Ceyhun Eksin

Distributed Network Optimization With Heuristic Rational Agents

A network of distributed agents wants to minimize a global cost given by a sum of local terms involving nonlinear convex functions of self and neighboring variables. Agents update their variables at random times by observing the values of neighboring agents and applying a random heuristic rule intent on minimizing the local cost with respect to their own variables. The heuristic rules are rational in that their average result is the actual optimal action with respect to the given values of neighboring variables. By identifying heuristic rational optimization with stochastic coordinate descent, it is shown that all agents visit a neighborhood of the optimal cost infinitely often with probability 1. An exponential probability bound on the worst deviation from optimality between visits to near optimal operating points is also derived. Commonly used models of consensus and opinion propagation in social networks, Markov random field estimation in wireless sensor networks, and cohesive foraging of animal herds are cast in the language of heuristic rational optimization. Numerical simulations for these three examples are presented to corroborate analytical results.

Learning in network games with incomplete information: asymptotic analysis and tractable implementation of rational behavior

The role of social networks in learning and opinion formation has been demonstrated in a variety of scenarios such as the dynamics of technology adoption [1], consumption behavior [2], organizational behavior [3], and financial markets [4]. The emergence of network-wide social phenomena from local interactions between connected agents has been studied using field data [5]?[7] as well as lab experiments [8], [9]. Interest in opinion dynamics over networks is further amplified by the continuous growth in the amount of time that individuals spend on social media Web sites and the consequent increase in the importance of networked phenomena in social and economic outcomes. As quantitative data become more readily available, a research problem is to identify metrics that could characterize emergent phenomena such as conformism or diversity in individuals? preferences for consumer products or political ideologies [10]. With these metrics available, a natural follow-up research goal is the study of mechanisms that lead to diversity or conformism and the role of network properties like neighborhood structures on these outcomes. All of these questions motivate the development of theoretical models of opinion formation through local interactions in different scenarios.

Demand Response Management in Smart Grids With Heterogeneous Consumer Preferences

Consumer demand profiles and fluctuating renewable power generation are two main sources of uncertainty in matching demand and supply. This paper proposes a model of the electricity market that captures the uncertainties on both the operator and user sides. The system operator (SO) implements a temporal linear pricing strategy that depends on real-time demand and renewable generation in the considered period combining real-time pricing with time-of-use pricing. The announced pricing strategy sets up a noncooperative game of incomplete information among the users with heterogeneous, but correlated consumption preferences. An explicit characterization of the optimal user behavior using the Bayesian Nash equilibrium solution concept is derived. This explicit characterization allows the SO to derive pricing policies that influence demand to serve practical objectives, such as minimizing peak-to-average ratio or attaining a desired rate of return. Numerical experiments show that the pricing policies yield close to optimal welfare values while improving these practical objectives.

An oscillating tragedy of the commons in replicator dynamics with game-environment feedback

Significance Classical game theory addresses how individuals make decisions given suitable incentives, for example, whether to use a commons rapaciously or with restraint. However, classical game theory does not typically address the consequences of individual actions that reshape the environment over the long term. Here, we propose a unified approach to analyze and understand the coupled evolution of strategies and the environment. We revisit the originating tragedy of the commons example and evaluate how overuse of a commons resource changes incentives for future action. In doing so, we identify an oscillatory tragedy of the commons in which the system cycles between deplete and replete environments and cooperation and defection behavior, highlighting new challenges for control and influence of feedback-evolving games. A tragedy of the commons occurs when individuals take actions to maximize their payoffs even as their combined payoff is less than the global maximum had the players coordinated. The originating example is that of overgrazing of common pasture lands. In game-theoretic treatments of this example, there is rarely consideration of how individual behavior subsequently modifies the commons and associated payoffs. Here, we generalize evolutionary game theory by proposing a class of replicator dynamics with feedback-evolving games in which environment-dependent payoffs and strategies coevolve. We initially apply our formulation to a system in which the payoffs favor unilateral defection and cooperation, given replete and depleted environments, respectively. Using this approach, we identify and characterize a class of dynamics: an oscillatory tragedy of the commons in which the system cycles between deplete and replete environmental states and cooperation and defection behavior states. We generalize the approach to consider outcomes given all possible rational choices of individual behavior in the depleted state when defection is favored in the replete state. In so doing, we find that incentivizing cooperation when others defect in the depleted state is necessary to avert the tragedy of the commons. In closing, we propose directions for the study of control and influence in games in which individual actions exert a substantive effect on the environmental state.

Bayesian Quadratic Network Game Filters

A repeated network game where agents have quadratic utilities that depend on information externalities-an unknown underlying state-as well as payoff externalities-the actions of all other agents in the network-is considered. Agents play Bayesian Nash Equilibrium strategies with respect to their beliefs on the state of the world and the actions of all other nodes in the network. These beliefs are refined over subsequent stages based on the observed actions of neighboring peers. This paper introduces the Quadratic Network Game (QNG) filter that agents can run locally to update their beliefs, select corresponding optimal actions, and eventually learn a sufficient statistic of the networks state. The QNG filter is demonstrated on a Cournot market competition game and a coordination game to implement navigation of an autonomous team.

