An evolutionary algorithmic approach to determine the Nash equilibrium in a duopoly with nonlinearities and constraints

This paper presents an algorithmic approach to obtain the Nash Equilibrium in a duopoly. Analytical solutions to duopolistic competition draw on principles of game theory and require simplifying assumptions such as symmetrical payoff functions, linear demand and linear cost. Such assumptions can reduce the practical use of duopolistic models. In contrast, we use an evolutionary algorithmic approach (EAA) to determine the Nash equilibrium values. This approach has the advantage that it can deal with and find optimum values for duopolistic competition modelled using non-linear functions. In the paper we gradually build up the competitive situation by considering non-linear demand functions, non-linear cost functions, production and environmental constraints, and production in discrete bands. We employ particle swarm optimization with composite particles (PSOCP), a variant of particle swarm optimization, as the evolutionary algorithm. Through the paper we explicitly demonstrate how EAA can solve games with constrained payoff functions that cannot be dealt with by traditional analytical methods. We solve several benchmark problems from the literature and compare the results obtained from EAA with those obtained analytically, demonstrating the resilience and rigor of our EAA solution approach

Real-time optimization of working memory in autonomous reasoning for high-level control of cognitive robots deployed in dynamic environments

High-level, real-time mission control of autonomous and semi-autonomous robots, deployed in remote and dynamic environments, remains a research challenge. Robots operating in these environments require some cognitive ability, provided by a simple, but robust, cognitive architecture. The most important process in a cognitive architecture is the working memory, with core functions being memory representation, memory recall, action selection and action execution, performed by the central executive. The cognitive reasoning process uses a memory representation, based on state flows, governed by state transitions with simple, quantified propositional transition formulae. In this thesis, real-time working memory quantification and optimization is performed using a novel adaptive entropy-based fitness quantification (AEFQ) algorithm and particle swarm optimization (PSO), respectively. A cognitive architecture, using an improved set-based PSO is developed for real-time, high-level control of single-task robots and a novel coalitional games-theoretic PSO (CG-PSO) algorithm extends the cognitive architecture for real-time, high-level control in multi-task robots. The performance of the cognitive architecture is evaluated by simulation, where a UAV executesfour use cases: Firstly, for real-time high-level, single-task control: 1) relocating the UAV to a charging station and 2) collecting and delivering medical equipment. Performance is measured by inspecting the success and completeness of the mission and the accuracy of autonomous flight control. Secondly, for real-time high-level control of multi-task autonomous vehicle control: 3) delivering medical equipment to an incident and 4) provide aerial security surveillance support. The performance of the architecture is measured in terms of completeness and cognitive processing time and cue processing time. The results show that coalitions correctly represent optimal memory and action selection in real-time, while overall processing time is within a feasible time limit, arbitrarily set to 2 seconds in this study