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International Game Theory Review
Journal Prestige (SJR): 0.236

Number of Followers: 1

Hybrid journal (It can contain Open Access articles)
ISSN (Print) 0219-1989 - ISSN (Online) 1793-6675
Published by World Scientific

[121 journals]

Rich Extensions of the Core and the Equal Split Off Set
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  Authors: Elena Yanovskaya
  Abstract: International Game Theory Review, Ahead of Print.
  This paper studies extensions of the core and the equal split off set (ESOS) for TU games, and also subsolutions of the extensions in order to derive some new egalitarian solutions for TU games. Stability of the allocations is weakened such that an allocation [math] can be blocked only by rich coalitions which together with a player will contain all players having payoffs not less than him. In accordance with such a definition of blocking, two new solutions — the rich core and the egalitarian rich core — are defined and characterized by means of weakening of axioms characterizing the ESOS on the class of all TU games [Dietzenbacher, B. and Yanovskaya, E. [2021] Consistency of the equal spit-off set, Int. J. Game Theory 50(1), 1–22]. Two subsolutions of the egalitarian rich core — the set of Lorenz undominated allocations and the set of allocations that lexicographically minimize maximal payoffs of players (Lmax solution) are characterized. The tight upper boundary of the number of allocations in the ESOS and in the egalitarian rich core is found.
  Citation: International Game Theory Review
  PubDate: 2023-01-31T08:00:00Z
  DOI: 10.1142/S0219198923500056
Author Index Volume 24 (2022)
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  Abstract: International Game Theory Review, Volume 24, Issue 04, December 2022.
  
  Citation: International Game Theory Review
  PubDate: 2022-12-09T08:00:00Z
  DOI: 10.1142/S0219198922990018
  Issue No: Vol. 24, No. 04 (2022)
Cooperative Game-Theoretic Models of the Cournot Oligopoly
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  Authors: Alexey V. Korolev, Guennady A. Ougolnitsky
  Abstract: International Game Theory Review, Ahead of Print.
  In this paper, we build and investigate cooperative games with different characteristic functions (von Neumann–Morgenstern, Petrosyan–Zaccour, Gromova–Petrosyan) on the base of symmetrical Cournot oligopoly game-theoretic models in normal form. We find Nash and Stackelberg equilibria and cooperative solutions for nonsymmetrical Cournot oligopoly game-theoretic models in normal form. Also, we build and investigate cooperative three-player games with the same characteristic functions on the base of these models, including the calculation of Shapley value. We compare payoffs received by the players according to different optimality principles of cooperative games and games in normal form.
  Citation: International Game Theory Review
  PubDate: 2022-11-30T08:00:00Z
  DOI: 10.1142/S0219198923500044
Faking Patience with Tacit Collusion
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  Authors: Elena Parilina, Alessandro Tampieri
  Abstract: International Game Theory Review, Ahead of Print.
  This paper analyzes coordination in tacit collusion when firms’ discount factor is private information. We consider an infinitely repeated duopoly where two states of the world randomly occur, with different incentives for collusion. Depending on its own discount factor, a firm chooses cooperative behavior in both states (patient), in none of the states (impatient) or in one state (mildly patient). The presence of different states affects the strategic role of beliefs. A mildly patient firm has an incentive in “faking patience” to get the deviation profit. Interestingly, this effect prevents or delays collusion when the belief in patience is strong.
  Citation: International Game Theory Review
  PubDate: 2022-11-15T08:00:00Z
  DOI: 10.1142/S0219198923500032
Sequential Auctions with Multiple Synergies
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  Authors: Pranjal Chandrakar, Manaswini Bhalla, Shubhabrata Das
  Abstract: International Game Theory Review, Ahead of Print.
  We examine the sequential auctions of nonidentical and synergistically related (complementary/substitutable) objects. The objects are divided into categories, which are collections of substitutable items. Inter-category objects are complements. Bidders demand one unit from each category and aim to create a bundle of inter-category objects. We solve for all equilibria of the game with an exogenous order of sale. We establish that the sequential auction mechanism can achieve efficient outcomes subject to the order in which objects are presented during the auction. Specifically, we show that an efficient outcome is achieved if, in each category, the object that is valued more by both bidders (if any) is auctioned first. We show that the sequential auction mechanism suffers from the exposure problem in the presence of multiple synergies. We establish that the order in which the categories are presented during the auction may affect objects’ selling prices. Specifically, a decreasing trend in selling prices is observed in some of the outcomes.
