On Nash Equilibrium and Evolutionarily Stable States that Are Not Characterised by the Folk Theorem

In evolutionary game theory, evolutionarily stable states are characterised by the folk theorem because exact solutions to the replicator equation are difficult to obtain. It is generally assumed that the folk theorem, which is the fundamental theory for non-cooperative games, defines all Nash equilibria in infinitely repeated games. Here, we prove that Nash equilibria that are not characterised by the folk theorem do exist. By adopting specific reactive strategies, a group of players can be better off by coordinating their actions in repeated games. We call it a type-k equilibrium when a group of k players coordinate their actions and they have no incentive to deviate from their strategies simultaneously. The existence and stability of the type-k equilibrium in general games is discussed. This study shows that the sets of Nash equilibria and evolutionarily stable states have greater cardinality than classic game theory has predicted in many repeated games

Equal Pay for all Prisoners / The Logic of Contrition

This report deals with two questions concerning the emergence of cooperative strategies in repeated games. The first part is concerned with the Perfect Folk Theorem and presents a vast class of equilibrium solutions based on Markovian strategies. Simple strategies, called equalizers, are introduced and discussed: if players adopt such strategies, the same payoff results for every opponent. The second part analyzes strategies implemented by finite automata. Such strategies are relevant in an evolutionary context; an important instance is called Contrite Tit For Tat. In populations of players adopting such strategies, Contrite Tit For Tat survives very well -- at least as long as errors are restricted to mistakes in implementation ("the trembling hand"). However, this cooperative strategy cannot persist if mistakes in perception are included as well

Coevolution of Deception and Preferences: Darwin and Nash Meet Machiavelli

We develop a framework in which individuals preferences co-evolve with their abilities to deceive others regarding their preferences and intentions. We show that a pure outcome is stable, essentially if and only if it is an efficient Nash equilibrium. All individuals have the same deception ability in such a stable state. In contrast, there are non-pure outcomes in which non-Nash outcomes are played, and different deception abilities co-exist. We extend our model to study preferences that depend also on the opponent's type

Modelling religious signalling

The origins of human social cooperation confound simple evolutionary explanation. But from Darwin and Durkheim onwards, theorists (anthropologists and sociologists especially) have posited a potential link with another curious and distinctively human social trait that cries out for explanation: religion. This dissertation explores one contemporary theory of the co-evolution of religion and human social cooperation: the signalling theory of religion, or religious signalling theory (RST). According to the signalling theory, participation in social religion (and its associated rituals and sanctions) acts as an honest signal of one's commitment to a religiously demarcated community and its way of doing things. This signal would allow prosocial individuals to positively assort with one another for mutual advantage, to the exclusion of more exploitative individuals. In effect, the theory offers a way that religion and cooperation might explain one another, but which that stays within an individualist adaptive paradigm. My approach is not to assess the empirical adequacy of the religious signalling explanation or contrast it with other explanations, but rather to deal with the theory in its own terms - isolating and fleshing out its core commitments, explanatory potential, and limitations. The key to this is acknowledging the internal complexities of signalling theory, with respect to the available models of honest signalling and the extent of their fit (or otherwise) with religion as a target system. The method is to take seriously the findings of formal modelling in animal signalling and other disciplines, and to apply these (and methods from the philosophy of biology more generally) to progressively build up a comprehensive picture of the theory, its inherent strengths and weaknesses. The first two chapters outline the dual explanatory problems that cooperation and religion present for evolutionary human science, and surveys contemporary approaches toward explaining them. Chapter three articulates an evolutionary conception of the signalling theory, and chapters four to six make the case for a series of requirements, limitations, and principles of application. Chapters seven and eight argue for the value of formal modelling to further flesh out the theory's commitments and potential and describe some simple simulation results which make progress in this regard. Though the inquiry often problematizes the signalling theory, it also shows that it should not be dismissed outright, and that it makes predictions which are apt for empirical testing

Preferences and Cooperation

Chapter 1: Evolution of reciprocator preferences when agents can pay for information A benchmark result in the evolutionary games literature is that a preference for reciprocity will evolve if preferences are observable (at zero cost), since reciprocators can cooperate with each other rather than with materialists, thereby achieving a fitness advantage. I investigate how a preference for reciprocity evolves if individuals can observe an opponent's preferences only by bearing a fitness cost. My main result applies when observing an opponent's type is cheap, but cooperating only gives a modest fitness advantage or the preference for reciprocity is intense. In this case, a preference for reciprocity cannot evolve from a small starting share in the mix of preferences, even if discovering an opponent's preferences is arbitrarily cheap. This is in sharp contrast to the benchmark result. Chapter 2: A theory of conditional cooperation on networks (with Julien Gagnon) Chapter 2 is a study of reciprocity on social networks. We model a group of connected agents who play a one-shot public good game. Some players are materialists and others are reciprocators. We characterise the maximal Nash equilibrium (ME) of this game for any network and a broad class of reciprocal preferences. At the ME, a novel concept, the q-linked set, fully determines the set of players who contribute. We show that influential players are those connected to players who are sufficiently interconnected, but not too much. Finally, we study the decision of a planner faced with an uncertain type profile who designs the network to maximise expected contributions. The ex ante optimal network comprises isolated cliques of degree k*, with k* decreasing with the incidence of materialists. We discuss an important application of our results: the workplace. Chapter 3: Ideological games Chapter 3 is a theory of ideology. I define a preference type to be a set of first-order preferences over the outcomes of a `game of life', together with a set of (`meta-') preferences over all players' first-order preferences. Players can influence each other's preferences via costly investment: if player A invests and B does not, B's preferences becomes those of A. Players may invest for instrumental reasons (i.e. to achieve better outcomes in the game of life) or `ideological' reasons (i.e. they want their opponents to have the same preferences they do). I characterise `strongly ideological', `weakly ideological' and `pragmatic' types. Weakly ideological types wish to preserve their own type, as do strongly ideological types, who also seek to convert others. A pragmatic player, in contrast, is willing to have her type changed if her new type would prefer the resulting equilibrium of the game of life to the status quo. I show that if two players of different ideological types meet, there is an equilibrium investment profile with lower aggregate welfare than the no-invest profile. If at least one type is strongly ideological, there is a unique such equilibrium. Finally, a `perfectly ideological' type is a strongly ideological type which, if held by all players, results in the best outcome of the game of life as judged by that type. If a perfectly ideological player plays a pragmatic player, aggregate welfare is always greater than in the no-invest profile.I am grateful to have received an Economic and Social Research Council studentshi

