Evolutionary games on graphs

Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of the field for physicists. The first three sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fourth section surveys the topological complications implied by non-mean-field-type social network structures in general. The last three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner's Dilemma, the Rock-Scissors-Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.Comment: Review, final version, 133 pages, 65 figure

Reputation and professional services: Survival, teams and incentives.

Following the opening chapter, which surveys existing literature on the issue of the interaction between individual and group reputation, the remaining chapters each address a simple question to better understand how reputation affects outcomes and incentives. Specifically: Even though good and bad luck might affect short term reputations, do agents end up with the reputations that they deserve, that is one that reflects their genuine underlying ability. The central result of Chapter 2 is that, if the agent knows her own ability (though customers can only make inferences by observing history) then eventually the truth will out. How can an agent, who has proven her ability, commit to working hard. Once an agent has established a reputation then it is a tautology to say that she has no reputational concern. However, if effort is efficient she may want to commit to exerting effort and get adequately rewarded. Chapter 3 shows that one way that she may be able to do this is by hiring and working with a junior agent of uncertain ability. Do teams care any more or less about their reputations than individuals. Joint work with Juanjo Ganuza and introduced in Chapter 4 suggests that an important aspect in answering this question would be to determine whether an agent or team's reputational concerns are primarily about a concern to show itself to be excellent and capable in every task, or about a concern to avoid customers thinking that it is inept. How does industry structure affect a firm's ability to commit to producing high quality. The final chapter discusses this question and suggests that a number of different effects are in play so that there is no simple answer

Deploying Affect-Inspired Mechanisms to Enhance Agent Decision-Making and Communication

Computer agents are required to make appropriate decisions quickly and efficiently. As the environments in which they act become increasingly complex, efficient decision-making becomes significantly more challenging. This thesis examines the positive ways in which human emotions influence people’s ability to make good decisions in complex, uncertain contexts, and develops computational analogues of these beneficial functions, demonstrating their usefulness in agent decision-making and communication. For decision-making by a single agent in large-scale environments with stochasticity and high uncertainty, the thesis presents GRUE (Goal Re-prioritization Using Emotion), a decision-making technique that deploys emotion-inspired computational operators to dynamically re-prioritize the agent’s goals. In two complex domains, GRUE is shown to result in improved agent performance over many existing techniques. Agents working in groups benefit from communicating and sharing information that would otherwise be unobservable. The thesis defines an affective signaling mechanism, inspired by the beneficial communicative functions of human emotion, that increases coordination. In two studies, agents using the mechanism are shown to make faster and more accurate inferences than agents that do not signal, resulting in improved performance. Moreover, affective signals confer performance increases equivalent to those achieved by broadcasting agents’ entire private state information. Emotions are also useful signals in agents’ interactions with people, influencing people’s perceptions of them. A computer-human negotiation study is presented, in which virtual agents expressed emotion. Agents whose emotion expressions matched their negotiation strategy were perceived as more trustworthy, and they were more likely to be selected for future interactions. In addition, to address similar limitations in strategic environments, this thesis uses the theory of reasoning patters in complex game-theoretic settings. An algorithm is presented that speeds up equilibrium computation in certain classes of games. For Bayesian games, with and without a common prior, the thesis also discusses a novel graphical formalism that allows agents’ possibly inconsistent beliefs to be succinctly represented, and for reasoning patterns to be defined in such games. Finally, the thesis presents a technique for generating advice from a game’s reasoning patterns for human decision-makers, and demonstrates empirically that such advice helps people make better decisions in a complex game.Engineering and Applied Science

Stabilising liberal societies in a world of radical innovation: committed actors, adaptive rules, and the origins of social order

