Metagame Autobalancing for Competitive Multiplayer Games

Automated game balancing has often focused on single-agent scenarios. In this paper we present a tool for balancing multi-player games during game design. Our approach requires a designer to construct an intuitive graphical representation of their meta-game target, representing the relative scores that high-level strategies (or decks, or character types) should experience. This permits more sophisticated balance targets to be defined beyond a simple requirement of equal win chances. We then find a parameterization of the game that meets this target using simulation-based optimization to minimize the distance to the target graph. We show the capabilities of this tool on examples inheriting from Rock-Paper-Scissors, and on a more complex asymmetric fighting game

Inside the Decentralised Casino : A Longitudinal Study of Actual Cryptocurrency Gambling Transactions

Decentralised gambling applications are a new way for people to gamble online. Decentralised gambling applications are distinguished from traditional online casinos in that players use cryptocurrency as a stake. Also, rather than being stored on a single centralised server, decentralised gambling applications are stored on a cryptocurrency's blockchain. Previous work in the player behaviour tracking literature has examined the spending profiles of gamblers on traditional online casinos. However, similar work has not taken place in the decentralised gambling domain. The profile of gamblers on decentralised gambling applications are therefore unknown. This paper explores 2,232,741 transactions from 24,234 unique addresses to three such applications operating atop the Ethereum cryptocurrency network over 583 days. We present spending profiles across these applications, providing the first detailed summary of spending behaviours in this technologically advanced domain. We find that the typical player spends approximately $110 equivalent across a median of 6 bets in a single day, although heavily involved bettors spend approximately$100,000 equivalent over a median of 644 bets across 35 days. Our findings suggest that the average decentralised gambling application player spends less than in other online casinos overall, but that the most heavily involved players in this new domain spend substantially more. This study also demonstrates the use of these applications as a research platform, specifically for large scale longitudinal in-vivo data analysis

Meta-Referential Games to Learn Compositional Learning Behaviours

Human beings use compositionality to generalise from past experiences to novel experiences. We assume a separation of our experiences into fundamental atomic components that can be recombined in novel ways to support our ability to engage with novel experiences. We frame this as the ability to learn to generalise compositionally, and we will refer to behaviours making use of this ability as compositional learning behaviours (CLBs). A central problem to learning CLBs is the resolution of a binding problem (BP). While it is another feat of intelligence that human beings perform with ease, it is not the case for state-of-the-art artificial agents. Thus, in order to build artificial agents able to collaborate with human beings, we propose to develop a novel benchmark to investigate agents' abilities to exhibit CLBs by solving a domain-agnostic version of the BP. We take inspiration from the language emergence and grounding framework of referential games and propose a meta-learning extension of referential games, entitled Meta-Referential Games, and use this framework to build our benchmark, that we name Symbolic Behaviour Benchmark (S2B). We provide baseline results showing that our benchmark is a compelling challenge that we hope will spur the research community towards developing more capable artificial agents.Comment: work in progres

Learning to Select SAT Encodings for Pseudo-Boolean and Linear Integer Constraints

Many constraint satisfaction and optimisation problems can be solved effectively by encoding them as instances of the Boolean Satisfiability problem (SAT). However, even the simplest types of constraints have many encodings in the literature with widely varying performance, and the problem of selecting suitable encodings for a given problem instance is not trivial. We explore the problem of selecting encodings for pseudo-Boolean and linear constraints using a supervised machine learning approach. We show that it is possible to select encodings effectively using a standard set of features for constraint problems; however we obtain better performance with a new set of features specifically designed for the pseudo-Boolean and linear constraints. In fact, we achieve good results when selecting encodings for unseen problem classes. Our results compare favourably to AutoFolio when using the same feature set. We discuss the relative importance of instance features to the task of selecting the best encodings, and compare several variations of the machine learning method.Comment: 24 pages, 10 figures, submitted to Constraints Journal (Springer