Problem Of Finding Optimal Strategies Research Articles

INFLUENCE OF EMOTIONAL INTELLIGENCE OF ELITE WOMEN’S HANDBALL PLAYERS ON THE CHOICE OF STRESS COPING STRATEGIES

Introduction. The problem of finding optimal strategies for overcoming stress by elite athletes remains relevant. Many authors study the problem of stress resistance in sports from the standpoint of forming a set of athlete’s personal qualities. The emotional intelligence is such athlete’s personal characteristics that affect the ability to withstand competitive stress.
 The aim of the study: to establish a relation between coping strategies and emotional intelligence of elite women’s handball players.
 Materials and methods: Athletes of the Ukrainian national women’s handball team (21 players aged 17 to 28, experience in this sport from 5 to 19 years) took part in the research. The following methods: questionnaire «Ways of coping behaviour» by R. Lazarus, the Nelson-Hall methodology devised to diagnose EI, was used. Data was processed by non-parametric descriptive statistics, Shapiro-Wilk normality test, and correlation analysis.
 Results: Strategies using by athletes to increase the ability of the psyche to adapt to anxiety, the level of emotional intelligence and its components, the characteristics of motivation to succeed and motivation to avoid failure have been identified. 61.9 % of elite women’s handball players showed a low level of general emotional intelligence; 38.1 % of people showed a middle level. Correlation analysis between athletes’ choice of coping strategies and manifestations of emotional intelligence revealed certain patterns. «Confrontational coping» correlated with empathy (r = 0.45). Coping «Distancing» correlated with self-control (r = 0.59) and self-motivation (r = 0.53). Coping «Positive reappraisal» correlated with emotional awareness (r = 0.47), self-emotion management (r = 0.52) and overall emotional intelligence (r = 0.59). Coping «Self-control» had a positive correlation with self-motivation (r = 0.53).
 Conclusions: The obtained results give grounds to assert the expediency of applying the correction of emotional intelligence by increasing one in the practice of psychological training of athletes, which will increase their stress resistance.

Duel-based neuroevolutionary method for Stackelberg Security Games with boundedly rational Attacker

This paper considers the problem of finding optimal strategies in Stackelberg Security Games when playing against a non-perfectly rational Attacker. To this end, a novel Duel-based NeuroEvolutionary approach to Security Games (DNESG) is proposed, which utilizes the Strategy Comparison Neural Network (SCNN) as a surrogate model to compare pairs of Defender’s strategies. SCNN is trained on historical data (past attack attempts) and does not require any direct information about the Attacker’s preferences regarding targets, payoff distribution, or decision-making model. SCNN is embedded in the Evolutionary Algorithm framework and implements a tournament-based selection method in place of a time-consuming direct strategy evaluation. The effectiveness of DNESG is assessed on a set of 90 benchmark Deep Packet Inspection games inspired by real cybersecurity scenarios. The proposed method provides high-quality solutions and outperforms state-of-the-art approaches (both exact and approximate) with statistical significance when playing against non-perfectly rational Attacker. Moreover, DNESG offers excellent time scalability, being two orders of magnitude faster than the state-of-the-art Mixed-Integer Linear Programming method.

Multi-player flow games

In the traditional maximum-flow problem, the goal is to transfer maximum flow in a network by directing, in each vertex in the network, incoming flow to outgoing edges. The problem corresponds to settings in which a central authority has control on all vertices of the network. Today's computing environment, however, involves systems with no central authority. In particular, in many applications of flow networks, the vertices correspond to decision-points controlled by different and selfish entities. For example, in communication networks, routers may belong to different companies, with different destination objectives. This suggests that the maximum-flow problem should be revisited, and examined from a game-theoretic perspective. We introduce and study \em multi-player flow games (MFGs, for short). Essentially, the vertices of an MFG are partitioned among the players, and a player that owns a vertex directs the flow that reaches it. Each player has a different target vertex, and the objective of each player is to maximize the flow that reaches her target vertex. We study the stability of MFGs and show that, unfortunately, an MFG need not have a Nash Equilibrium. Moreover, the Price of Anarchy and even the Price of Stability of MFGs are unbounded. That is, the reduction in the flow due to selfish behavior is unbounded. We study the problem of deciding whether a given MFG has a Nash Equilibrium and show that it is Σ_2^P$-complete, as well as the problem of finding optimal strategies for the players (that is, best-response moves), which we show to be NP-complete. We continue with some good news and consider a variant of MFGs in which flow may be swallowed. For example, when routers in a communication network may drop messages. We show that, surprisingly, while this model seems to incentivize selfish behavior, a Nash Equilibrium that achieves the maximum flow always exists, and can be found in polynomial time. Finally, we consider MFGs in which the strategies of the players may use non-integral flows, which we show to be stronger.