Long-standing questions about social order, and about liberal democratic capitalist orders in particular, remain unsettled. They are of renewed importance in our age of crisis and democratic backsliding. Adam Smith addressed two such questions at the founding of political economy: First, what are the forces that sustain all societies, and liberal societies in particular? Second, what combination of market and state makes such societies prosperous and powerful? A third question, addressed by Hayek, Polanyi, and Keynes in their own period of crisis and backsliding, pertains to interactions between the two: how does the combination of market and state affect the stability of liberal democracy? If we are to answer these questions, I argue we need a realistic theory of innovation. Real-world innovation is Schumpeterian: it is uncertain and often radical, so the future may unexpectedly break with the past. Real-world innovation is Baumolian: it is socially ambiguous, and may be productive or extractive. Consequently, the innovations of political and economic entrepreneurs bring the rise, but also the fall, of societies. Given the last two decades, we may be more open to the idea that Fukuyama’s “End of History” never arrives. Our task is to stabilise and optimise cooperation in both politics and the market. “Cooperation” is defined as the alignment of private returns with social returns; it is exemplified by Smith’s “invisible hand”, and is the precondition for growth. The usual formal methods for identifying cooperative equilibria fail in a world of Schumpeterian and Baumolian innovation. Beyond the short-run, there are no lasting Nash equilibria. Game forms are destroyed and remade. The institutional forces that we hope will restore cooperative equilibria are themselves subject to innovative attack. How, in this unstable world, is it possible to sustain cooperation over long periods of time? And how can we model and predict cooperation? This thesis adopts an analytic strategy that makes this problem tractable. I borrow concepts and formal models from evolutionary sociobiology, a field that deals with cooperation under radical and ambiguous innovation. As in Acemoglu and Robinson’s Narrow Corridor, the core concept is the adversarial innovation race (the “Red Queen’s race”). Most important in this thesis is the race between 4 innovating cooperators and defectors. Social order becomes the probabilistic outcome of a dynamic process—of whether cooperator or defector innovations are superior in a given period. Under the right circumstances, outcomes are predictable. All complex social orders, anthropic and biological, combine “commitment” and “rules” (which, in the definitions of this thesis, includes institutions) into a self-sustaining system. Commitments are essential. They are motives that are exogenous to the innovation race; while all else changes, they continue to draw the system towards a cooperative equilibrium. They come in two forms: one is an intrinsic interest in others’ payoffs, and one is an extrinsic dependence on others’ payoffs. However, commitments are impotent, and indeed are destroyed, if there are no rules or institutions that can control defectors—or if committed actors fail to invest sufficiently in adapting rules so that they keep up in the race against defectors. In short, social order depends on (A) commitments (i.e. motives to run the race that are innovation-proof) that (B) are channelled into the adaptation of rules, to run the race against defectors. Accordingly, the outcomes of innovation races are predictable under two circumstances: when (A) there is no source of commitment to group payoffs, or (B) when committed actors perversely disinvest from running the race, so play the “sleeping Hare” of Aesop’s fable. In either case, loss of the race and collapse of cooperation is guaranteed. On the first question raised by Smith, I present an impossibility theorem for any society built from rules—from institutions, incentives, and so on—alone. Both liberal and authoritarian orders rest on commitment. Smith’s Theory of Moral Sentiments is supported: the “very existence” of liberal orders rests on other-regarding preferences (which, I show, is a product of trust). It is the only innovation-proof force available to them. Authoritarian orders can be explained via the ruler’s extrinsic commitments alone, though other-regarding preferences sometimes play an important role. On the second question, every regime of economic regulation is within the innovation race and vulnerable to unanticipated counter-innovations. I show that every regulatory regime can be described as a particular “division of regulatory labour” between institutional actors and market actors. Institutional actors and market actors are essential complements, with distinct comparative advantages. A 5 principal task for the institutional regulator is to structurally simplify complex markets; otherwise, those defectors that have advantages in the innovation race (of which there are many) will predictably exploit both regulator and market actor. Central planners and Hayekian liberals (and libertarians) endorse extreme divisions of labour between regulator and market actor. They are mirror images and fail in predictable ways. Central planners refuse to use market actors, so allocate hyper-complex (and impossible) regulatory tasks to the state. This produces broad inefficiencies and blocks productive innovation. Hayekian liberals refuse to adapt institutions, so allocate hyper-complex (and impossible) tasks to market actors. This produces crises specifically in complex markets—finance, healthcare, insurance, education, and so on—and soaring rents. Its end point is anarchy. Hayekian liberals suppose advance knowledge of the consequences of basic market institutions. But the unforeseeability of innovation, and distributed nature of knowledge, are double-edged swords: markets produce both productive and extractive innovations that the theorist cannot foresee. To block institutional adaptation is to play the sleeping Hare, and guarantees loss of the innovation race. On the third question, central planning and Hayek’s classical liberalism ultimately lead to authoritarianism. In the case of central planning, Hayek’s argument is supported: to attempt the impossible tasks allocated to it, the state must concentrate power, and voters cannot win the political innovation race to control such a state. In the case of Hayekian liberalism, the state cannot run the market innovation race. Market anarchy and crisis erode the commitments on which liberal orders depend, fuelling distrust and parochiality. As Smith observes, “faction” and “fanaticism” are the greatest threats to the liberal order. To use Hayek’s terms, central planning and his own classical liberalism are “fatal conceits”: they suppose access to distributed and future knowledge that no one possesses. They are both “roads to serfdom”: one via excessive control, the other via anarchy. I describe the “middle of the road”, where commitments are channelled into the adaptive, mixed economic strategy advocated by Keynes. As after the Great Depression, this in turn can create economic outcomes that sustain other-regarding commitments. There, the liberal order can make its home

Models of Political Economy

Models of Political Economy will introduce students to the basic methodology of political economics. It covers all core theories as well as new developments including: decision theory game theory mechanism design games of asymmetric information. Hannu Nurmi's text will prove to be invaluable to all students who wish to understand this increasingly technical field

