Myopically Forward-Looking Agents in a Network Formation Game: Theory and Experimental Evidence

A population of players is considered in which each agent can select her neighbors in order to play a 2x2 Hawk-Dove game with each of them. We design our experiment in continuous time where participants may change their Hawk-Dove action and/or their neighborhood at any point in time. We are interested in the resulting formation of networks and the action distributions. Compared with static Nash equilibrium (e.g., Berninghaus and Vogt, 2004, 2006; Bramoulle, Lopez-Pintado, Goyal, and Vega-Redondo, 2004) and social optimum as theoretical benchmark solutions, subjects seem to employ a more complex, forward-looking thinking. We develop an other benchmark solution, called one-step-ahead stability, that combines forward-looking belief formation with rational response and that fits the data much better.

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

Evolution of Prosocial Behavior through Preferential Detachment and Its Implications for Morality.

The current project introduces a general theory and supporting models that offer a plausible explanation and viable mechanism for generating and perpetuating prosocial behavior. The proposed mechanism is preferential detachment and the theory proposed is that agents utilizing preferential detachment will sort themselves into social arrangements such that the agents who contribute a benefit to the members of their group also do better for themselves in the long run. Agents can do this with minimal information about their environment, the other agents, the future, and with minimal cognitive/computational ability. The conclusion is that self-organizing into groups that maintain prosocial behaviors may be simpler and more robust than previously thought. The primary contribution of this research is that a single, simple mechanism operating in different contexts generates the conceptually distinct prosocial behaviors achieved by other models, and in a manner that is more amenable to evolutionary explanations. It also bears importantly on explanations of the evolution of our moral experiences and their connection with prosociality.Ph.D.Political Science and PhilosophyUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/91448/1/bramson_1.pd

Group Decision-Making

The present work explores improvements in group decision-making. It begins with a practical example using state-of-the-art techniques for a complex, high-risk decision. We show how these techniques can reveal a better alternative. Although we created an improved decision process, decision-makers were apt to protect their own organizations instead of the project. This tendency was reduced over the course of the decision-making process but inspired the first conceptual component of this work. The first concept describes the “Cost of Conflict” that can arise in a group decision, using game theory to represent the non-cooperative approach and comparing the outcome to the cooperative approach. We demonstrate that it is possible for the group to settle on a non-Paretto Nash equilibrium. The sensitivity of the decision-maker weights is revealed which led to the second conceptual portion of this work. The second concept applies social network theory to study the influence between decision-makers in a group decision. By examining the number and strength of connections between decision-makers, we build from intrinsically derived weights to extrinsically derived weights by adding the network influences from other decision-makers. The two conceptual approaches provide a descriptive view of non-cooperative decisions where decision-makers still influence each other. These concepts suggest a prescriptive approach to achieving a higher group utility

Graphical game Theory with Mobility

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

Biological Evolution and Statistical Physics

This review is an introduction to theoretical models and mathematical calculations for biological evolution, aimed at physicists. The methods in the field are naturally very similar to those used in statistical physics, although the majority of publications appeared in biology journals. The review has three parts, which can be read independently. The first part deals with evolution in fitness landscapes and includes Fisher's theorem, adaptive walks, quasispecies models, effects of finite population sizes, and neutral evolution. The second part studies models of coevolution, including evolutionary game theory, kin selection, group selection, sexual selection, speciation, and coevolution of hosts and parasites. The third part discusses models for networks of interacting species and their extinction avalanches. Throughout the review, attention is paid to giving the necessary biological information, and to pointing out the assumptions underlying the models, and their limits of validity.Comment: Review article accepted for publication in Advances in Physics. 106 page

Representing spatial interactions in simple ecological models

The real world is a spatial world, and all living organisms live in a spatial environment. For mathematical biologists striving to understand the dynamical behaviour and evolution of interacting populations, this obvious fact has not been an easy one to accommodate. Space was considered a disposable complication to systems for which basic questions remained unanswered and early studies ignored it. But as understanding of non-spatial systems developed attention turned to methods of incorporating the effects of spatial structure. The essential problem is how to usefully manage the vast amounts of information that are implicit in a fully heterogeneous spatial environment. Various solutions have been proposed but there is no single best approach which covers all circumstances. High dimensional systems range from partial differential equations which model continuous population densities in space to the more recent individual-based systems which are simulated with the aid of computers. This thesis develops a relatively new type of model with which to explore the middle ground between spatially naive models and these fully complex systems. The key observation is to note the existence of correlations in real systems which may naturally arise as a consequence of their dynamical interaction amongst neighbouring individuals in a local spatial environment. Reflecting this fact - but ignoring other large scale spatial structure - the new models are developed as differential equations (pair models) which are based on these correlations. Effort is directed at a first-principles derivation from explicit assumptions with well stated approximations so the origin of the models is properly understood. The first step is consideration of simple direct neighbour correlations. This is then extended to cover larger local correlations and the implications of local spatial geometry. Some success is achieved in establishing the necessary framework and notation for future development. However, complexity quickly multiplies and on occasion conjectures necessarily replace rigorous derivations. Nevertheless, useful models result. Examples are taken from a range of simple and abstract ecological models, based on game theory, predator-prey systems and epidemiology. The motivation is always the illustration of possibilities rather than in depth investigation. Throughout the thesis, a dual interpretation of the models un-folds. Sometimes it can be helpful to view them as approximations to more complex spatial models. On the other hand, they stand as alternative descriptions of space in their own right. This second interpretation is found to be valuable and emphasis is placed upon it in the examples. For the game theory and predator-prey examples, the behaviour of the new models is not radically different from their non-spatial equivalents. Nevertheless, quantitative behavioural consequences of the spatial structure are discerned. Results of interest are obtained in the case of infection systems, where more realistic behaviour an improvement on non-spatial models is observed. Cautiously optimistic conclusions are reached that this, middle road of spatial modelling has an important contribution to make to the field