Potential games in volatile environments

This papers studies the co-evolution of networks and play in the context of finite population potential games. Action revision, link creation and link destruction are combined in a continuous-time Markov process. I derive the unique invariant distribution of this process in closed form, as well as the marginal distribution over action profiles and the conditional distribution over networks. It is shown that the equilibrium interaction topology is an inhomogeneous random graph. Furthermore, a characterization of the set of stochastically stable states is provided, generalizing existing results to models with endogenous interaction structures.

Different Approaches to Influence Based on Social Networks and Simple Games

We present an overview of research on a certain model of influence in a social network. Each agent has to make an acceptance/rejection decision, and he has an inclination to choose either the yes-action or the no-action. The agents are embedded in a social network which models influence between them. Due to the influence, a decision of an agent may differ from his preliminary inclination. Such a transformation between the agents' inclinations and their decisions are represented by an influence function. Follower functions encode the players who constantly follow the opinion of a given unanimous coalition. We examine properties of the influence and follower functions and study the relation between them. The model of influence is also compared to the framework of command games in which a simple game is built for each agent. We study the relation between command games and influence functions. We also define influence indices and determine the relations between these indices and some well-known power indices. Furthermore, we enlarge the set of possible yes/no actions to multi-choice games and investigate the analogous tools related to influence in the multi-choice model.influence ; social network ; influence function ; command game ; follower ; voting

Influence functions, followers and command games

We study and compare two frameworks: a model of influence, and command games. In the influence model, in which players are to make a certain acceptance/rejection decision, due to influence of other players, the decision of a player may be different from his inclination. We study a relation between two central concepts of this model: influence function, and follower function. We deliver sufficient and necessary conditions for a function to be a follower function, and we describe the structure of the set of all influence functions that lead to a given follower function. In the command structure introduced by Hu and Shapley, for each player a simple game called the command game is built. One of the central concepts of this model is the concept of command function. We deliver sufficient and necessary conditions for a function to be a command function, and describe the minimal sets generating a normal command game. We also study the relation between command games and influence functions. A sufficient and necessary condition for the equivalence between an influence function and a normal command game is delivered.influence function;follower function;lower and upper inverses;kernel;command game;command function;minimal sets generating a command game

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.

Pairwise Interaction on Random Graphs

We analyze dynamic local interaction in population games where the local interaction structure (modeled as a graph) can change over time: A stochastic process generates a random sequence of graphs. This contrasts with models where the initial interaction structure (represented by a deterministic graph or the realization of a random graph) cannot change over time.

Constrained Interactions and Social Coordination

We consider a co-evolutionary model of social coordination and network formation whereagents may decide on an action in a 2 x 2- coordination game and on whom to establish costly links to. We find that a payoff dominant convention is selected for a wider parameter range when agents may only support a limited number of links as compared to a scenario where agents are not constrained in their linking choice. The main reason behind this result is that constrained interactions create a tradeoff between the interactions an agent has and those he would rather have. Further, we discuss convex linking costs and provide suffcient conditions for the payoff dominant convention to be selected in mxm coordination games.

Myopic behavior and overall utility maximization - A study of linked hawks and doves

At present, in the domain of simultaneous action selection and network formation games, game-theoretic behavior and experimental observations are not consistent. While theory typically predicts inefficient outcomes for (anti- )co-ordination games, experiments show that subjects tend to play efficient (non-Nash) strategy profiles. One reason for this discrepancy is the tendency to model corresponding games as one-shot and derive predictions. In this paper, we calculate the equilibria for a finitely repeated version of the Hawk-Dove game with endogenous network formation and show that the repetition leads to additional sub-game perfect equilibria; namely, the efficient strategy profiles played by human subjects. However, efficiency crucially depends on the design of the game. This paper theoretically demonstrates that, although technically feasible, the efficient profiles are not sub-game perfect equilibria if actions are fixed after an initial period. We confirm this result using an experimental study that demonstrates how payoffs are higher if actions are never fixed

Pairwise interaction on random graphs

We analyze dynamic local interaction in population games where the local interaction structure (modeled as a graph) can change over time: A stochastic process generates a random sequence of graphs. This contrasts with models where the initial interaction structure (represented by a deterministic graph or the realization of a random graph) cannot change over time

Identity, Community and Segregation

I develop a framework to explain why identity divides some communities and not others. An identity group is defined as a group of individuals with the same `culture'. A community is divided when different identities are socially segregated; a community is integrated when there is no social segregation between different identities. I find three possible outcomes for a community: assimilation, where groups socially integrate and one group conforms to the culture of another; non-assimilative integration, where groups integrate but individuals retain their own identity; and segregation, where groups socially segregate and retain their own culture. I find that certain community environments encourage segregation: (i) communities with similar sized identity groups; (ii) larger communities; (iii) communities with greater cultural distance between identities. Further, when segregation occurs, the cultural divide between the two groups can increase endogenously beyond ex-ante differences

Local Interaction on Random Graphs

We analyze dynamic local interaction in population games where the local interaction structure (modeled as a graph) can change over time: A stochastic process generates a random sequence of graphs. This contrasts with models where the initial interaction structure (represented by a deterministic graph or the realization of a random graph) cannot change over time