This short note demonstrates how one can define a transformation of a non-zero sum game into a zero sum, so that the optimal mixed strategy achieving equilibrium always exists. The transformation is equivalent to introduction of a passive player into a game (a player with a singleton set of pure strategies), whose payoff depends on the actions of the active players, and it is justified by the l...

We consider a situation in which an agent M (the “maven”) possesses information relevant to the players of an n-person game in which he is not a participant. We define the “inducible set” as the set of ah outcomes which can be made unique Nash equilibria of a game resulting from the maven’s transmission of information. This inducible set is a formal expression of M’s ability to manipulate the g...

In this paper, we study a two-person knapsack game. Two investors, each with an individual budget, bid on a common pool of potential projects. To undertake a project, investors have their own cost estimation to be charged against their budgets. Associated with each project, there is a potential market profit that can be taken by the only bidder or shared proportionally by both bidders. The obje...

Put your wallet on the table next to mine. The game is this: The person whose wallet has less money wins all the money in the other person’s wallet. Do you want to play? You might think along these lines: “I don’t know how much money that other wallet has, and I’m not even sure how much is in mine. If I have more money, then I’ll lose it, but if I have less, I’ll win the larger amount. I have n...

For generations programmed mammal aging was widely thought to be theoretically impossible. However, new evolutionary mechanics concepts have led to renewed interest in programmed aging resulting in a schism between programmed and non-programmed proponents. This article argues that this lack of consensus is damaging medical research and therefore steps should be taken to pro-actively resolve the...

Motivated by authentication, intrusion and spam detection applications we consider single-class classification (SCC) as a two-person game between the learner and an adversary. In this game the learner has a sample from a target distribution and the goal is to construct a classifier capable of distinguishing observations from the target distribution from observations emitted from an unknown othe...

Non-orthogonal multiple access technology (NOMA), as a potentially promising in the 5G/B5G era, suffers from ubiquitous security threats due to broadcast nature of wireless medium. In this paper, we focus on artificial-signal-assisted and relay-assisted secure downlink transmission schemes against external eavesdropping context physical layer security, respectively. To characterize non-cooperat...

We formulate the problem of finding a Nash equilibrium point for the non-zero sum three-person game as a nonconvex optimization problem by generalizing Mills’s theorem [10]. For solving the problem, we propose the curvilinear algorithm which allows us to find global solutions. The proposed algorithm was tested numerically on some examples as well as on 3 competitive companies which share the br...

We propose and investigate a game-theoretic approach to the malware filtering and detector placement problem which arises in network security. Our main objective is to develop optimal detector algorithms taking into account attacker strategies and actions. Assuming rational and intelligent attackers, we present a two-person zero-sum noncooperative Markov security game framework as a basis for m...

In this paper the classical estimators of the shape parameter for the Burr Type XII distribution, such as, the Maximum Likelihood Estimator (MLE), the Uniformly Minimum Variance Unbiased Estimator (UMVUE), and the Minimum Mean Squared Error (MinMSE) estimator are obtained. Then the problem of finding the minimax estimators of this parameter under the squared log error, precautionary, and weight...