Pedestrian flow dynamics in a lattice gas model coupled with an evolutionary game

Twofold effect of self-interest in pedestrian room evacuation

Evacuation dynamics of pedestrians in a square room with one exit is studied. The movement of the pedestrians is guided by the static floor field model. Whenever multiple pedestrians are trying to move to the same target position, a game theoretical framework is introduced to address the conflict. Depending on the payoff matrix, the game that the pedestrians are involved in may be either hawk-dove or prisoner's dilemma, from which the reaped payoffs determine the capacities, or probabilities, of the pedestrians occupying the preferred vacant sites. The pedestrians are allowed to adjust their strategies when competing with others, and a parameter κ is utilized to characterize the extent of their self-interest. It is found that self-interest may induce either positive or negative impacts on the evacuation dynamics depending on whether it can facilitate the formation of collective cooperation in the population or not. Particularly, a resonance-like performance of evacuation is realized in the regime of prisoner's dilemma. The effects of placing an obstacle in front of the exit and the diversity of responses of the pedestrians to the space competition on the evacuation dynamics are also discussed.

Modeling Helping Behavior in Emergency Evacuations Using Volunteer’s Dilemma Game

People often help others who are in trouble, especially in emergency evacuation situations. For instance, during the 2005 London bombings, it was reported that evacuees helped injured persons to escape the place of danger. In terms of game theory, it can be understood that such helping behavior provides a collective good while it is a costly behavior because the volunteers spend extra time to assist the injured persons in case of emergency evacuations. In order to study the collective effects of helping behavior in emergency evacuations, we have performed numerical simulations of helping behavior among evacuees in a room evacuation scenario. Our simulation model is based on the volunteer’s dilemma game reflecting volunteering cost. The game theoretic model is coupled with a social force model to understand the relationship between the spatial and social dynamics of evacuation scenarios. By systematically changing the cost parameter of helping behavior, we observed different patterns of collective helping behaviors and these collective patterns are summarized with a phase diagram.

Spatial game in cellular automaton evacuation model

For numerical simulations of crowd dynamics in an evacuation we need a computationally light environment, such as the cellular automaton model (CA). By choosing the right model parameters, different types of crowd behavior and collective effects can be produced. But the CA does not answer why, when, and how these different behaviors and collective effects occur. In this article, we present a model, where we couple a spatial evacuation game to the CA. In the game, an agent chooses its strategy by observing its neighbors' strategies. The game matrix changes with the distance to the exit as the evacuation conditions develop. In the resulting model, an agent's strategy choice alters the parameters that govern its behavior in the CA. Thus, with our model, we are able to simulate how evacuation conditions affect the behavior of the crowd. Also, we show that some of the collective effects observed in evacuations are a result of the simple game the agents play.

Game theory in models of pedestrian room evacuation

We analyze the pedestrian evacuation of a rectangular room with a single door considering a lattice gas scheme with the addition of behavioral aspects of the pedestrians. The movement of the individuals is based on random and rational choices and is affected by conflicts between two or more agents that want to advance to the same position. Such conflicts are solved according to certain rules closely related to the concept of strategies in game theory, cooperation and defection. We consider game rules analogous to those from the Prisoner's Dilemma and Stag Hunt games, with payoffs associated to the probabilities of the individuals to advance to the selected site. We find that, even when defecting is the rational choice for any agent, under certain conditions, cooperators can take advantage from mutual cooperation and leave the room more rapidly than defectors.

Evacuation of pedestrians from a single room by using snowdrift game theories

Game theory is introduced to simulate the complicated interaction relations among the conflicting pedestrians in a pedestrian flow system, which is defined on a square lattice with the parallel update rule. Modified on the traditional lattice gas model, each pedestrian can move to not only an empty site, but also an occupied site. It is found that each individual chooses its neighbor randomly and occupies the site with the probability W(x→y)=1/1+exp[-(P(x)-U(x))/κ], where P(x) is the x's payoff representing his personal energy, and U(x) is the average payoff of its neighborhood indicating the potential well energy if he stays. Two types of pedestrians are considered, and they interact with their neighbors following the payoff matrix of snowdrift game theory. The cost-to-benefit ratio r=c/(2b-c) (where b is the perfect payoff and c is the labor cost) represents the fear index of the pedestrians in this model. It is found that there exists a moderate value of r leading to the shortest escape time, and the situation for large values of r is better than that for small ones in general. In addition, the pedestrian flow system always arrives at a consistent state in which the two types of walkers have the same number and evolve by the same law irrespectively of the parameters, which can be interpreted as the self-organization effect of pedestrian flow. It is also proven that the time point of the onset of the steady state is unrelated to the scale of the pedestrians and the square lattice. Meanwhile, the system exhibits different dynamics before reaching the consistent state: the number of the two types of walkers oscillates when P(C)>0.5 (i.e., probability to change the present strategy), while no oscillation happens for P(C)≤0.5. Finally, it is shown that a smaller density of pedestrians ρ induces a shorter average escape time.

Dynamical traffic light strategy in the Biham-Middleton-Levine model

In this paper, we study dynamical traffic light strategies in the Biham-Middleton-Levine traffic flow model. The strategies use local vehicular information to control urban traffic, which take into account the interaction of vehicles traveling in different directions via considering their dynamical spatial configuration. Simulations find out two strategies, in which local information at nearby sites is used. The two strategies perform much better than the alternating strategy. Under these two strategies, vehicles can self-organize into a new intermediate state with band structure. The analytical solutions of velocity of this state have been presented, which are in good agreement with simulations.

Patient and impatient pedestrians in a spatial game for egress congestion

Large crowds evacuating through narrow bottlenecks may create clogging and jams that slow down the egress flow. Especially if people try to push towards the exit, the so-called faster-is-slower effect may occur. We propose a spatial game to model the interaction of agents in such situations. Each agent has two possible modes of play that lead to either patient or impatient behavior. The payoffs of the game are derived from simple assumptions and correspond to a hawk-dove game, where the game parameters depend on the agent's location in the crowd and on external conditions. Equilibrium configurations are computed with a myopic best-response rule and studied in both a continuous space and a discrete lattice. We apply the game model to a continuous-time egress simulation, where the patient and impatient agents are given different individual parameter values, which are updated according to the local conditions in the crowd. The model shows how threatening conditions can increase the proportion of impatient agents, which leads to clogging and reduced flows through bottlenecks, even when smooth flows would be possible.

Quantitative analysis of pedestrian counterflow in a cellular automaton model

Pedestrian dynamics exhibits various collective phenomena. Here, we study bidirectional pedestrian flow in a floor field cellular automaton model. Under certain conditions, lane formation is observed. Although it has often been studied qualitatively, e.g., as a test for the realism of a model, there are almost no quantitative results, either empirically or theoretically. As basis for a quantitative analysis, we introduce an order parameter which is adopted from the analysis of colloidal suspensions. This allows us to determine a phase diagram for the system where four different states (free flow, disorder, lanes, gridlock) can be distinguished. Although the number of lanes formed is fluctuating, lanes are characterized by a typical density. It is found that the basic floor field model overestimates the tendency towards a gridlock compared to experimental bounds. Therefore, an anticipation mechanism is introduced which reduces the jamming probability.