Mathematical Game Theory

These lecture notes attempt a mathematical treatment of game theory akin to mathematical physics. A game instance is defined as a sequence of states of an underlying system. This viewpoint unifies classical mathematical models for 2-person and, in particular, combinatorial and zero-sum games as well as models for investing and betting. n-person games are studied with emphasis on notions of utilities, potentials and equilibria, which allows to subsume cooperative games as special cases. The represenation of a game theoretic system in a Hilbert space furthermore establishes a link to the mathematical model of quantum mechancis and general interaction systems

From Quantified CTL to QBF

QCTL extends the temporal logic CTL with quantifications over atomic propositions. This extension is known to be very expressive: QCTL allows us to express complex properties over Kripke structures (it is as expressive as MSO). Several semantics exist for the quantifications: here, we work with the structure semantics, where the extra propositions label the Kripke structure (and not its execution tree), and the model-checking problem is known to be PSPACE-complete in this framework. We propose a model-checking algorithm for QCTL based on a reduction to QBF. We consider several reduction strategies, and we compare them with a prototype (based on the SMT-solver Z3) on several examples

Summarizing Strategy Card Game AI Competition

This paper concludes five years of AI competitions based on Legends of Code and Magic (LOCM), a small Collectible Card Game (CCG), designed with the goal of supporting research and algorithm development. The game was used in a number of events, including Community Contests on the CodinGame platform, and Strategy Card Game AI Competition at the IEEE Congress on Evolutionary Computation and IEEE Conference on Games. LOCM has been used in a number of publications related to areas such as game tree search algorithms, neural networks, evaluation functions, and CCG deckbuilding. We present the rules of the game, the history of organized competitions, and a listing of the participant and their approaches, as well as some general advice on organizing AI competitions for the research community. Although the COG 2022 edition was announced to be the last one, the game remains available and can be played using an online leaderboard arena

Full Issue (Volume 4, Issue 1)

The full contents of PURE Insights, Volume 4, Issue 1

Coevolutionary algorithms for the optimization of strategies for red teaming applications

Red teaming (RT) is a process that assists an organization in finding vulnerabilities in a system whereby the organization itself takes on the role of an “attacker” to test the system. It is used in various domains including military operations. Traditionally, it is a manual process with some obvious weaknesses: it is expensive, time-consuming, and limited from the perspective of humans “thinking inside the box”. Automated RT is an approach that has the potential to overcome these weaknesses. In this approach both the red team (enemy forces) and blue team (friendly forces) are modelled as intelligent agents in a multi-agent system and the idea is to run many computer simulations, pitting the plan of the red team against the plan of blue team. This research project investigated techniques that can support automated red teaming by conducting a systematic study involving a genetic algorithm (GA), a basic coevolutionary algorithm and three variants of the coevolutionary algorithm. An initial pilot study involving the GA showed some limitations, as GAs only support the optimization of a single population at a time against a fixed strategy. However, in red teaming it is not sufficient to consider just one, or even a few, opponent‟s strategies as, in reality, each team needs to adjust their strategy to account for different strategies that competing teams may utilize at different points. Coevolutionary algorithms (CEAs) were identified as suitable algorithms which were capable of optimizing two teams simultaneously for red teaming. The subsequent investigation of CEAs examined their performance in addressing the characteristics of red teaming problems, such as intransitivity relationships and multimodality, before employing them to optimize two red teaming scenarios. A number of measures were used to evaluate the performance of CEAs and in terms of multimodality, this study introduced a novel n-peak problem and a new performance measure based on the Circular Earth Movers‟ Distance. Results from the investigations involving an intransitive number problem, multimodal problem and two red teaming scenarios showed that in terms of the performance measures used, there is not a single algorithm that consistently outperforms the others across the four test problems. Applications of CEAs on the red teaming scenarios showed that all four variants produced interesting evolved strategies at the end of the optimization process, as well as providing evidence of the potential of CEAs in their future application in red teaming. The developed techniques can potentially be used for red teaming in military operations or analysis for protection of critical infrastructure. The benefits include the modelling of more realistic interactions between the teams, the ability to anticipate and to counteract potentially new types of attacks as well as providing a cost effective solution

M2ICAL: A technique for analyzing imperfect comparison algorithms using Markov chains

Ph.DDOCTOR OF PHILOSOPH