Strategy dynamics in groups of prey

Group living is a widespread and ubiquitous phenomenon in the animal kingdom. Animals in groups are subjected to numerous costs and benefits. Of the benefits, increased protection from predators is the most theoretically and experimentally researched. Three ``principal'' effects explain the anti-predation benefits of grouping: collective vigilance, dilution of risk, and the confusion effect. In this thesis, new theoretical models are developed to study the behaviours that emerge from groups of prey. Using a mathematical approach, this research analyses how the principal anti-predation effects interact to influence the behaviours of grouping animals. Through an analytical approach, the first part of this thesis examines the role of anti-predation effects on individuals with discrete behavioural choices. The outcomes of group interactions are classified by exact analytical conditions. Results are provided which show how factors relating to predation risk, such as group size, affect anti-predator behaviours. Another component of this research uses field data to assess the theoretical results that are presented. The relative influence of each anti-predation effect, and how the anti-predation effect interact to influence individual behaviours within groups is assessed. Consideration of how predation risk and other factors of grouping affect behaviours is also analysed. The final section of research considers highly flexible and continuous anti-predator behaviours. This shift in theory is relevant in groups of prey, for example in models of vigilance. Intuitive results are presented, and conditions are provided which determine qualitatively distinct behavioural dynamics when groups are characterised by continuous behaviours. Equivalences to the discrete behaviour analogue case are shown. It is also shown that individuals may choose neither of the discrete behavioural options. Conditions are derived which specify the occurrence of multiple distinct anti-predator behaviours emerging from a group initially composed of one behaviour, and when the reserve process occurs

Institutions and reciprocity in the employment relationship

Homo oeconomicus has dominated mainstream Economics during the last century. One of the main assumptions of this model is that humans maximise their own utility functions. In other words, homo oeconomicus, before taking action, considers the consequences on their own future interests, which are generally assumed to be monetary. This thesis provides experimental results showing that human behaviour often differs from that of homo oeconomicus, particularly in environments where trust and reciprocity are salient concerns. To be precise, this dissertation analyses the employment relationship, focusing particularly on the importance of trust and the role of direct reciprocity in the relationship between managers and workers. Reciprocity is an important contract enforcement device in the presence of incomplete labour contracts. By reciprocity between employer and employee, what is meant is a predisposition, within the institutional context of defined employment tasks, to cooperate with the other party even at personal cost, and a willingness to punish the other party if they violate cooperative norms, even when punishment is costly to the individual. The original contribution of this thesis goes beyond this result and shows the impact of informal employment rules on reciprocity. In particular, it uses experimental methods to identify two distinct governance patterns for employment relationships: the rigid governance structure and the flexible governance structure. The former is characterised by task-centred rules and defines the boundaries of jobs in a much more specific way than the latter, which is characterised by function-centred rules, and gives rise to a more flexible and discretionary model of employment relationships. The most important original experimental result of this thesis is that rigid governance characterised by taskcentred rules and low reciprocity is better suited to one-shot transactions, whereas flexible governance characterised by function-centred rules and a high level of reciprocity is better suited to repeated transactions

Economic Analysis of International Law

The topics covered in this volume range from classics of the on-going discussion on the economic analysis of international law – such as the issue of legitimacy of customary international law – to more recent topics such as internet privacy, private military contractors, the fight against piracy, the International Criminal Court and the highly topical issue of land grabbing

An economic enquiry into the welfare effects of fair-trade

PhDThe copyright of this thesis rests with the author. Quotation from it is permitted, provided that full acknowledgement is made. This thesis may not be reproduced without the prior written consent of the author.Fair-trade is investigated at three levels. Each level relates to a specific group of actors. The first group are the consumers of fair-trade. In this respect fair-trade overlaps with altruism. A model is developed which seeks out parameters by which to judge whether or not a person will engage into this gesture of altruism, and accordingly measures the fair-trade utility of the consumer. On the basis that it is voluntary, fair-trade is deemed to be virtuous in that it either uplifts consumer utility, or else the consumer withdraws their patronage. Information is hypothesised to play a key role in determining the depth of this relationship. The second group are neighbouring producers, that is the non fair-trade producers who compete in the same market. A situation is modelled in which fair-trade is viewed as a switch in demand preference rather than new demand. The model allows an evaluation based on the standard tenets of welfare economics: to inform upon which movements are value-creating, which are merely transfers, the symmetry of those transfers and where Pareto improvements can and cannot be realised. The policymaker is afforded a logical overview, but with the implication that many of the relevant variables may be lie beyond their direct influence. The third group are landless vineyard labours in South Africa who are empirically analysised. We observed the strongest performance of fair-trade with respect to subjective improvement in wellbeing and the sort of participation that could be categorised as empowerment.Arts and Humanities Research Council (AHRC