Investigation of Game-Theoretic Mechanisms for the Valuation of Energy Resources

Electricity systems are facing the pressure to change in response to the effects of new technology, particularly the proliferation of renewable technologies (such as solar PV systems and wind generation) leading to the retirement of traditional generation technologies that provide stabilising inertia. These changes create an imperative to consider potential future market structures to facilitate the participation of distributed energy resources (DERs; such as EVs and batteries) in grid operation. However, this gives rise to general questions surrounding the ethics of market structures and how they could be fairly applied in future electricity systems. Particularly the most basic question "how should electricity be valued and traded" is fundamentally a moral question without any easy answer. We give a survey of philosophical attitudes around such a question, before presenting a series of ways that these intuitions have been cast into mathematics, including: the Vickrey-Clarke-Groves mechanism, Locational Marginal Pricing, the Shapley Value, and Nash bargaining solution concepts. We compared these different methods, and attempted a new synthesis that brought together the best features of each of them; called the 'Generalised Neyman and Kohlberg Value' or the GNK-value for short. The GNK value was developed as a novel bargaining solution concept for many player non-cooperative transferable utility generalised games, and thus it was intrinsically flexible in its application to various aspects of powersystems. We demonstrated the features of the GNK-value against the other mathematical solutions in the context of trading the immediate consumption/generation of power on small sized networks under linear-DC approximation, before extending the computation to larger networks. The GNK value proved to be difficult to compute for large networks but was shown to be approximable for larger networks with a series of sampling techniques and a proxy method. The GNK value was ethically compared to other mechanisms with the unfortunate discovery that it allowed for participants to be left worse-off for participating, violating the ethical notion of 'euvoluntary exchange' and 'individual rationality'; but was offered as an interesting innovation in the space of transferable utility generalised games notwithstanding. For sampling the GNK value, there was a range of new and different techniques developed for stratified random sampling which iteratively minimise newly derived concentration inequalities on the error of the sampling. These techniques were developed to assist in the computation of the GNK value to larger networks, and they were evaluated in the context of sampling synthetic data, and in computation of the Shapley Value of cooperative game theory. These new sampling techniques were demonstrated to be comparable to the more orthodox Neyman sampling method despite not having access to stratum variances

A game-theoretic analysis of a market for long-term relationships

In my thesis, I study social interaction of the following form: each agent of an infinite population plays a certain stage game (for example the prisoner’s dilemma) with some opponent in each period. After observing the partners action choice, each player has the option to quit or to maintain the current relationship. If the latter action is chosen by both agents, they will play the game together in the next period, otherwise they return to a “market” for long-term relationships and will be matched randomly with another opponent. The matching process in the market is global and non-assortative: everybody can be matched together with anybody and own behaviour does not affect the probability of being paired up with an agent who plays a certain strategy. Furthermore, there are no information flows between pairs. In the first chapter, “COOPERATIVE EQUILIBRIA IN REPEATED GAMES WITH ENDOGENOUS MATCHING DECISION”, I extend the standard Folk Theorems of Friedman (1971) and Fudenberg and Maskin (1986) to games of this form: I establish a structural difference between models with finitely and infinitely many agents: While with finitely many players any individually rational average payoff can be reached under certain restrictions, this is not possible with infinitely many agents in games of conflicting interests. Nevertheless, it is possible to establish a Folk Theorem for the latter case. Furthermore, I investigate the structure of supporting strategies and prove their optimality for certain stage games. In the second chapter, “IMMITATING COOPERATION AND THE FORMATION OF LONG-TERM RELATIONSHIPS”, I show that the option to maintain or to quit relationships can enforce cooperation in the prisoner's dilemma between boundedly rational agents in a large population if players imitate successful behavior and sometimes choose to experiment. Opposed to the first paper, agents are myopic and do not have the ability to follow history-dependent strategies. However, they have sometimes access to information about what behavior is on average the most successful one. Cooperative behavior in a homogenous population emerges if both the imitation and experimentation rate are sufficiently small. In a heterogeneous population where agents have certain preferences regarding their partner, the same holds without a restriction on the imitation rate. The results resemble Eshel et al. (AER, 1998), but the assumption of local interaction is substituted by the endogenous formation of relationships. Finally, in the third chapter, “ON THE DYNAMICS IN THE MARKET FOR LONG-TERM RELATIONSIPS” (a joint work with Alexander Gaigl), we consider agents who understand the trade-off in the game above, but have no knowledge about the aggregate play of individuals in the market. Agents learn their current opponent's strategy in finitely many periods. Their subjective believe about the aggregate play in the market is based on past experiences. In a first step, we assume that there are infinitely many agents in the population and impose structure on strategies and updating rules. Analytically, and by simulating the model, we derive conditions under which a significant degree of cooperation can be expected. Then, we extend the model to finite populations and show that the dynamics are similar to the infinite case if there are sufficiently many agents. It strikes that the repeated play of strategies which would not support an equilibrium in the same framework with common knowledge, is a stable outcome in many cases