Two-person Non-cooperative Game Research Articles

A Game Approach for Defending System Security from an Attacker

In this paper, a system security problem is studied based on a two-person non-cooperative dynamic game. Security of the system is regarded in the context of observability. Namely a system is secure if it is not observable. Both the defender and attacker are assumed to have means to modify the dimension of unobservable subspace, which is set as the value function. The strategies and algorithms to minimize or maximize the value function are given respectively. Finally, examples are provided to demonstrate the effectiveness of the proposed algorithms and show some interesting game results, including accumulation mode, loop mode and locked mode.

A Mathematical Modeling Approach of Target Damage Strategy on the Intersection Confrontation

The efficiency of target damage is to measure the effect of projectile attacks. Because there is antagonism at the intersection of projectiles and targets, it is very difficult to establish scientific damage assessment strategy model and a numerical calculation method. To scientifically evaluate the target damage effect when the projectile attacks the aircraft target, this paper introduces a game confrontation mechanism and proposes a numerical calculation method of aircraft target damage game strategy under the intersection confrontation. According to the theory of two-person non-cooperative games, the projectile is regarded as one of the players in the confrontation damage game, and the aircraft target is regarded as the other player. The damage gain model and gain function of the intersection confrontation of both sides are established. The effective expectation function and the minimum and maximum theorem are used to obtain the optimal Nash equilibrium solution of the game matrix strategy, and the Nash equilibrium point of the strategy space set is derived. Through calculation and comparative analysis, the results show that the optimal gain degree composed of the damage strategy selected by both the projectile and aircraft target under the Nash equilibrium solution brings the greatest gain. The proposed hybrid game strategy of damage assessment can be an effective reference for air combat decision making in the state of intersection confrontation.

A q-rung orthopair fuzzy non-cooperative game method for competitive strategy group decision-making problems based on a hybrid dynamic experts\u2019 weight determining model

How to select the optimal strategy to compete with rivals is one of the hottest issues in the multi-attribute decision-making (MADM) field. However, most of MADM methods not only neglect the characteristics of competitors’ behaviors but also just obtain a simple strategy ranking result cannot reflect the feasibility of each strategy. To overcome these drawbacks, a two-person non-cooperative matrix game method based on a hybrid dynamic expert weight determination model is proposed for coping with intricate competitive strategy group decision-making problems within q-rung orthopair fuzzy environment. At the beginning, a novel dynamic expert weight calculation model, considering objective individual and subjective evaluation information simultaneously, is devised by integrating the superiorities of a credibility analysis scale and a Hausdorff distance measure for q-rung orthopair fuzzy sets (q-ROFSs). The expert weights obtained by the above model can vary with subjective evaluation information provided by experts, which are closer to the actual practices. Subsequently, a two-person non-cooperative fuzzy matrix game is formulated to determine the optimal mixed strategies for competitors, which can present the specific feasibility and divergence degree of each competitive strategy and be less impacted by the number of strategies. Finally, an illustrative example, several comparative analyses and sensitivity analyses are conducted to validate the reasonability and effectiveness of the proposed approach. The experimental results demonstrate that the proposed approach as a CSGDM method with high efficiency, low computation complexity and little calculation burden.

Nash Bargaining-Based Economic Analysis of Opportunistic Cognitive Cellular Networks

We analyse a cognitive cellular network comprising of a primary and a secondary network operator (PNO and SNO). The SNO implements distributed detection to opportunistically access the licensed band. In return, the PNO requests the SNO to pay a remuneration. The PNO judiciously balances between the revenue gained from its subscribers and the payment earned from the SNO. On the other hand, the SNO must earn a positive utility to maintain its infrastructure. Consequently, a two-person non-cooperative bargaining game is formulated where the operators agree upon the value of the following factors: base station activity probabilites and the payment from the SNO. The PNO is aware of detection and false-alarm probabilities of spectrum sensing by the SNO and hence can infer how the interference created by missed detection degrades its capacity. We establish that our formulated game has a unique Nash solution. For linear demands, we derive an approximate closed-form solution. Numerical analysis reveals several insightful results. For example, we exhibit that, if the user number of the SNO lies below a certain threshold, the cognitive network appears to be economically unsustainable. We also show the functional dependence of the bargaining outcome on various system parameters.

Multimedia Portfolio Behavior Analysis Based on Bayesian Game Algorithm

A portfolio prediction model based on Bayesian game algorithm is proposed to improve the accuracy of correlation analysis model in portfolio application. Firstly, the portfolio problem is analyzed. The market value constraint and the upper bound constraint are combined considering the general portfolio model according to Markowitz theory, it improves the portfolio model and obtains the portfolio model with mixed constraints. Secondly, a probabilistic portfolio monitoring strategy based on incomplete information non-cooperative Bayesian game is proposed. The framework combines the enterprise investment behavior detection module with the specified rules to identify the portfolio pattern, the interaction between portfolio selection and monitored investment behavior is modeled as a two-person non-cooperative Bayesian game, which allows portfolio selection to adopt a probability monitoring strategy based on game Bayesian Nash equilibrium, thereby reducing the computational complexity of the portfolio approach introduced into the game algorithm. Finally, the effectiveness of the proposed algorithm is verified by simulation experiments.

