Search Results (15)

Eigenvector-based centrality captures recursive notions of importance in networks. While the direct problem computes centrality from given edge weights, the inverse eigenvector centrality problem seeks edge weights that reproduce a prescribed centrality profile; for directed multigraphs, this inverse task is typically non-unique and depends on the admissible arc structure. We study the direct and inverse problems on directed multigraphs and derive an explicit linear characterization of the set of admissible edge-weight vectors that are compatible with a given centrality target. On this feasible set, we formulate a generalized Nash equilibrium problem with shared centrality constraints, in which multiple agents select edge weights to maximize economically interpretable payoffs that incorporate arc-level competition effects. We provide conditions under which the induced game admits a concave potential function, yielding equilibrium existence and, under standard strict concavity assumptions, uniqueness. Finally, we illustrate the model on an airport network where nodes represent airports and parallel arcs represent airline-specific routes, showing that equilibrium selection produces a feasible and interpretable weight configuration that preserves the prescribed centrality. Full article

In this work, we study n-agent Bayesian games with m-dimensional vector types and linear payoffs, also called linear multidimensional Bayesian games. This class of games is equivalent with n-agent, m-game uniform multigames. We distinguish between games that have a discrete type space and those with a continuous type space. More specifically, we are interested in the existence of pure Bayesian Nash equilibriums for such games and efficient algorithms to find them. For continuous priors, we suggest a methodology to perform Nash equilibrium searches in simple cases. For discrete priors, we present algorithms that can handle two-action and two-player games efficiently. We introduce the core concept of threshold strategy and, under some mild conditions, we show that these games have at least one pure Bayesian Nash equilibrium. We illustrate our results with several examples like the double-game prisoner’s dilemma (DGPD), the game of chicken, and the sustainable adoption decision problem (SADP). Full article

In order to improve the autonomous lane-changing performance of unmanned vehicles, this paper aims to solve the problem of inaccurate decision classification in traditional support vector machine (SVM) algorithms applied to the lane-changing decision-making stage of intelligent driving vehicles. By using game theory-related theories and combining the improved support vector machine (SSA-SVM) method, a vehicle autonomous lane-changing strategy based on game theory is established. The optimized SVM method has certain advantages for vehicle lane-changing decision-making with a small sample size in actual production processes. The lane-changing decision judgment accuracy rate of the SSA-SVM algorithm model can reach 93.6% compared with the SVM algorithm model without algorithm optimization; the SSA-SVM algorithm model has obvious advantages in decision performance and running speed. Therefore, the proposed new algorithm can effectively solve the problem of the objective consideration of the payoff function in conventional decision game theory. Full article

In the classical approach of von Neumann and Morgenstern to cooperative games, it was assumed that the worth of all coalitions must be given. However, in real-world problems, the worth of some coalitions may be unknown. Therefore, in this study, we consider the Shapley value for convex partially defined games using two approaches. Firstly, we introduce a polytope that includes the set of Shapley values that can be obtained from a given convex partially defined game and select one rational value in some sense from the set. The elements of this polytope are said to be the Shapley payoff vectors. Secondly, we obtain the set of Shapley values that can be obtained from a given convex partially defined game and select one rational value in some sense from the set. Moreover, we axiomatize the proposed two values. Full article

Motivated by the concept of cooperative equilibria with a single objective, we introduce the concepts of weakly cooperative equilibria and strong cooperative equilibria of multi-objective population games. We give some examples to explain the difference between the cooperative equilibrium point and noncooperative equilibrium point of multi-objective population games. Under appropriate assumptions, we study the existence and stability of weakly cooperative equilibria and strong cooperative equilibria of multi-objective population games. Full article

In this paper, we obtain an existence theorem of general strong noncooperative equilibrium point of vector-valued games, in which every player maximizes all goals. We also obtain an existence theorem of strong equilibrium point of vector-valued games with single-leader–multi-follower framework by using the upper semicontinuous of parametric strong noncooperative equilibrium point set of the followers. Moreover, we obtain some results on the generic stability of general strong noncooperative equilibrium point vector-valued games. Full article

We propose a model of network formation as a two-stage game with chance moves and players of various types. First, the leader suggests a connected communication network for the players to join. Second, nature selects a type vector for players based on the given probability distribution, and each player decides whether or not to join the network keeping in mind only his own type and the leader’s type. The game is of incomplete information since each player has only a belief over the payoff functions of others. As a result, the network is formed, and each player gets a payoff related to both the network structure and his type. We prove the existence of the Bayesian equilibrium and propose a new definition of the stable partially Bayesian equilibrium defining the network to be formed and prove its existence. The connection between the stable partially Bayesian equilibrium and the Nash equilibrium in the game is examined. Finally, we investigate the characteristics of the network structures under the stable partially Bayesian equilibrium in a three-player game with the major player as well as in the n-player game with a specific characteristic function. Full article

In stochastic games, the player’s payoff is a stochastic variable. In most papers, expected payoff is considered as a payoff, which means the risk neutrality of the players. However, there may exist risk-sensitive players who would take into account “risk” measuring their stochastic payoffs. In the paper, we propose a model of stochastic games with mean-variance payoff functions, which is the sum of expectation and standard deviation multiplied by a coefficient characterizing a player’s attention to risk. We construct a cooperative version of a stochastic game with mean-variance preferences by defining characteristic function using a maxmin approach. The imputation in a cooperative stochastic game with mean-variance preferences is supposed to be a random vector. We construct the core of a cooperative stochastic game with mean-variance preferences. The paper extends existing models of discrete-time stochastic games and approaches to find cooperative solutions in these games. Full article

