Two-person Matrix Games Research Articles

Evolutionary Game Dynamics with Environmental Feedback in a Network with Two Communities

Recent developments of eco-evolutionary models have shown that evolving feedbacks between behavioral strategies and the environment of game interactions, leading to changes in the underlying payoff matrix, can impact the underlying population dynamics in various manners. We propose and analyze an eco-evolutionary game dynamics model on a network with two communities such that players interact with other players in the same community and those in the opposite community at different rates. In our model, we consider two-person matrix games with pairwise interactions occurring on individual edges and assume that the environmental state depends on edges rather than on nodes or being globally shared in the population. We analytically determine the equilibria and their stability under a symmetric population structure assumption, and we also numerically study the replicator dynamics of the general model. The model shows rich dynamical behavior, such as multiple transcritical bifurcations, multistability, and anti-synchronous oscillations. Our work offers insights into understanding how the presence of community structure impacts the eco-evolutionary dynamics within and between niches.

Two-person game with hesitant fuzzy payoff: An application in MADM

Hesitant Fuzzy Set (HFS) permits the membership function having a collection of probable values which are more effective for modelling the real-life problems. Multiple Attribute Decision Making (MADM) process apparently assesses multiple conflicting attribute in decision making. In traditional decision making problems, each player is moving independently whereas in reality it is seen that each player aims to maximize personal profit which causes a negative impact on other player. MADM problem treats with candidate to the best alternative corresponding to the several attributes. Here, we present an MADM problem under hesitant fuzzy information and then transforming it into two-person matrix game, referred to herein as MADM game. The Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is one of the prominent approach for solving the MADM problems. In this work, we develop the TOPSIS based on Ordered Weighted Aggregation (OWA) operator and hybrid hesitant fuzzy normalized Euclidean distance.Please check whether short title on odd pages have been set correctly. Then the two approaches, namely Hybrid Hesitant Fuzzy Ordered Weighted Aggregation-TOPSIS (HHFOWA-TOPSIS) and the Linear Programming Problem (LPP) are applied to solve the formulated MADM game. For solving MADM game, we apply LPP by considering the various values of α,ψ, and HHFOWA-TOPSIS for finding the optimal alternative according to their scores.Please provide missing AMS classification codes. An investment selection problem is included to explain the feasibility and superiority of our formulated approaches. A comparison analysis is drawn among the obtained results which are derived from the two approaches. LPP and HHFOWA-TOPSIS provide the best alternative for the proposed problem. Finally, conclusions about our findings and outlooks are described.

On solution of constraint matrix games under rough interval approach

The aim of this article is to propose an effective technique for solving constraint matrix games with rough interval payoffs, which are a class of non-cooperative two-person matrix games with rough interval payoffs and the strategies of the players are constrained. Since the payoffs of the rough constraint matrix games are rough intervals, then its game value is also a rough interval. In this technique, we derived four linear programming problems, which are used to obtain the upper–lower bound, lower–lower bound, lower–upper bound and upper–upper bound of the rough interval game values of the players in rough constraint matrix games. Moreover, the expected value operator and trust measure of rough interval have been used to obtain the α-trust equilibrium strategies and the expected equilibrium strategies of the problem under study. In addition, the different advantages of the proposed technique over those existing are discussed. Finally, a numerical experiment of market share game model is given and solved by the three mentioned methods to illustrate the effectiveness and practicality of the proposed method.

A model of discrete zero-sum two-person matrix games with grey numbers to solve dispute resolution problems in construction

Conflict between parties is a common issue in construction projects. In the present article, the conflicts be-tween contractor and employer in delayed Design-Bid-Build projects have been studied. Defining a case study, a dispute resolution method has been proposed. This case has been considered as a MCDM problem. This problem has been as-sumed as a discrete zero-sum two-person matrix game with grey numbers. Among the four alternatives available for con-tractor and employer in the proposed case study, termination is the last alternative that decision makers choose. Based on different risk values, authors determined the optimal solution for both parties. This article integrates some linguistic criteria together with time and cost, providing the better conditions to avoid lengthy bargaining.

On the efficiency of a randomized mirror descent algorithm in online optimization problems

A randomized online version of the mirror descent method is proposed. It differs from the existing versions by the randomization method. Randomization is performed at the stage of the projection of a subgradient of the function being optimized onto the unit simplex rather than at the stage of the computation of a subgradient, which is common practice. As a result, a componentwise subgradient descent with a randomly chosen component is obtained, which admits an online interpretation. This observation, for example, has made it possible to uniformly interpret results on weighting expert decisions and propose the most efficient method for searching for an equilibrium in a zero-sum two-person matrix game with sparse matrix.

