Game theory has been an undoubted success in recent years with several Nobel prizes and dedicated journals reflecting its acclaim and widespread recognition in academic circles. This success has been built on theorising about the ways in which choices and competitive interactions are formulated. Game theorists frequently choose to place a reliance on neoclassical economic concepts of hyper-rationality, perfect information and static equilibria as predicates to general solutions. Concepts which are often implausible in reality and in many cases run counter to both intuition and empirical study. There is little unchallenged evidence for the success of applied game theory. There are many reasons for this lack of success, with the focus revolving around the reliance on redundant neoclassical economic assumptions, the overly abstract nature of much of the literature and the unnecessary use of complex and esoteric mathematical constructs. Methods of addressing the perceived weaknesses of applied game theory have been examined in this work. In particular, various alternative simulation techniques with a practical or applied focus have been investigated; agent based modelling, discrete event and continuous simulation modelling. From this range, the continuous simulation modelling technique system dynamics was chosen as a means of extending game theory into the domain of applied science. The neoclassical assumptions which are at the root of the current failure of applied game theory were investigated in detail. It is concluded that hyper-rationality couldonly be applied as a general assumption when considering entities of low, or no, intellectual sophistication and its applicability generally reduced with increasing intellectual sophistication. A series of models are developed, using the system dynamics paradigm, with the objective of addressing the perceived failings of both the underpinning neoclassical assumptions and impractical implementation of game theory. It is demonstrated and concluded that there are benefits to both game theory and system dynamics from collaboration. System dynamics adds a practical edge to esoteric game theory and game theory can add a significant theoretical insight to system dynamics

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This study aimed to resolve disparities between the human behaviour predicted by game theoretic models and the behaviours observed in the real world. The existing model of graphical games was analysed and expanded to create a new model in which agents can move themselves around the graph over time. By adopting different configurations of variables, this model can simulate a very wide range of different scenarios. The concept of meta-games was applied to expand this range yet further and introduce more real-world applications. The interactions between different elements of the configuration were investigated to develop an understanding of the model's emergent properties. The study found that this new model is more accurate and more widely applicable than all other pre-existing candidate models. This suggests that human irrationality can generally be accounted for with a better understanding of the environment within which interaction is occurring.

Game semantics extends the Curry-Howard isomorphism to a three-way correspondence: proofs, programs, strategies. But the universe of strategies goes beyond intuitionistic logics and lambda calculus, to capture stateful programs. In this thesis we describe a logical counterpart to this extension, in which proofs denote such strategies. The system is expressive: it contains all of the connectives of Intuitionistic Linear Logic, and first-order quantification. Use of a novel sequoid operator allows proofs with imperative behaviour to be expressed. Thus, we can embed first-order Intuitionistic Linear Logic into this system, Polarized Linear Logic, and an expressive imperative total programming language. We can use the first-order structure to express properties on the imperative programs. The proof system has a tight connection with a simple game model, where games are forests of plays. Formulas are modelled as games, and proofs as history-sensitive winning strategies. We provide a strong full and faithful completeness result with respect to this model: each finitary strategy is the denotation of a unique analytic (cut-free) proof. Infinite strategies correspond to analytic proofs that are infinitely deep. Thus, we can normalise proofs, via the semantics. The proof system makes novel use of the fact that the sequoid operator allows the exponential modality of linear logic to be expressed as a final coalgebra.

Bilateral exchange networks are structures in which a finite set of players have a restricted framework of bargaining opportunities with each other. The key restrictions are that each player may participate in only one 'exchange' and each of these may only involve a pair of players. There is a large sociology literature which investigates these networks as a simplified model of social exchange. This literature contains many predictions and experimental results, but not a non-cooperative game theoretic analysis. The aim of the thesis is to provide this. The analysis builds on the economic theory literature on non-cooperative bar gaining, principally the alternating offers and Nash demand games. Two novel perfect information models based on the alternating offers game are considered and it is demonstrated that they suffer from several difficulties. In particular, analysis of an example network shows that for these two models multiple subgame perfect equilibria exist with considerable qualitative differences. It is argued that an alternating offers approach to the problem is therefore unlikely to be successful for general networks. Models based on Nash demand games also have multiple solutions, but their simpler structure allows investigation of equilibrium selection by evolutionary methods. An agent based evolutionary model is proposed. The results of computer simulations based on this model under a variety of learning rules are presented. For small networks the agents often converge to unique long-term outcomes which offer support both for theoretical predictions of 2 and 3 player alternating offers models and experimental results of the sociology literature. For larger networks the results become less precise and it is shown they sometimes leave the core. It is argued that a modified evolutionary model has scope for avoiding these difficulties and providing a constructive approach to the problem for large networks.

