Road Pricing Design Based on Game Theory and Multi-agent Consensus

Consensus theory and noncooperative game theory respectively deal with cooperative and noncooperative interactions among multiple players/agents. They provide a natural framework for road pricing design, since each motorist may myopically optimize his or her own utility as a function of road price and collectively communicate with his or her friends and neighbors on traffic situation at the same time. This paper considers the road pricing design by using game theory and consensus theory. For the case where a system supervisor broadcasts information on the overall system to each agent, we present a variant of standard fictitious play called average strategy fictitious play(ASFP) for large-scale repeated congestion games.Only a weighted running average of all other players actions is assumed to be available to each player. The ASFP reduces the burden of both information gathering and information processing for each player. Compared to the joint strategy fictitious play(JSFP) studied in the literature, the updating process of utility functions for each player is avoided. We prove that there exists at least one pure strategy Nash equilibrium for the congestion game under investigation, and the players actions generated by the ASFP with inertia(players reluctance to change their previous actions) converge to a Nash equilibrium almost surely. For the case without broadcasting, a consensus protocol is introduced for individual agents to estimate the percentage of players choosing each resource, and the convergence property of players action profile is still ensured. The results are applied to road pricing design to achieve socially local optimal trip timing. Simulation results are provided based on the real traffic data for the Singapore case study.

Exploration on the stability conditions in bubble columns by noncooperative game theory

The energy-minimization multiscale(EMMS)model,originally proposed for gas-solid fluidization,features a stability condition to close the simplified conservation equations.It was put forward to physically reflect the compromise of two dominant mechanisms,i.e.,the particle-dominated with minimal potential energy of particles,and the gas-dominated with the least resistance for gas to penetrate through the particle bed.The stability condition was then formulated as the minimization of the ratio of these two physical quantities.Analogously,the EMMS approach was later extended to the gas-liquid flow in bubble columns,termed dual-bubble-size model.It considers the compromise of two dominant mechanisms,i.e.,the liquid-dominated regime with small bubbles,and the gas-dominated regime with large bubbles.The stability condition was then formulated as the minimization of the sum of these two physical quantities.Obviously,the two stability conditions were expressed in different manner,though gas-solid and gas-liquid systems bear some analogy.In addition,both the conditions transform the original multiobjective variational problem into a single-objective problem.The mathematical formulation of stability condition remains therefore an open question.This study utilizes noncooperative game theory and noninferior solutions to directly solve the multi-objective variational problem,aiming to explo re the different pathways of compromise of dominant mechanisms.The results show that only keeping the single dominant mechanism cannot capture the jump change of gas holdup,which is associated with flow regime transition.Hybrid of dominant mechanisms,noninferior solutions and noncooperative game theory can predict the flow regime transition.However,the game between the two mechanisms makes the two-bubble structure degenerate and reduce to the single-bubble structure.The game of the three mechanisms restores the two-bubble structure.The exploration on the formulation of stability conditions may help to understa nd the roles and interactions of different domina nt mechanisms in the origin of complexity in multiphase flow systems.

Understanding information interactions in diffusion： an evolutionary game-theoretic perspective

Social networks are fundamental media for dif- fusion of information and contagions appear at some node of the network and get propagated over the edges. Prior re- searches mainly focus on each contagion spreading indepen- dently, regardless of multiple contagions＇ interactions as they propagate at the same time. In the real world, simultaneous news and events usually have to compete for user＇s attention to get propagated. In some other cases, they can cooperate with each other and achieve more influences. In this paper, an evolutionary game theoretic framework is proposed to model the interactions among multiple con- tagions. The basic idea is that different contagions in social networks are similar to the multiple organisms in a popula- tion, and the diffusion process is as organisms interact and then evolve from one state to another. This framework statis- tically learns the payoffs as contagions interacting with each other and builds the payoff matrix. Since learning payoffs for all pairs of contagions IS almost impossible （quadratic in the number of contagions）, a contagion clustering method is proposed in order to decrease the number of parameters to fit, which makes our approach efficient and scalable. To ver- ify the proposed framework, we conduct experiments by us- ing real-world information spreading dataset of Digg. Exper- imental results show that the proposed game theoretic frame- work helps to comprehend the information diffusion process better and can predict users＇ forwarding behaviors with more accuracy than the previous studies. The analyses of evolution dynamics of contagions and evolutionarily stable strategy re- veal whether a contagion can be promoted or suppressed by others in the diffusion process.