  Citation: International Game Theory Review
  PubDate: 2022-09-13T07:00:00Z
  DOI: 10.1142/S0219198923500019
A Model to Coordinate Interests in Investment Management
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  Authors: G. I. Belyavsky, N. V. Danilova, G. A. Ougolnitsky
  Abstract: International Game Theory Review, Ahead of Print.
  The portfolio selection problem is treated as a two-player game: one player [Unit Investment Trust (UIT)] deals with investments, and the other (agent) allocates funds for it. The game is described in formal terms, and its solution is found. Note that the condition of sustainable development is derived directly from the game solution. UIT’s learning is analyzed. Three possible statements of the UIT’s learning problem are investigated, each corresponding to a particular machine learning model. An online learning model is considered to predict the information necessary for the agent’s optimal behavior in the game. A computational experiment is provided: the three learning models are applied, and the simulation results are discussed.
  Citation: International Game Theory Review
  PubDate: 2022-09-08T07:00:00Z
  DOI: 10.1142/S0219198923500020
A Note on Linear Complementarity via Two-Person Zero-Sum Games
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  Authors: Dipti Dubey, S. K. Neogy, T. E. S. Raghavan
  Abstract: International Game Theory Review, Ahead of Print.
  The matrix [math] of a linear complementarity problem can be viewed as a payoff matrix of a two-person zero-sum game. Lemke’s algorithm can be successfully applied to reach a complementary solution or infeasibility when the game satisfies the following conditions: (i) Value of [math] is equal to zero. (ii) For all principal minors of [math] (transpose of [math]) value is non-negative. (iii) For any optimal mixed strategy [math] of the maximizer either [math] or [math] for each coordinate [math].
  Citation: International Game Theory Review
  PubDate: 2022-08-02T07:00:00Z
  DOI: 10.1142/S0219198922500190
Associated Consistency and the Aumann–Drèze Value
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  Authors: Florian Navarro
  Abstract: International Game Theory Review, Ahead of Print.
  This paper presents an axiomatic characterization of the Aumann–Drèze value [Aumann, R. J. and Drèze, J. H. [1974] Cooperative games with coalition structures, Int. J. Game Theory 3, 217–237] for cooperative games with coalition structures. We build an associated game that extends the original associated game presented by Hamiache [[2001] Associated consistency and Shapley value, Int. J. Game Theory 30, 279–289] to cooperative games with coalition structures. We use a similar approach to the one used in Hamiache and Navarro [[2020] Associated consistency, value and graphs, Int. J. Game Theory 49, 227–249]. This new associated game is expressed through a matrix form. We show that the series of successive associated games is convergent and that its limit is an inessential game. This allows us to propose a characterization of the Aumann–Drèze value that relies on associated consistency, inessential game and continuity axioms. Hence, this paper strengthens the results of Hamiache [[2001] Associated consistency and Shapley value, Int. J. Game Theory 30, 279–289] and Hamiache and Navarro [[2020] Associated consistency, value and graphs, Int. J. Game Theory 49, 227–249] considering that if these axioms are viewed as desirable, we are now able to provide a unique value for three different types of problems: the Shapley value on standard games [Hamiache, G. [2001] Associated consistency and Shapley value, Int. J. Game Theory 30, 279–289], the Hamiache–Navarro value on games with graphs [Hamiache, G. and Navarro, F. [2020] Associated consistency, value and graphs, Int. J. Game Theory 49, 227–249] and the Aumann–Drèze value for games with coalition structures.
  Citation: International Game Theory Review
  PubDate: 2022-07-11T07:00:00Z
  DOI: 10.1142/S0219198922500189
Fuzzy Ranking Approach to Bi-Matrix Games with Interval Payoffs in
Marketing-Management Problem
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  Authors: Monika Bisht, Rajesh Dangwal
  Abstract: International Game Theory Review, Ahead of Print.
  World is full of uncertainties. In decision-making problems, uncertainty occurs in many forms such as fuzzy, rough, interval, soft and researchers use data in one of these forms for presenting uncontrollable factors. This paper aims to develop an effective method for solving bi-matrix game problem with interval payoffs assuming that the players know the upper and lower bounds on payoffs. First, bi-matrix game model with interval payoffs is considered. This model is then transformed to another model with fuzzy payoffs. Finally, ranking approach is used to convert the model to crisp-valued bi-matrix game model. Further, due to correspondence between games and programming problem, the Nash equilibrium of interval bimatrix game is obtained by solving a deterministic nonlinear programming problem with nonlinear objective and linear constraints. Finally, a real-life problem of marketing management is solved to validate, approve and illustrate the effectiveness of the proposed model and its solution method. The results derived are compared with some previously defined methods and conclusions are drawn further.
