Navigating the Topology of 2x2 Games: An Introductory Note on Payoff Families, Normalization, and Natural Order

The Robinson-Goforth topology of swaps in adjoining payoffs elegantly arranges 2x2 ordinal games in accordance with important properties including symmetry, number of dominant strategies and Nash Equilibria, and alignment of interests. Adding payoff families based on Nash Equilibria illustrates an additional aspect of this order and aids visualization of the topology. Making ties through half-swaps not only creates simpler games within the topology, but, in reverse, breaking ties shows the evolution of preferences, yielding a natural ordering for the topology of 2x2 games with ties. An ordinal game not only represents an equivalence class of games with real values, but also a discrete equivalent of the normalized version of those games. The topology provides coordinates which could be used to identify related games in a semantic web ontology and facilitate comparative analysis of agent-based simulations and other research in game theory, as well as charting relationships and potential moves between games as a tool for institutional analysis and design.Comment: 8 pages including 4 figures in text and 4 plate

Chris Cannings: A Life in Games

Chris Cannings was one of the pioneers of evolutionary game theory. His early work was inspired by the formulations of John Maynard Smith, Geoff Parker and Geoff Price; Chris recognized the need for a strong mathematical foundation both to validate stated results and to give a basis for extensions of the models. He was responsible for fundamental results on matrix games, as well as much of the theory of the important war of attrition game, patterns of evolutionarily stable strategies, multiplayer games and games on networks. In this paper we describe his work, key insights and their influence on research by others in this increasingly important field. Chris made substantial contributions to other areas such as population genetics and segregation analysis, but it was to games that he always returned. This review is written by three of his students from different stages of his career

Global adaptation in networks of selfish components: emergent associative memory at the system scale

In some circumstances complex adaptive systems composed of numerous self-interested agents can self-organise into structures that enhance global adaptation, efficiency or function. However, the general conditions for such an outcome are poorly understood and present a fundamental open question for domains as varied as ecology, sociology, economics, organismic biology and technological infrastructure design. In contrast, sufficient conditions for artificial neural networks to form structures that perform collective computational processes such as associative memory/recall, classification, generalisation and optimisation, are well-understood. Such global functions within a single agent or organism are not wholly surprising since the mechanisms (e.g. Hebbian learning) that create these neural organisations may be selected for this purpose, but agents in a multi-agent system have no obvious reason to adhere to such a structuring protocol or produce such global behaviours when acting from individual self-interest. However, Hebbian learning is actually a very simple and fully-distributed habituation or positive feedback principle. Here we show that when self-interested agents can modify how they are affected by other agents (e.g. when they can influence which other agents they interact with) then, in adapting these inter-agent relationships to maximise their own utility, they will necessarily alter them in a manner homologous with Hebbian learning. Multi-agent systems with adaptable relationships will thereby exhibit the same system-level behaviours as neural networks under Hebbian learning. For example, improved global efficiency in multi-agent systems can be explained by the inherent ability of associative memory to generalise by idealising stored patterns and/or creating new combinations of sub-patterns. Thus distributed multi-agent systems can spontaneously exhibit adaptive global behaviours in the same sense, and by the same mechanism, as the organisational principles familiar in connectionist models of organismic learning

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

The Role of Rivalry. Public Goods versus Common-Pool Resources

Despite a large theoretical and empirical literature on public goods and common-pool resources, a systematic comparison of these two types of social dilemmas is lacking. In fact, there is considerable confusion about these two types of dilemma situations. As a result, they are often treated alike. In this paper we argue that the degree of rivalry is the fundamental difference between the two games. We show that rivalry implies that both games cannot be represented by the same game theoretic structure. Fur-thermore, we experimentally study behavior in a quadratic public good and a quadratic common-pool resource game with identical Pareto opti-mum but divergent interior Nash equilibria. The results show that partici-pants clearly perceive the differences in rivalry. Aggregate behavior in both games starts relatively close to Pareto efficiency and converges to the respective Nash equilibrium.

