Best Reply Player Against Mixed Evolutionarily Stable Strategy User

We consider matrix games with two phenotypes (players): one following a mixed evolutionarily stable strategy and another one that always plays a best reply against the action played by its opponent in the previous round (best reply player, BR). We focus on iterated games and well-mixed games with repetition (that is, the mean number of repetitions is positive, but not infinite). In both interaction schemes, there are conditions on the payoff matrix guaranteeing that the best reply player can replace the mixed ESS player. This is possible because best reply players in pairs, individually following their own selfish strategies, develop cycles where the bigger payoff can compensate their disadvantage compared with the ESS players. Well-mixed interaction is one of the basic assumptions of classical evolutionary matrix game theory. However, if the players repeat the game with certain probability, then they can react to their opponents’ behavior. Our main result is that the classical mixed ESS loses its general stability in the well-mixed population games with repetition in the sense that it can happen to be overrun by the BR player.

Solutions of Matrix Games Involving Linguistic Interval-Valued Intuitionistic Fuzzy Sets

In real-life decision-making challenges, experts quite frequently have a preference for expressing their perspective in natural linguistic terms rather than definite numerical format. These linguistic representation has been utilized to resolve plenty of decision-making problems. This paper displays the thorough study of matrix games where in the payoffs are characterized through linguistic interval-valued intuitionistic fuzzy sets (LIVIFSs). Solution of these matrix games are attained by resolving a duo of linear or nonlinear programming problems, originated through non-linear bi-objective programming problems. Finally, a numerical example is used to demonstrate the applicability of the suggested approach.

Evaluating the Effectiveness of an Intrusion Detection System Based on Matrix Games and Fuzzy Sets

We consider a problem formulated as a matrix game in which the gain of officials using a specific intrusion detection system (criminal actions) of intruders (player 1) is the probability of timely detection of these criminal actions (player 2). As a rule, it is not possible to unambiguously set the probability of timely detection of criminal actions, so it is proposed to use the apparatus of fuzzy set theory to evaluate it. Reviewed and discussed the basic concepts of fuzzy set theory, and an example of practical application of this theory to assess the efficiency of the detection system of criminal damage. Application of fuzzy set theory in assessing the possible actions of an attacker can detect existing vulnerabilities in information security of automated systems continue to spend improving the detection of criminal acts (hackers) to prevent the possibility of applying economic and other damage to the company.

Decomposed 2*2 games - a conceptual review

2*2 games, such as the Prisoner's Dilemma, are a common tool for studying cooperation and social decision-making. In experiments, 2*2 games are usually presented in matrix form, such that participants see only the possible outcomes. Some 2*2 games can be decomposed into payoffs for self and other, such that participants see the direct consequences of two actions. While the final outcomes of the decomposed form and the matrix-form can be identical, the framing differs: the matrix form emphasises the outcome, the decomposed form emphasises the action. This allows decomposed games to address questions that could not be answered with matrix games. Here, we provide a conceptual overview of decomposed games that is accessible without knowing the underlying mathematics. We explain which 2*2 games can be decomposed, why the same payoff matrix can be decomposed into infinitely many decompositions, and we apply this to (a)symmetric games, (a)symmetric decompositions, and games with ties. Finally, we show how to calculate all decompositions for a given game and we suggest when the decomposed form might be more appropriate than the matrix form for an experimental design.

Nash equilibria in human sensorimotor interactions explained by Q-learning with intrinsic costs

The Nash equilibrium concept has previously been shown to be an important tool to understand human sensorimotor interactions, where different actors vie for minimizing their respective effort while engaging in a multi-agent motor task. However, it is not clear how such equilibria are reached. Here, we compare different reinforcement learning models to human behavior engaged in sensorimotor interactions with haptic feedback based on three classic games, including the prisoner’s dilemma, and the symmetric and asymmetric matching pennies games. We find that a discrete analysis that reduces the continuous sensorimotor interaction to binary choices as in classical matrix games does not allow to distinguish between the different learning algorithms, but that a more detailed continuous analysis with continuous formulations of the learning algorithms and the game-theoretic solutions affords different predictions. In particular, we find that Q-learning with intrinsic costs that disfavor deviations from average behavior explains the observed data best, even though all learning algorithms equally converge to admissible Nash equilibrium solutions. We therefore conclude that it is important to study different learning algorithms for understanding sensorimotor interactions, as such behavior cannot be inferred from a game-theoretic analysis alone, that simply focuses on the Nash equilibrium concept, as different learning algorithms impose preferences on the set of possible equilibrium solutions due to the inherent learning dynamics.