Distributed demand side management of heterogeneous rational consumers in smart grids with renewable sources

We consider a demand side management model in which the power provider adopts an adaptive pricing strategy that depends on fluctuations in renewable sources and consumption behavior of customers with heterogeneous marginal utilities in the smart grid. Given the adaptive pricing strategy, we formulate the power consumption behavior of customers as a repeated noncooperative game with incomplete information. We provide an explicit characterization of unique Bayesian Nash equilibrium strategy in terms of individual marginal utilities. The rational behavior is also characterized in a communication scheme where smart meters exchange consumption levels with neighboring meters. A local algorithm that computes equilibrium consumption and propagates beliefs is presented when the network is known. Simulation results show that communication is beneficial for welfare and that power provider can lower the peak-to-average ratio of total consumption by adjusting its target profit ratio.

Epidemic spread over networks with agent awareness and social distancing

We study an SIS epidemic model over an arbitrary connected network topology when the agents receive personalized information about the current epidemic state. The agents utilize their available information to either reduce interactions with their neighbors (social distancing) when they believe the epidemic is currently prevalent or resume normal interactions when they believe there is low risk of becoming infected. The information is a weighted combination of three sources: 1) the average states of nodes in contact neighborhoods 2) the average states of nodes in an information network 3) a global broadcast of the average epidemic state of the network. A 2n-state Markov Chain is first considered to model the disease dynamics with awareness, from which a mean-field discrete-time n-state dynamical system is derived, where each state corresponds to an agents probability of being infected. The nonlinear model is a lower bound of its linearized version about the origin. Hence, global stability of the origin (the diseasefree equilibrium) in the linear model implies global stability in the nonlinear model. When the origin is not stable, we show the existence of a nontrivial fixed point in the awareness model, which obeys a strict partial order in relation to the nontrivial fixed point of the dynamics without distancing. In simulations, we define two performance metrics to understand the effectiveness agent awareness has in reducing the spread of an epidemic.

Distributed fictitious play in potential games of incomplete information

We consider a networked multi-agent system with common unknown state of the world. A potential payoff function, that depends on the actions of agents and the state of the world, captures the systems global well-being. Agents with different information about the state of the world needs to reason about the actions of others to maximize the payoff. We introduce the distributed fictitious play algorithm as a decentralized decision-making model given only local network information in this setup. In the algorithm, agents observe past actions of their neighbors and keep an empirical distribution on the centroid population action. In addition, agents form beliefs on the state of the world through a parallel state learning process. At each stage, agents take an action that maximizes the expected global payoff assuming that others are going to play with respect to their estimated centroid empirical distribution given their belief on the state of the world. We show that this behavior converges to a consensus Nash equilibrium strategy when the potential payoff function is symmetric and agents reach a consensus in their beliefs on the state of the world fast enough. We exemplify the convergence behavior of the algorithm in a coordination game.

Rational consumer behavior models in smart pricing

A game-theoretic framework based on smart pricing in power grids that incorporates heterogeneous user preferences and renewable power uncertainty is considered. The system operator adopts an adaptive pricing policy that depends on total consumption and renewable generation. The pricing policy sets up a non-cooperative game of incomplete information among users with heterogeneous preferences. Selfish, altruistic and welfare maximizing user behavior models are proposed. Information exchange models in which users only have private information, communicate or receive broadcasted information are considered. For each pair of behavior and information exchange models, rational consumption strategy is characterized. Numerical analyses reveal that communication is beneficial for the expected aggregate payoff while it does not affect the expected net revenue of the system operator. Moreover, the additional information to the users helps reduce the variance of total consumption among runs increasing the accuracy of demand predictions.

Disease dynamics in a stochastic network game: a little empathy goes a long way in averting outbreaks

Individuals change their behavior during an epidemic in response to whether they and/or those they interact with are healthy or sick. Healthy individuals may utilize protective measures to avoid contracting a disease. Sick individuals may utilize preemptive measures to avoid spreading a disease. Yet, in practice both protective and preemptive changes in behavior come with costs. This paper proposes a stochastic network disease game model that captures the self-interests of individuals during the spread of a susceptible-infected-susceptible disease. In this model, individuals strategically modify their behavior based on current disease conditions. These reactions influence disease spread. We show that there is a critical level of concern, i.e., empathy, by the sick individuals above which disease is eradicated rapidly. Furthermore, we find that risk averse behavior by the healthy individuals cannot eradicate the disease without the preemptive measures of the sick individuals. Empathy is more effective than risk-aversion because when infectious individuals change behavior, they reduce all of their potential infections, whereas when healthy individuals change behavior, they reduce only a small portion of potential infections. This imbalance in the role played by the response of the infected versus the susceptible individuals on disease eradication affords critical policy insights.