Optimal growth trajectories with finite carrying capacity.

We consider the problem of finding optimal strategies that maximize the average growth rate of multiplicative stochastic processes. For a geometric Brownian motion, the problem is solved through the so-called Kelly criterion, according to which the optimal growth rate is achieved by investing a constant given fraction of resources at any step of the dynamics. We generalize these finding to the case of dynamical equations with finite carrying capacity, which can find applications in biology, mathematical ecology, and finance. We formulate the problem in terms of a stochastic process with multiplicative noise and a nonlinear drift term that is determined by the specific functional form of carrying capacity. We solve the stochastic equation for two classes of carrying capacity functions (power laws and logarithmic), and in both cases we compute the optimal trajectories of the control parameter. We further test the validity of our analytical results using numerical simulations.

Finding optimal satisficing strategies for and-or trees

Many tasks require evaluating a specified Boolean expression φ over a set of probabilistic tests whose costs and success probabilities are each known. A strategy specifies when to perform which test, towards determining the overall outcome of φ. We are interested in finding the strategy with the minimum expected cost. As this task is typically NP-hard—for example, when tests can occur many times within φ, or when there are probabilistic correlations between the test outcomes—we consider those cases in which the tests are probabilistically independent and each appears only once in φ. In such cases, φ can be written as an and-or tree, where each internal node corresponds to either the “and” or “or” of its children, and each leaf node is a probabilistic test. In this paper we investigate “probabilistic and-or tree resolution” ( PAOTR), namely the problem of finding optimal strategies for and-or trees. We first consider a depth-first approach: evaluate each penultimate rooted subtree in isolation, replace each such subtree with a single “mega-test”, and recurse on the resulting reduced tree. We show that the strategies produced by this approach are optimal for and-or trees with depth at most two but can be arbitrarily sub-optimal for deeper trees. Each depth-first strategy can be described by giving the linear relative order in which tests are to be executed, with the understanding that any test whose outcome becomes irrelevant is skipped. The class of linear strategies is strictly larger than depth-first strategies. We show that even the best linear strategy can also be arbitrarily sub-optimal. We next prove that an optimal strategy honors a natural partial order among tests with a common parent node (“leaf-sibling tests”), and use this to produce a dynamic programming algorithm that finds the optimal strategy in time O ( d 2 ( r + 1 ) d ) , where r is the maximum number of leaf-siblings and d is the number of leaf-parents; hence, for trees with a bounded number of internal nodes, this run-time is polynomial in the tree size. We also present another special class of and-or trees for which this task takes polynomial time. We close by presenting a number of other plausible approaches to PAOTR, together with counterexamples to show their limitations.

A note on the complexity of determining optimal strategies in games with common payoffs

In a recent paper [Int J Game Theory (2001) 30:99–106], Chu and Halpern investigated the problem of finding optimal strategies in certain games with common payoffs. This short technical note answers a computational complexity question that was left open in their paper.

The Construction of Optimal Designs for the One-Way Classification Analysis of Variance

SUMMARY A consideration of the purpose of some one-way classification experiments leads us to introduce a criterion of F-optimality of design, a compromise measure which concentrates on the detection of certain specified effects while allowing at least the inspection of a wider class of effects. to give added validity to this notion we first establish its equivalence to a min–max weighted variance design criterion. The actual construction of F-optimal designs is our main purpose. The direct min–max approach is difficult, and so our next main result directs attention to the equivalent problem of finding optimal strategies for a certain two-person zero-sum non-matrix game. Finally, we provide a computational scheme for the solution of this game and illustrate the technique by examples.