Study on the Attacking Intelligent Decision-Making Technology Based on the Game Theory

This paper focuses on the game decision-making technology for the multi-agent confrontational environment. A new mission decision-making method of multi-agent cooperative attack on the multi-object is elaborated based on two-person non-cooperative complete information static game model. The proposed method is implemented into the intelligent decision-making technology for the two sides’ attack via the Nash equilibrium optimization. A case study is analyzed, which results illustrate that this method can realize the intelligent forecasting and multi-agent decision-making, as well as confirm the feasibility of this technology in the confrontational intelligent decision-making.

On Hobbes’s state of nature and game theory

Hobbes’s state of nature is often analyzed in two-person two-action non-cooperative games. By definition, this literature only focuses on duels. Yet, if we consider general games, i.e., with more than two agents, analyzing Hobbes’s state of nature in terms of duel is not completely satisfactory, since it is a very specific interpretation of the war of all against all. Therefore, we propose a definition of the state of nature for games with an arbitrary number of players. We show that this definition coincides with the strategy profile considered as the state of nature in two-person games. Furthermore, we study what we call rational states of nature (that is, strategy profiles which are both states of nature and Nash equilibria). We show that in rational states of nature, the utility level of any agent is equal to his maximin payoff. We also show that rational states of nature always exist in inessential games. Finally, we prove the existence of states of nature in a class of (not necessarily inessential) symmetric games.

Approximation of Isomorphic Infinite Two-Person Non-Cooperative Games by Variously Sampling the Players’ Payoff Functions and Reshaping Payoff Matrices into Bimatrix Game

Abstract Approximation in solving the infinite two-person non-cooperative games is studied in the paper. An approximation approach with conversion of infinite game into finite one is suggested. The conversion is fulfilled in three stages. Primarily the players’ payoff functions are sampled variously according to the stated requirements to the sampling. These functions are defined on unit hypercube of the appropriate Euclidean finite-dimensional space. The sampling step along each of hypercube dimensions is constant. At the second stage, the players’ payoff multidimensional matrices are reshaped into ordinary two-dimensional matrices, using the reversible index-to-index reshaping. Thus, a bimatrix game as an initial infinite game approximation is obtained. At the third stage of the conversion, the player’s finite equilibrium strategy support is checked out for its weak consistency, defined by five types of inequalities within minimal neighbourhood of every specified sampling step. If necessary, the weakly consistent solution of the bimatrix game is checked out for its consistency, strengthened in that the cardinality of every player’s equilibrium strategy support and their densities shall be non-decreasing within minimal neighbourhood of the sampling steps. Eventually, the consistent solution certifies the game approximation acceptability, letting solve even games without any equilibrium situations, including isomorphic ones to the unit hypercube game. A case of the consistency light check is stated for the completely mixed Nash equilibrium situation.

Alfa-cut based linear programming methodology for constrained matrix games with payoffs of trapezoidal fuzzy numbers

The purpose of this paper is to develop an effective methodology for solving constrained matrix games with payoffs of trapezoidal fuzzy numbers (TrFNs), which are a type of two-person non-cooperative games with payoffs expressed by TrFNs and players' strategies being constrained. In this methodology, it is proven that any Alfa-constrained matrix game has an interval-type value and hereby any constrained matrix game with payoffs of TrFNs has a TrFN-type value. The auxiliary linear programming models are derived to compute the interval-type value of any Alfa-constrained matrix game and players' optimal strategies. Thereby the TrFN-type value of any constrained matrix game with payoffs of TrFNs can be directly obtained through solving the derived four linear programming models with data taken from only 1-cut and 0-cut of TrFN-type payoffs. Validity and applicability of the models and method proposed in this paper are demonstrated with a numerical example of the market share game problem.

Stochastic dominance equilibria in two-person noncooperative games

Two-person noncooperative games with finitely many pure strategies are considered, in which the players have linear orderings over sure outcomes but incomplete preferences over probability distributions resulting from mixed strategies. These probability distributions are evaluated according to t-degree stochastic dominance. A t-best reply is a strategy that induces a t-degree stochastically undominated distribution, and a t-equilibrium is a pair of t-best replies. The paper provides a characterization and an existence proof of t-equilibria in terms of representing utility functions, and shows that for large t behavior converges to a form of max–min play. Specifically, increased aversion to bad outcomes makes each player put all weight on a strategy that maximizes the worst outcome for the opponent, within the supports of the strategies in the limiting sequence of t-equilibria.

In Support of Trigger Strategies: Experimental Evidence from Two-Person Non-cooperative Games

Cooperative equilibria can be supported in a repeated game when players use trigger strategies. This paper tests how well trigger strategies explain behavior in two-person experimental games. Reducing payoffs for choices larger than the Cournot level induces smaller average outputs, consistent with trigger strategy models generally. Reducing payoffs for choices well above the Cournot level will not affect agents' behavior if it is consistent with a grim strategy, but would matter for trigger strategies with short-lived but intense punishment phases. We find that behavior is most consistent with a trigger strategy that involves a longer-lived, less intense punishment phase.

