theory Review, Ahead of Print.
Terms like inducement, incentivization, persuasion, and to some extent enticement, are used in our daily lives to describe situations where one individual (decision maker, or entity) acts in a way to influence the decision-making process of another individual or individuals, where the outcome could benefit all involved or only the one who has initiated the process. Such influence could be exerted in two different ways (though variations do exist): via a direct input by the influencer into the utility or reward (or loss) of the receiving party, or by controlling (and possibly crafting) the information flow to the latter, in an attempt to shape beliefs at the receiving end (as in spread of disinformation). Both scenarios (and those that fall in between) could be analyzed within a dynamic Stackelberg game-theoretic framework, with a precise notion of equilibrium, which this paper addresses. The focus will naturally be on soft inducement (incentivization, persuasion) policies, rather than hard enforcement (such as threat) ones which are not that interesting or practical. This overview paper introduces some explicit models that lead to appealing such policies. It also includes a discussion on the impact of various factors, such as population size and uncertainty in modeling, on the resulting equilibria, and identify several challenges that lie ahead.
Citation: International Game Theory Review
PubDate: 2024-03-22T07:00:00Z
DOI: 10.1142/S0219198924400024
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- Multiple Exploitation of a Renewable Resource — Optimal Solution of a
Deterministic Singular Control Model-
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Authors: Alain Jean-Marie, M. Tidball
Abstract: International Game Theory Review, Ahead of Print.
In this paper, we consider a singular control optimization problem which generalizes the Gordon–Schaefer model. A population of individuals with endogenous growth is harvested by two independent agents, and their joint profit is maximized. We show that adding a second control to the standard model greatly complicates the standard solution, which is a Most Rapid Approach. We prove that no solution where both controls are singular can exist. Using numerical experiments, we exhibit situations where the optimal steady state corresponds to one of the controls singular, and the other one is equal to one of its specific bounds. In some cases, the optimal path resembles the one-control solution, but with an additional threshold on the population beyond which both controls must be used. However, in other cases, the optimal control has more switching points and is not monotonous. We even exhibit cases where the optimal policy admits two steady states.
Citation: International Game Theory Review
PubDate: 2024-03-22T07:00:00Z
DOI: 10.1142/S0219198924400073
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- Dynamic Oligopolistic Competition with Uncertainty and Supply Disruption
Effects-
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Authors: Elena M. Parilina, Stefan Wrzaczek, Georges Zaccour
Abstract: International Game Theory Review, Ahead of Print.
We consider a finite-horizon discrete-time dynamic model of oligopolistic competition, with uncertain supply. The firms (retailers) make their decisions on quantities (sales) and orders of goods from a nonstrategic manufacturer taking into account uncertainty in demand parameters and available supply capacity. The retailers need to satisfy the joint available supply capacity constraint. The model is described as a game played over an event tree with given transition probabilities. We find a normalized equilibrium for the game with coupling constraints. The two-step procedure to find this equilibrium is described. We provide the necessary conditions of the equilibrium and examine different scenarios of uncertainties in the model by numerical simulations.
Citation: International Game Theory Review
PubDate: 2024-03-16T07:00:00Z
DOI: 10.1142/S0219198924400097
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- Cognitive Load and Mixed Strategies: On Brains and Minimax
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Authors: Sean Duffy, J. J. Naddeo, David Owens, John Smith
Abstract: International Game Theory Review, Ahead of Print.
It is well known that laboratory subjects often do not play mixed strategy equilibria games according to the theoretical predictions. However, little is known about the role of cognition in these strategic settings. We therefore conduct an experiment where subjects play a repeated hide and seek game against a computer opponent. Subjects play with either fewer available cognitive resources (high cognitive load treatment) or with more available cognitive resources (low cognitive load treatment). Surprisingly, we find some evidence that subjects in the high load treatment earn more than subjects in the low treatment. However, we also find that subjects in the low treatment exhibit a greater rate of increase in earnings across rounds, thus suggesting more learning. Our evidence is consistent with subjects in the low load treatment over-experimenting. Further, while we observe that subjects do not mix in the predicted proportions and that their actions exhibit serial correlation, we do not find strong evidence these are related to their available cognitive resources. This suggests that the standard laboratory deviations from the theoretical predictions are not associated with the availability of cognitive resources. Our results shed light on the extent to which cognitive resources affect (and do not affect) behavior in games with mixed strategy equilibria.
Citation: International Game Theory Review
PubDate: 2024-03-14T07:00:00Z
DOI: 10.1142/S021919892450004X
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- A New Method to Solve Matrix Game with Interval Payoffs and its MATLAB
Code-
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Authors: Monika Bisht, Ismat Beg, Shivam Rawat
Abstract: International Game Theory Review, Ahead of Print.