In sequential decision problems in unknown environments, decision makers often face dilemmas over whether to explore to discover more about the environment, or to exploit current knowledge. In this thesis, we address this exploration/exploitation dilemma in a general setting encompassing both standard and contextualised bandit problems, and also multi-agent (game-theoretic) problems. We consider an approach of Thompson (1933) which makes use of samples from the posterior distributions for the instantaneous value of each action. Our initial focus is on problems with a single decision maker acting. We extend the approach of Thompson (1933) by introducing a new algorithm, Optimistic Bayesian Sampling (OBS), in which the probability of playing an action increases with the uncertainty in the estimate of the action value. This results in better directed exploratory behaviour. We prove that, under unrestrictive assumptions, both approaches result in optimal behaviour with respect to the average reward criterion of Yang and Zhu(2002) . The problem has recently resurfaced in the context of contextual bandits for maximising revenue in sponsored web search advertising. We implement OBS and test its performance in several simulated domains. We find that it performs consistently better than numerous competitor methods. Our second focus is that of extending the method of Thompson (1933) to problems with more than one decision maker acting, and individual rewards depending on actions of others. Each agent must predict the actions of others to maximise reward. We consider combining Thompson sampling with fictitious play and establish conditions under which agents strategies converge to best responses to the empirical frequencies of opponent play, and also under which the belief process is a generalised weakened fictitious play process of Leslie and Collins (2006). Fictitious play is a deterministic algorithm, and so is not entirely consistent with the philosophy of Thompson sampling. We consider combining Thompson sampling with a randomised version of fictitious play that guarantees players play best responses to the empirical frequencies of opponent play. We also consider how the LTS and OBS algorithms can be extended to team games, where all agents receive the same reward. We suggest a novel method of achieving 'perfect coordination', in the sense that the multi-agent problem is effectively reduced to a single-agent problem.

This thesis explores two kinds of foundational issues in game theory. The first is concerned with the interpretation of the basic structure of a game, especially the definitions of outcomes and payoffs. This discussion leads to the second issue; namely the nature of solution concepts and their relation to both explicit and implicit assumptions in game theory concerning hypothetical reasoning. Interpreting utility functions in game theory, I argue that the notion of revealed preferences is ill-suited for counterfactual reasoning and for taking account of the implicit normativity of instrumental rationality. An alternative interpretation is outlined that treats preferences as determinants of choice. Accordingly, outcomes have to be individuated so as to capture everything that matters to an agent. I consider whether this is problematic when properties of outcomes depend on choice processes themselves. Turning to a decision theoretic problem, I question Verbeek's (2001) claim that modal outcome individuation conflicts with axioms of consequentialism. Next, I critically assess Rabin's (1993) model of fairness equilibria. Hypothesising about unilateral deviation is shown to be incompatible with belief-dependent utility definitions. Counterfactuals in games are then analysed more generally. It proves to be crucial for solution concepts whether our formal framework allows us to differentiate between indicative and subjunctive conditionals. Stalnaker's (1996) prima facie counterexample to Aumann's (1995) theorem that common knowledge of rationality implies a subgame perfect equilibrium is questioned on the grounds of a plausibility criterion. Again drawing on what has been established about the structure of a game and the meaning of its elements, Gauthier's (1986) notion of constrained maximisation, an attempt to overcome the non-cooperative equilibrium of the finitely iterated prisoner's dilemma, is shown to be incompatible with orthodox game theoretical methodology. The approach of treating the unit of agency as endogenous is addressed.

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Recent advances in automating Dialogue Management have been mainly made in cooperative environments -where the dialogue system tries to help a human to meet their goals. In non-cooperative environments though, such as competitive trading, there is still much work to be done. The complexity of such an environment rises as there is usually imperfect information about the interlocutors’ goals and states. The thesis shows that non-cooperative dialogue agents are capable of learning how to successfully negotiate in a variety of trading-game settings, using Reinforcement Learning, and results are presented from testing the trained dialogue policies with humans. The agents learned when and how to manipulate using dialogue, how to judge the decisions of their rivals, how much information they should expose, as well as how to effectively map the adversarial needs in order to predict and exploit their actions. Initially the environment was a two-player trading game (“Taikun”). The agent learned how to use explicit linguistic manipulation, even with risks of exposure (detection) where severe penalties apply. A more complex opponent model for adversaries was also implemented, where we modelled all trading dialogue moves as implicitly manipulating the adversary’s opponent model, and we worked in a more complex game (“Catan”). In that multi-agent environment we show that agents can learn to be legitimately persuasive or deceitful. Agents which learned how to manipulate opponents using dialogue are more successful than ones which do not manipulate. We also demonstrate that trading dialogues are more successful when the learning agent builds an estimate of the adversarial hidden goals and preferences. Furthermore the thesis shows that policies trained in bilateral negotiations can be very effective in multilateral ones (i.e. the 4-player version of Catan). The findings suggest that it is possible to train non-cooperative dialogue agents which successfully trade using linguistic manipulation. Such non-cooperative agents may have important future applications, such as on automated debating, police investigation, games, and education.