  Citation: International Game Theory Review
  PubDate: 2022-07-05T07:00:00Z
  DOI: 10.1142/S0219198922500165
Rank Reduction in Bimatrix Games
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  Authors: Joseph L. Heyman, Abhishek Gupta
  Abstract: International Game Theory Review, Ahead of Print.
  The rank of a bimatrix game is defined as the rank of the sum of the payoff matrices of the two players. The rank of a game is known to impact both the most suitable computation methods for determining a solution and the expressive power of the game. Under certain conditions on the payoff matrices, we devise a method that reduces the rank of the game without changing the equilibria of the game. We leverage matrix pencil theory and the Wedderburn rank reduction formula to arrive at our results. We also present a constructive proof of the fact that in a generic square game, the rank of the game can be reduced by 1, and in generic rectangular game, the rank of the game can be reduced by 2 under certain assumptions.
  Citation: International Game Theory Review
  PubDate: 2022-07-04T07:00:00Z
  DOI: 10.1142/S0219198922500177
Detailed Proof of Existence of Value Function in Time-Optimal Games with
Lifeline
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  Authors: Nataly V. Munts, Sergey S. Kumkov
  Abstract: International Game Theory Review, Ahead of Print.
  The paper discusses the existence of the value function of a time-optimal differential game with lifeline in a quite general formulation. In such a game, the first player tries to lead the trajectory of the system to a terminal set as soon as possible avoiding the lifeline. The aim of the second player is to lead the trajectory to the lifeline or, if it is not possible, to keep it outside the terminal set, or, if the latter is impossible too, to postpone maximally reaching the terminal set.
  Citation: International Game Theory Review
  PubDate: 2022-06-16T07:00:00Z
  DOI: 10.1142/S0219198922500141
A Shapley Value Index for Market Basket Analysis: Efficient Computation
Using an Harsanyi Dividend Representation
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  Authors: Jayden Fitzsimon, Shrikant Agrawal, Kirti Khade, Evan Shellshear, Jonathon Allport, Archie C. Chapman
  Abstract: International Game Theory Review, Ahead of Print.
  Market basket analysis (MBA) aims to discover purchasing patterns and item associations from customer transaction data. A major drawback of current techniques for MBA is a lack of quantitative metrics to measure the real value associated with basket items. This paper addresses this gap by deriving a practical game-theoretic measure for MBA based on the Shapley value of cooperative games, which we call Shapley value index for MBA (SIMBA). The SIMBA of an item represents the average revenue it earns, including its influence on the revenue earned from sales of other items. A significant challenge when applying Shapley value-inspired approaches in practical domains is the exponential complexity of Shapley value computation. However, for the MBA domain, we show that SIMBA admits a scalable exact computation method that does not require sampling or other approximations. Specifically, a characteristic function for the MBA game is constructed so that the transaction dataset input corresponds to the game’s Harsanyi dividends. The relationship between Harsanyi dividends and the Shapley value is then exploited to efficiently compute SIMBA. This approach scales linearly in the number of transactions, making SIMBA a feasible approach for quantitative MBA. SIMBA can be used to screen conventional MBA techniques, such as association rules, to identify significant rules based on the items’ cross-selling capacity. This combination of existing MBA methods and SIMBA will generate rules based not only on frequency of co-occurrence, but also on the significance of the items. We demonstrate the working of the algorithm by analyzing openly available transaction data from an online retail store. To the best of our knowledge, this is the first time Shapley value is used in this way to solve market basket analyses of a practical size.
  Citation: International Game Theory Review
  PubDate: 2022-06-16T07:00:00Z
  DOI: 10.1142/S0219198922500153
Market Exit and Minimax Regret
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  Authors: Gisèle Umbhauer
  Abstract: International Game Theory Review, Ahead of Print.
  This paper shows how minimax regret sheds new light on an old economic topic, market-exit games. It focuses on wars of attrition, namely overcrowded duopoly markets where the strategic variable is the exit time. The only symmetric Nash equilibrium (NE) of the game studied is a mixed-strategy equilibrium that leads to a null expected payoff, i.e., the payoff a firm gets when it immediately exits the market. This result is not convincing, both from a behavioral and from a strategic viewpoint. The minimax regret approach that builds upon opposite regrets — exiting the market too late and exiting the market too early — is more convincing and ensures that both firms obtain a strictly positive expected payoff. Highlights Minimax regret behavior sheds new light on the optimal exit-times in overcrowded markets. Minimax regret behavior provides a new behavioral content to mixed strategies. In overcrowded duopolies, if the firms’ aim consists in minimizing regrets, then they get better payoffs than in the mixed-strategy NE.