Normative Conflict & Feuds: The Limits of Self-Enforcement

A normative conflict arises when there exist multiple plausible norms of behavior. In such cases, norm enforcement can lead to a sequence of mutual retaliatory sanctions, which we refer to as a feud. We investigate the hypothesis that normative conflict enhances the likelihood of a feud in a public-good experiment. We find that punishment is much more likely to trigger counter-punishment and start a feud when there is a normative conflict, than in a setting in which no conflict exists. While the possibility of a feud sustains cooperation,the cost of feuding fully offsets the efficiency gains from increased cooperation.normative conflict; peer punishment; feuds; counter-punishment; social norms

Discrete stochastic processes, replicator and Fokker-Planck equations of coevolutionary dynamics in finite and infinite populations

Finite-size fluctuations in coevolutionary dynamics arise in models of biological as well as of social and economic systems. This brief tutorial review surveys a systematic approach starting from a stochastic process discrete both in time and state. The limit $N\to \infty$ of an infinite population can be considered explicitly, generally leading to a replicator-type equation in zero order, and to a Fokker-Planck-type equation in first order in $1/\sqrt{N}$. Consequences and relations to some previous approaches are outlined.Comment: Banach Center publications, in pres

Mechanisms for Automated Negotiation in State Oriented Domains

This paper lays part of the groundwork for a domain theory of negotiation, that is, a way of classifying interactions so that it is clear, given a domain, which negotiation mechanisms and strategies are appropriate. We define State Oriented Domains, a general category of interaction. Necessary and sufficient conditions for cooperation are outlined. We use the notion of worth in an altered definition of utility, thus enabling agreements in a wider class of joint-goal reachable situations. An approach is offered for conflict resolution, and it is shown that even in a conflict situation, partial cooperative steps can be taken by interacting agents (that is, agents in fundamental conflict might still agree to cooperate up to a certain point). A Unified Negotiation Protocol (UNP) is developed that can be used in all types of encounters. It is shown that in certain borderline cooperative situations, a partial cooperative agreement (i.e., one that does not achieve all agents' goals) might be preferred by all agents, even though there exists a rational agreement that would achieve all their goals. Finally, we analyze cases where agents have incomplete information on the goals and worth of other agents. First we consider the case where agents' goals are private information, and we analyze what goal declaration strategies the agents might adopt to increase their utility. Then, we consider the situation where the agents' goals (and therefore stand-alone costs) are common knowledge, but the worth they attach to their goals is private information. We introduce two mechanisms, one 'strict', the other 'tolerant', and analyze their affects on the stability and efficiency of negotiation outcomes.Comment: See http://www.jair.org/ for any accompanying file

The UN in the lab

We consider two alternatives to inaction for governments combating terrorism, which we term Defense and Prevention. Defense consists of investing in resources that reduce the impact of an attack, and generates a negative externality to other governments, making their countries a more attractive objective for terrorists. In contrast, Prevention, which consists of investing in resources that reduce the ability of the terrorist organization to mount an attack, creates a positive externality by reducing the overall threat of terrorism for all. This interaction is captured using a simple 3×3 “Nested Prisoner’s Dilemma” game, with a single Nash equilibrium where both countries choose Defense. Due to the structure of this interaction, countries can benefit from coordination of policy choices, and international institutions (such as the UN) can be utilized to facilitate coordination by implementing agreements to share the burden of Prevention. We introduce an institution that implements a burden-sharing policy for Prevention, and investigate experimentally whether subjects coordinate on a cooperative strategy more frequently under different levels of cost sharing. In all treatments, burden sharing leaves the Prisoner’s Dilemma structure and Nash equilibrium of the game unchanged. We compare three levels of burden sharing to a baseline in a between-subjects design, and find that burden sharing generates a non-linear effect on the choice of the efficient Prevention strategy and overall performance. Only an institution supporting a high level of mandatory burden sharing generates a significant improvement in the use of the Prevention strategy