Game theory is of substantial significance in diverse domains, acting as a potent instrument to comprehend and assess strategic engagements among rational decision-makers. It formulates mathematical models to represent strategic interactions among rational decision-makers in the competitive world. Due to ambiguity in the real-world problems, acquiring the precise payoff values of a matrix game proves challenging. However, in numerous scenarios, these payoffs fluctuate within specific ranges, making them suitable for consideration as interval numbers. This leads to the formulation of a special form of game problem known as the interval valued game problem (IVGP). Some methodologies exist in the literature to find the optimal strategies as well as the value of game for IVGP, but most of them possess some limitations, resulting in the need for proposing a new methodology to find the optimal strategies and value of game. Thus, in this paper, a new solution method for game problems with payoffs represented as interval numbers is presented, utilizing the fuzzy concept. The process begins by transforming the interval payoffs into fuzzy numbers using a ranking function. Subsequently, these fuzzy payoffs are converted into crisp values, leading to the formulation of the crisp matrix game. The resulting crisp matrix game is then solved using linear programming approach. Additionally, MATLAB code for the proposed method is developed and proposed to streamline the computation process, enhancing comparison and decision-making efficiency, particularly when dealing with large payoff matrices. Furthermore, three numerical examples are provided to illustrate the validity of the proposed approach as well as its MATLAB code. A real-life example of IVGP in the realm of tourism industry is also provided. Finally, a comparative analysis is conducted, comparing the proposed method with some existing methods.
Citation: International Game Theory Review
PubDate: 2024-03-09T08:00:00Z
DOI: 10.1142/S0219198924500014
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- Optimal Goods Production Subject to Emissions Trading with Price Floor
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Authors: Ryle S. Perera
Abstract: International Game Theory Review, Ahead of Print.
In this paper, we propose a novel approach to study the production of consumption goods within a price floor carbon emission trading scheme. A stochastic Stackelberg game is set up between the environment authority (Player 1), and the manufacturer/producer (Player 2). In such a hybrid emission trading scheme, the authority sets an emissions target and producers will choose to participate in carbon trading on this basis, subject to a stochastic demand with information delayed. When the stochastic demand is determined by the market sale price and the scale of carbon emission reduction, we apply the maximum principle to obtain both the optimal production and market price. We show when the demand is determined by both the market sales price and carbon emission reduction, manufacturers are persuaded to set the market sales price first (ex ante incentive) and then proceed to a carbon trading scheme, thus providing a backward-looking advantage to manufacturers. Consequently, the manufacturer and the environmental authority can find a subgame-perfect Nash equilibrium via backward induction.
Citation: International Game Theory Review
PubDate: 2024-03-05T08:00:00Z
DOI: 10.1142/S0219198924500038
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- On the Hotelling Game with Close Players
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Authors: Luis Garcia-Perez, Juan Grau-Climent, Juan C. Losada, Ramon Alonso-Sanz
Abstract: International Game Theory Review, Ahead of Print.
The principle of minimum differentiation stated by Hotelling in his pioneer paper was proved to be invalid 50 years later, since there is a region where the players are so close that Nash equilibrium does not exist. Some authors have contributed with amendments to the original game in the aim of ensuring the existence of Nash equilibrium independently of the location of the players. However, this work analyzes the less frequently studied case of the Hotelling game with close players under different implementations of the game, considering elastic and inelastic demand (conventional Hotelling game, the Hotelling game with reservation cost and Hotelling-Smithies game). The study is supported by means of numerical simulation of the game.
Citation: International Game Theory Review
PubDate: 2024-02-29T08:00:00Z
DOI: 10.1142/S0219198924500026
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- The Marriage Game Revisited: New Insights About Domestic Labor, Divorces
and Men’s Expectations About Marriage-
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Authors: Stefano Benati
Abstract: International Game Theory Review, Ahead of Print.
In the Marriage Game, women decide whether to get married and afterward men decide whether to cooperate in the domestic tasks. Then, if a husband is not cooperative, a wife can divorce or remain married. The sequence of decisions can be formalized as a game in extensive form, in which the strategic interaction between partners turns out evident. A husband may deceive, hoping that the divorce threat is not realistic, and a woman may decide not to get married from the beginning. If players had perfect knowledge about partners’ attitude, then divorce would not exist. Unfortunately, partners’ type is revealed only after the wedding. So, it is assumed that the game is played by different type of players, both men and women, and they interact with incomplete information. The model is solved by calculating all the perfect Bayes–Nash equilibria and it is shown that they depend on a complex interaction between model parameters, as multiple or mixed strategy equilibria can be found same parameters configuration. Comparing equilibria, we argue that the model can describe the marriage evolution that has been experienced by contemporary society. Following the increasing women’s participation in the job market, the number of marriages started to decline, but surprisingly, we are observing its resurgence in the most advanced societies. Our solution to the Marriage Game points to both the active role of autonomous women and the men’s expectations about marriage. As the number of autonomous women increases, men realize that divorce is credible and they change their expectations on women.
Citation: International Game Theory Review
PubDate: 2024-01-11T08:00:00Z
DOI: 10.1142/S0219198923500214
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