Game Optimization of Gas Market Development

A two-person noncooperative game is studied with special payoff functions for which standard existence theorems and algorithms for computing the Nash equilibrium solutions are not applicable. The problem is motivated by the questions related to the determination of the commencement of construction and timing of new gas pipelines.

In Support of Trigger Strategies: Experimental Evidence from Two‐Person Noncooperative Games

Cooperative equilibria can be supported in a repeated game when players use trigger strategies. This paper tests how well trigger strategies explain behavior in two‐person experimental games. Reducing payoffs for choices larger than the Cournot level induces smaller average outputs, behavior generally consistent with trigger strategy models. Reducing payoffs for choices well above the Cournot level will not affect behavior if actions are consistent with a trigger strategy involving longer‐lived, less intense punishment phases (the grim‐reaper strategy), but would matter for trigger strategies with short‐lived but intense punishment phases. Results show that behavior is most consistent with the former.

In Support of Trigger Strategies: Experimental Evidence from Two-Person Noncooperative Games

In Support of Trigger Strategies: Experimental Evidence from Two-Person Noncooperative Games

Timely inspection and deterrence

Verification of compliance to formal agreements requires the performance of routine inspections for detection of illegal behavior. Deterrence of violations is generally taken to be the primary objective of any verification regime. If the inspections are carried out in such a way that the gain the inspectee may expect from illegal behavior is smaller than that for behaving legally, then the inspections may indeed be said to have deterred violation. In this paper inspection problems characterized additionally by a `critical time' are considered for the first time in this context. The critical time is the maximum time interval within which illegal activity must be detected in order to meet the objectives of the agreement. Critically time-dependent inspection problems are modeled as two-person non-cooperative games between inspector and inspectee. They extend over a reference time interval in which the inspector performs by agreement precisely k inspections and in which the inspectee behaves illegally at most once. The inspections are assumed to incur statistical errors of the first and second kind, the former being detrimental to both protagonists. Variants for which the inspectee may or may not be in a position to take advantage of information gained during the reference time interval are considered. Equilibria are investigated and conditions for the existence of deterring inspection strategies are determined.

On the Value of Some Infinite Matrix Games

It is shown that a zero-sum two-person noncooperative game A defined by a bounded infinite matrix in which each row converges to the same real number β and each column to the same real number α has a value V(A) if and only if α ≤ β, in which case α ≤ V(A) ≤ β. For any game defined by a bounded infinite matrix A = (aij), a necessary condition for V(A) to exist is that infj lim infi aij ≤ supi lim supj aij.

An experimental evaluation of strategic preemption

This paper reports the results of a series of two-stage, two-person noncooperative games where one player can strategically preempt the other. In one of our designs, the subgame perfect equilibrium entails complete preemption; in the other, it entails partial preemption. The data show that players tend to completely preempt when it is privately optimal. However, when partial preemption is privately optimal, a non-trivial fraction of players persist in choosing the non-preemptive structure. This may result because of occasional irrational behavior following preemptive play, which induces some dominant agents to play less aggressively.

A two-person noncooperative game for assets selling problem: Independent case

This paper is concerned with a game variant of an asset selling problem, that is, prices of players' assets take several values according to the number of persons who want to sell them. We formulate the above situation as a stopping problem of a two-person noncooperative game and prove the existence theorem of an equilibrium point under the independence assumption of players' information.

An Experimental Evaluation of Strategic Preemption

This paper reports the results of a series of two-stage, two-person non-cooperative games where one player can strategically preempt the other. In one of our designs, the subgame perfect equilibrium entails complete preemption; in the other, it entails partial preemption. Logit analysis indicates that players tend to completely preempt when it is optimal. However, when partial preemption is optimal, a non-trivial fraction of players persist in choosing the non-preemptive structure. This may result because of occasional irrational behavior following preemptive play, which induces some dominant agents to play less aggressively.

Game theory as a tool for understanding information services outsourcing

In recent years, game theory has provided valuable insights into many different types of organizational arrangements. In this paper we investigate some of the ways in which game theory can help us to understand the structure and function of information systems outsourcing arrangements. We provide a brief review of two-person non-cooperative game theory. We discuss the basic concepts of dominance and Nash equilibria. In particular we stress the importance of the information structure of two-person games. We then provide a general game-theoretic interpretation of many key aspects of information systems outsourcing arrangements. In particular, we investigate the rationales behind many of the different ways of determining fees and the effects of the transfer of assets between the outsourcing company and the outsourcing vendor. Finally, we discuss how one particular type of non-cooperative two-person game might be useful as a model of information systems outsourcing arrangements. This model, the principal-agent model, has been extensively studied and in the hands of the authors has provided some initial insights into information systems outsourcing arrangements.