Best neighbor strategy to enforce cooperation among selfish nodes in wireless ad hoc network

Trust among nodes in a self-organizing network such as a mobile ad hoc network presents a number of problems and paradoxes. One of the challenging characteristics of wireless and mobile ad hoc networks consists in exploring ways to cope up with selfish behavior of neighbors towards network functions such as routing and forwarding. This paper attempts to deal with such mechanisms and as a result it introduces a distinct model to study the behavior of selfish neighbors using strategic, non-cooperative game theory. Many research works have used Tit-For-Tat strategy for analysis when they deploy game theory to stimulate cooperation. A compliant and an adaptable strategy called Best Neighbor Strategy [BNS] is proposed in this paper for the packet forwarding game in a wireless ad hoc environment. The behavior of nodes is probed varying the proportion of selfishness and also the size of the population while forwarding the packets. The investigations have brought out that the proposed cooperation enforcement policy is scalable, is able to converge faster and is robust against selfishness. BNS achieves evolutionary stability even under the invasion of selfish strategy at different proportions. Further, BNS proves to be a pure evolutionary stable strategy as it evolves to dominate the population from whatever the initial frequency it starts with and it totally out-competes the malign behavior shown by selfish strategy, which means that BNS is immune to invaders. The observations and analysis have shown that the ad hoc paradigm can be modeled significantly using an approach, which has been developed for game theory.     

The role of physical representations in solving number problems: A comparison of young children’s use of physical and virtual materials

This research aims to explore the role of physical representations in young children’s numerical learning then identify the benefits of using a graphical interface in order to understand the potential for developing interactive technologies in this domain. Three studies are reported that examined the effect of using physical representations (blocks) on children’s (aged 4–8 years) strategies in a numerical partitioning task. The first study describes the role of certain perceptual and manipulative properties of the physical materials, comparing performance with paper and no materials conditions. The study demonstrated an advantage for physical materials and identified a key property reflecting strategies: whether blocks were moved individually or as a group. This finding was investigated in the second study by comparing strategies when children were asked to constrain movements to one block at a time. Significant differences were found in strategies used although differences were reduced by children moving individual blocks quickly in succession using both hands. The final study examined the effect of constraining manipulation using a graphical user interface, where on screen squares could only be moved individually. As predicted, significant differences were found for strategies used between physical and virtual conditions. The findings suggest that differences in the manipulative properties of interfaces may affect children’s numerical strategies and are discussed with respect to the design of effective interactive technologies in this domain.