Computable Analysis and Game Theory: From Foundations to Applications

This body of research showcases several facets of the intersection between computer science and game theory. On the foundational side, we explore the obstructions to the computability of Nash equilibria in the setting of computable analysis. In particular, we study the Weihrauch degree of the problem of finding a Nash equilibrium for a multiplayer game in normal form. We conclude that the Weihrauch degree Nash for multiplayer games lies between AoUC∗[0,1] and AoUC⋄[0,1] (Theorem 5.3). As a slight detour, we also explore the demarcation between computable and non-computable computational problems pertaining to the verification of machine learning. We demonstrate that many verification questions are computable without the need to specify a machine learning framework (Section 7.2). As well as looking into the theory of learners, robustness and sparisty of training data. On the application side, we study the use of Hypergames in Cybersecurity. We look into cybersecurity AND/OR attack graphs and how we could turn them into a hypergame (8.1). Hyper Nash equilibria is not an ideal solution for these games, however, we propose a regret-minimisation based solution concept. In Section 8.2, we survey the area of Hypergames and their connection to cybersecurity, showing that even if there is a small overlap, the reach is limited. We suggest new research directions such as adaptive games, generalisation and transferability (Section 8.3)

A Temporal Framework for Hypergame Analysis of Cyber Physical Systems in Contested Environments

Game theory is used to model conflicts between one or more players over resources. It offers players a way to reason, allowing rationale for selecting strategies that avoid the worst outcome. Game theory lacks the ability to incorporate advantages one player may have over another player. A meta-game, known as a hypergame, occurs when one player does not know or fully understand all the strategies of a game. Hypergame theory builds upon the utility of game theory by allowing a player to outmaneuver an opponent, thus obtaining a more preferred outcome with higher utility. Recent work in hypergame theory has focused on normal form static games that lack the ability to encode several realistic strategies. One example of this is when a player’s available actions in the future is dependent on his selection in the past. This work presents a temporal framework for hypergame models. This framework is the first application of temporal logic to hypergames and provides a more flexible modeling for domain experts. With this new framework for hypergames, the concepts of trust, distrust, mistrust, and deception are formalized. While past literature references deception in hypergame research, this work is the first to formalize the definition for hypergames. As a demonstration of the new temporal framework for hypergames, it is applied to classical game theoretical examples, as well as a complex supervisory control and data acquisition (SCADA) network temporal hypergame. The SCADA network is an example includes actions that have a temporal dependency, where a choice in the first round affects what decisions can be made in the later round of the game. The demonstration results show that the framework is a realistic and flexible modeling method for a variety of applications

Deception in Game Theory: A Survey and Multiobjective Model

Game theory is the study of mathematical models of conflict. It provides tools for analyzing dynamic interactions between multiple agents and (in some cases) across multiple interactions. This thesis contains two scholarly articles. The first article is a survey of game-theoretic models of deception. The survey describes the ways researchers use game theory to measure the practicality of deception, model the mechanisms for performing deception, analyze the outcomes of deception, and respond to, or mitigate the effects of deception. The survey highlights several gaps in the literature. One important gap concerns the benefit-cost-risk trade-off made during deception planning. To address this research gap, the second article introduces a novel approach for modeling these trade-offs. The approach uses a game theoretic model of deception to define a new multiobjective optimization problem called the deception design problem (DDP). Solutions to the DDP provide courses of deceptive action that are efficient in terms of their benefit, cost, and risk to the deceiver. A case study based on the output of an air-to-air combat simulator demonstrates the DDP in a 7 x 7 normal form game. This approach is the first to evaluate benefit, cost, and risk in a single game theoretic model of deception

Opportunistic Synthesis in Reactive Games under Information Asymmetry

Reactive synthesis is a class of methods to construct a provably-correct control system, referred to as a robot, with respect to a temporal logic specification in the presence of a dynamic and uncontrollable environment. This is achieved by modeling the interaction between the robot and its environment as a two-player zero-sum game. However, existing reactive synthesis methods assume both players to have complete information, which is not the case in many strategic interactions. In this paper, we use a variant of hypergames to model the interaction between the robot and its environment; which has incomplete information about the specification of the robot. This model allows us to identify a subset of game states from where the robot can leverage the asymmetrical information to achieve a better outcome, which is not possible if both players have symmetrical and complete information. We then introduce a novel method of opportunistic synthesis by defining a Markov Decision Process (MDP) using the hypergame under temporal logic specifications. When the environment plays some stochastic strategy in its perceived sure-winning and sure-losing regions of the game, we show that by following the opportunistic strategy, the robot is ensured to only improve the outcome of the game - measured by satisfaction of sub-specifications - whenever an opportunity becomes available. We demonstrate the correctness and optimality of this method using a robot motion planning example in the presence of an adversary.Comment: Submitted to Conference on Decision and Control 201