This paper studies the characterizations of (weakly) Pareto-Nash equilibria for multiobjective population games with a vector-valued potential function called multiobjective potential population games, where agents synchronously maximize multiobjective functions with finite strategies via a partial order on the criteria-function set. In such games, multiobjective payoff functions are equal to the transpose of the Jacobi matrix of its potential function. For multiobjective potential population games, based on Kuhn-Tucker conditions of multiobjective optimization, a strongly (weakly) Kuhn-Tucker state is introduced for its vector-valued potential function and it is proven that each strongly (weakly) Kuhn-Tucker state is one (weakly) Pareto-Nash equilibrium. The converse is obtained for multiobjective potential population games with two strategies by utilizing Tucker’s Theorem of the alternative and Motzkin’s one of linear systems. Precisely, each (weakly) Pareto-Nash equilibrium is equivalent to a strongly (weakly) Kuhn-Tucker state for multiobjective potential population games with two strategies. These characterizations by a vector-valued approach are more comprehensive than an additive weighted method. Multiobjective potential population games are the extension of population potential games from a single objective to multiobjective cases. These novel results provide a theoretical basis for further computing (weakly) Pareto-Nash equilibria of multiobjective potential population games and their practical applications. Full article

Players’ choices in quantum game schemes are often correlated by a quantum state. This enables players to obtain payoffs that may not be achievable when classical pure or mixed strategies are used. On the other hand, players’ choices can be correlated due to a classical probability distribution, and if no player benefits by a unilateral deviation from the vector of recommended strategies, the probability distribution is a correlated equilibrium. The aim of this paper is to investigate relation between correlated equilibria and Nash equilibria in the MW-type schemes for quantum games. Full article

A class of solutions are introduced by lexicographically minimizing the complaint of coalitions for cooperative games with transferable utility. Among them, the nucleolus is an important representative. From the perspective of measuring the satisfaction of coalitions with respect to a payoff vector, we define a family of optimal satisfaction values in this paper. The proportional division value and the proportional allocation of non-separable contribution value are then obtained by lexicographically maximizing two types of satisfaction criteria, respectively, which are defined by the lower bound and the upper bound of the core from the viewpoint of optimism and pessimism respectively. Correspondingly, we characterize these two proportional values by introducing the equal minimal satisfaction property and the associated consistency property. Furthermore, we analyze the duality of these axioms and propose more approaches to characterize these two values on basis of the dual axioms. Full article

We design a mechanism of the players’ sustainable cooperation in multistage n-person game in the extensive form with chance moves. When the players agreed to cooperate in a dynamic game they have to ensure time consistency of the long-term cooperative agreement. We provide the players’ rank based (PRB) algorithm for choosing a unique cooperative strategy profile and prove that corresponding optimal bundle of cooperative strategies satisfies time consistency, that is, at every subgame along the optimal game evolution a part of each original cooperative trajectory belongs to the subgame optimal bundle. We propose a refinement of the backwards induction procedure based on the players’ attitude vectors to find a unique subgame perfect equilibrium and use this algorithm to calculate a characteristic function. Finally, to ensure the sustainability of the cooperative agreement in a multistage game we employ the imputation distribution procedure (IDP) based approach, that is, we design an appropriate payment schedule to redistribute each player’s optimal payoff along the optimal bundle of cooperative trajectories. We extend the subgame consistency notion to extensive-form games with chance moves and prove that incremental IDP satisfies subgame consistency, subgame efficiency and balance condition. An example of a 3-person multistage game is provided to illustrate the proposed cooperation mechanism. Full article

The aims of this paper are twofold. First, it is shown, for the first time, which types of nonsmooth functions are characterized by all vector critical points as being efficient or weakly efficient solutions of vector optimization problems in constrained and unconstrained scenarios on Hadamard manifolds. This implies the need to extend different concepts, such as the Karush–Kuhn–Tucker vector critical points and generalized invexity functions, to Hadamard manifolds. The relationships between these quantities are clarified through a great number of explanatory examples. Second, we present an economic application proving that Nash’s critical and equilibrium points coincide in the case of invex payoff functions. This is done on Hadamard manifolds, a particular case of noncompact Riemannian symmetric spaces. Full article

We study the class of directed simple games, assuming that only integer solutions are admitted; i.e., the players share a resource that comes in discrete units. We show that the integer nucleolus—if nonempty—of such a game is composed of the images of a particular payoff vector under all symmetries of the game. This payoff vector belongs to the set of integer imputations that weakly preserve the desirability relation between the players. We propose an algorithm for finding the integer nucleolus of any directed simple game with a nonempty integer imputation set. The algorithm supports the parallel execution of multiple threads in a computer application. We also consider the integer prenucleolus and the class of directed generalized simple games. Full article

We study contracting and costly renegotiation in settings of complete, but unverifiable information, using the mechanism-design approach. We show how renegotiation activity is best modeled in the fundamentals of the mechanism-design framework, so that noncontractibility of renegotiation amounts to a constraint on the problem. We formalize and clarify the Renegotiation-Proofness Principle (RPP), which states that any state-contingent payoff vector that is implementable in an environment with renegotiation can also be implemented by a mechanism in which renegotiation does not occur in equilibrium. We observe that the RPP is not valid in some settings. However, we prove a general monotonicity result that confirms the RPP’s message about renegotiation opportunities having negative consequences. Our monotonicity theorem states that, as the costs of renegotiation increase, the set of implementable state-contingent payoffs becomes larger. Full article