An Alternative Approach for Solving Fuzzy Matrix Games

In this paper, two-person matrix games is considered whose elements of pay-off matrix are triangular fuzzy numbers (TFNs). To solve such game a new methodology based on -cut of TFN is developed for each of the players. In this methodology, two auxiliary bi-objective linear programming (BOLP) models are derived. Then using average weighted approach these two BOLP models are decomposed into two auxiliary crisp linear programming (LP) problems. Finally, the value of the matrix game for each player is obtained by solving two corresponding auxiliary LP problems using the existing simplex method. Validity and applicability of this methodology are illustrated with practical example compared to existing methods.

What Should We Do Before Running a Social Simulation?

Before running a model simulation, it is important to accumulate as much information about the model as possible. Although an analysis of relations among model components is considered a promising means of accomplishing this task, the social simulation literature offers very little guidance in performing such analyses. We use an analytical framework to demonstrate how model analysis can facilitate the simulation process, with the Iterated Prisoner's Dilemma serving as a primary example. Our results show that the analysis was helpful in identifying important strategies and simulation phenomena, thus reducing the amount of work required for the simulation. We suggest that this framework is applicable to other types of two-person matrix games, and that the methods we use are also suitable for other macro-or agent-based simulation models.

Co-operative and non-co-operative bases of food-calling

We ask how the threat of starvation and the hazard of predation might influence the economics of food-calling behavior. These vocalizations, such as the “chirrup” call of house sparrows ( Passer domesticus ), alert conspecifics to the location of a patch of food discovered by the caller. The resulting social response ordinarily implies that the caller takes less food from a patch than it could obtain by not calling and remaining solitary. We analyze the behavior with two-person matrix games where an individual may or may not inform the other after finding food. When starvation alone imposes a mortality hazard, or when the individual's susceptibility to predation is the same for solitary and social foraging, a pure strategy of not informing must qualify as an evolutionarily stable strategy (ESS). Depending on the probability distribution of patch sizes, this game may conform to a Prisoner's Dilemma where co-operation equates with a pure strategy of informing. A sufficiently high probability of repeated play, an event obviously requiring survival of both individuals, might favor informing through the stability of co-operation conditional upon reciprocity. The likelihood of informing increases as either the mean size of food patches or the patch-size variance increases. When a solitary incurs a greater predation hazard than a social forager does, as many empirical studies suggest, both starvation and predation directly govern the solution to the game. In this case one or the other pure strategy (but not both simultaneously) qualifies as an ESS whether the game will be played only once or repeatedly. If solitaries are sufficiently more susceptible to predation than social foragers are, informing is the only ESS and does not require reciprocity for stability. When pure not informing is an ESS, informing may succeed via the stability of conditional co-operation over repeated play, again depending on the probability distribution of patch sizes. Hence foodcalling may arise in the absence of co-operation or as a conditionally co-operative strategy when solitaries suffer greater mortality from predation.

The Influence of Moral Considerations on the Perceived Consequences of an Action

It is proposed that the need to believe in a just world influences the subjective probabilities a person assigns to various outcomes. That is, moral actions will be thought likely to receive rewards, and immoral actions will be thought likely to be punished. This was tested with both survey data and an experiment. The survey data showed that respondents who saw civil rights tactics as violent (immoral) saw them as self-defeating, while those who saw them as peaceful (moral) saw them as useful. In the experiment, subjects were exposed to one of two two-person matrix games and were asked to specify the economically optimal strategy. The two games had the same strategic structure, but different equitable choices. In one set of conditions subjects thought both players were people (here equity should be regarded as morally required), while in the other set, subjects thought one player was a computer (here equity should be morally irrelevant). As predicted, (1) in the person conditions, the equitable strategy was regarded as more economically rational; (2) in the computer conditions, equity had no influence on the subjects' assessment of the economically rational strategy.

Quasikonkav-quasikonvexe spiele unter ausnutzung gegneriseker schwäcken und lexikographisehe optimierung1

There exists at least one pure strategy for each player of zero-sum two-person matrix-game which, if used against anyone of his opponent's optimal mixed strategic, yields the value of the game. This assertion will be extend to games where the payoff function is quasi concave quasi convex and upper/lower semi continuous. The result will be applied to games where one of the two players takes maximum advantage of the mistakes, if any, of his opponent. It will be shown that this problem is equivalence to a problem of Lexicographic multi objective Programming.

Quantile criteria for the selection of strategies in game theory

The use of quantile criteria in two-person matrix games is explored: maximizing the confidence of a fixed payoff level or maximizing the payoff level for a given confidence level.

Matrix games with forbidden situations

ZERO-SUM two-person matrix games with forbidden situations are discussed. It is assumed that, in the presence of forbidden situations, at least informational combinations of players are required.