  Citation: International Game Theory Review
  PubDate: 2022-06-11T07:00:00Z
  DOI: 10.1142/S021919892250013X
A Differential Game Analysis of the Firms’ Process Innovation with
Technological Spillover Under Different Market Structures in a Duopoly
Market
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  Authors: Shoude Li
  Abstract: International Game Theory Review, Ahead of Print.
  In this paper, we formulated a dynamic game model of the firms’ process innovation with technological spillover under different market structures (market competition intensity) in a duopoly market, in which the firms are concerned about relative profits as well as their own profits and investigated the relationship between the degree of competitiveness faced by the firms and their R&D expenditure. Our results showed that, under certain conditions, the system always admits saddle point steady-state equilibrium under independent ventures and R&D cartel games, respectively, and although the process innovation investment under R&D cartel is higher than that under the independent ventures, whether the marginal production cost under R&D cartel is less (higher) than that under the independent ventures depends on the degree of technological R&D spillover and the market competition intensity. Furthermore, the marginal production cost under independent ventures is not monotonically decreasing with spillover for the given region of market competition intensity; while the marginal production cost under R&D cartel game always monotonically decreases with spillover for any market competition intensity.
  Citation: International Game Theory Review
  PubDate: 2022-03-30T07:00:00Z
  DOI: 10.1142/S0219198922500128
Consensus Game: An Extension of Battle of the Sexes Game
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  Authors: Chunlin Wang, Joyendu Bhadury
  Abstract: International Game Theory Review, Ahead of Print.
  This paper introduces “Consensus Game” as a multiplayer extension of the well-known “Battle of the Sexes” game to model situations where multiple parties (e.g., buyers–sellers) need to come to an agreement on a common issue in order for all players to be better off. We develop closed-form analytical expressions for the mixed-strategy Nash Equilibrium of a Consensus Game and thereafter, under a mildly restrictive assumption of completely mixed strategies, demonstrate the uniqueness of this equilibrium. We also show that in the constant-sum version of the Consensus Game, this unique Nash Equilibrium guarantees equal payoffs to all players. This result pertaining to equal payoffs as the only Nash Equilibrium suggests that in applications where multiple parties need to arrive at a consensus in order to share a common and fixed pool of a resource, an equal-utility distribution of the pool is the only stable solution that does not provide any party a unilateral incentive to deviate.
  Citation: International Game Theory Review
  PubDate: 2022-03-28T07:00:00Z
  DOI: 10.1142/S0219198922500116
Comparative Dynamics and Envelope Theorems of Open-Loop Stackelberg
Equilibria in Differential Games
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  Authors: Chen Ling
  Abstract: International Game Theory Review, Ahead of Print.
  A direct proof of the envelope theorems and intrinsic comparative dynamics of locally differentiable open-loop Stackelberg equilibria (OLSE) is given using an extended primal-dual method. It is shown that the follower’s envelope and comparative dynamics results agree in form with those of any player in an open-loop Nash equilibrium, while those of the leader differ. This difference allows, in principle, an empirical test of the leader–follower role in a differential game. Separability conditions are identified on the instantaneous payoff and transition functions under which, for certain parameters, the intrinsic comparative dynamics of the leader’s time-inconsistent OSLE and those in the corresponding optimal control problem are qualitatively identical. However, similar conditions do not exist for time-consistent OSLE.
  Citation: International Game Theory Review
  PubDate: 2022-02-11T08:00:00Z
  DOI: 10.1142/S0219198922500104
A Capital-Labor Compact and Green Production
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  Authors: Romar Correa
  Abstract: International Game Theory Review, Ahead of Print.
  The relation between Capital and Labor is well known to comprise of cooperation and noncooperation. Greater profits mean a lower wage bill. At the same time, increasing output brings expanding employment. We confine ourselves to class conflict or cooperation between Capital and Labor in the context of climate change. Our ‘socio-technical’ setup incorporates green technical change. We provide a macro-growth dynamic game with outcomes on output, employment, accumulation, and the use of a ‘solar technology’ between the classes.
  Citation: International Game Theory Review
  PubDate: 2022-01-19T08:00:00Z
  DOI: 10.1142/S0219198922500098