Analysis of Urban Car Owners Commute Mode Choice Based on Evolutionary Game Model

With the aggravation of the traffic congestion in the city, car owners will have to give up commuting with private cars and take the public transportation instead. The paper uses the replication dynamic mechanism to simulate the learning and adjustment mechanism of the automobile owners commuting mode selection. The evolutionary stable strategy is used to describe the longterm evolution of competition game trend. Finally we simulate equilibrium and stability of an evolution of the game under a payoff imbalance situation. The research shows that a certain proportion of car owners will choose public transit under the pressure of public transport development and heavy traffic, and the proportion will be closely related to the initial conditions and urban transportation development policy.


Characteristics of Urban Transportation
e core issue of urban transportation development is how to treat private car and public transportation development in almost big cities worldwide.Di erent urban transportation development policies are roughly divided into three patterns: the rst category is the automobile dependence mode, the representative of the country is USA, the family car ownership is very high, and private car used in commute ratio also is high.e second type is the private car synchronization coordinated with rail transit development, such as London, Paris, and Tokyo, and so forth, the car ownership is not lower than the north American cities, but the car utilization rate is low, and people commute mainly using the subway.e third type of city transportation mainly relies on public transport, inhibiting vehicle holdings growth and car use ratio, such as Singapore, Hong Kong, and other cities.It has formed a consensus on urban transportation development policy that a city must be rational to increase the number of cars, and none of the big cities can satisfy the unlimited increase of the cars through continuous road construction only.e big city transportation depends on the priority development of public transport.e big cities tra c problems are very complex; the cities must formulate their own transportation strategy according to their respective conditions and study.Chinaisintheperiodofsocialandeconomyhighspeed development.e speeding-up development of urbanization and motorization of big cities caused a series of problems as tra c jams, pollutions, energy consumption, and so on.With the improvement of people's living standard in recent years, more and more families have private cars; the tra c congestion becomes more serious in many cities. e road mileage growth cannot meet the growth of tra c demand.
e government should take some policies to limit the use of private cars through economic means to reduce the private car use, alleviate the pressure of the tra c jams, and implement bus priority strategy.Public transportation is a tra c mode of less per capita road resources and large passenger capacity; with the characteristics of energy conservation and environmental protection, it is an intensive mode of transportation.As the important infrastructure of the city, for most people the equal rights, public transportation embodies the social fairness and justice.Under the condition of tra c individual freedom to choose the means of commute, rational individuals prefer to consume public road resource from the self-interest.Because of two de ning characteristics, nonexcludability and nonrivalry of the public facilities, the individual pro t in the use of public resources completely from self-interest is far lower than the overall optimal pro t, which results in the di culties of sustainable development of the urban tra c system; it is the typical "public facilities tragedy" in game theory, which was known as the "Harding Tragedy." erefore the government must control the increase in the number of cars and the usage of private cars; at the same time the government should encourage the use of public transportation way to commute.
A larger amount of research results in the urban transportation development patterns by using the game theory.Only two types of travel modes, namely, autobus and private car, are considered in [ ], and a two-level game model has been formulated with the purpose to make reasonable and su cient use of the limited tra c resources.In [ ], the evolutionary process of trip model choice behavior o ft r a ct r a v e l e ri sa n a l y z e db yu s i n ge v o l u t i o n a r yg a m e , and an evolutionary model is proposed.
en the main parameters' a ection to the choice behavior is also analyzed.
e results show that the government's impelling to the public transport and penalty to the private vehicle play an important role in evolution of tra c individual's behavior, which may provide corresponding reference to the government's decision-making body.Reference [ ]p r e s e n t sa n evolutionary game model of travel mode choice for single population and proposes the evolutionary stable strategy about travel mode choice, which provides some academic support and evaluation for tra c management measures.In these articles, the researchers have been trying to analyse the result of urban transportation choice by using the game theory, and some of the city tra c travel choice behaviors a r ea n a l y z e d ,b u tt h e s es t u d i e sh a v en e g l e c t e dt h ec a ro w ners' choice di erence, especially under the conditions that the city tra c development will be a great change in the future.
Forresearchofcommutetra cmodeselection,theinitial conditions are the most important factor of the method of random utility theory.Reference [ ]formulatesanestedlogit NL model which is based on the random utility maximum theory, and they believe the commute mode choice mainly is decided by the e ects of sociodemographics, land use characteristics, and trip attributes, so they investigate the income, age, employment accessibility, travel time, and travel cost of commuters.Reference [ ] examines system optimum solutions for neighborhood-sized urban networks with cars andtransitthatserveademandwhichisdistributedintime and space, and which may include a population of captive transit riders.e research shows that the network capacity for cars is reduced if transit operations receive dedicated street space.e analysis shows how the transit agency should operate and how to set fares and tolls to minimize the system's generalized cost.
In this paper, we study the choice of the mode of China's urban transportation development based on the following assumptions: ( ) Urban car ownership will continue to increase; the growth will keep the high level because of China's economic development and urban residents' income increase in a relatively long period of time.
( ) ough the urban car ownership maintains growth, the public transit will get further development for the city tra c capacity constraints.Under some restrictionsonprivatecaruseandpoliciesonimprovingthe service level of public transport, part of commuters may give up using car commuter and switch to public transportation mode.So in the future urban transportation development mode, there is not a necessarily direct correspondence between car usage andthegrowthofcarownership.W ehopetoanalyse the choice of commute mode of urban car ownership family in the future under these assumptions.It would provide the bene cial reference for the public transportation development strategy and help us to plan development policy of urban transportation.

The Evolutionary Game Model of Car Owners' Travel Mode Choice
In the classical game theory, Nash equilibrium is the most important concept, it requires that the game players be perfectly rational and with in nite regression reasoning ability.In the process of game the players always make strategy works best for themselves.But in reality, we cannot assume that game participants always make perfectly rational decisions and must consider the game player's decision may be limited by the uncertainty factors of interference, which m a yl e a dt oa nu n a c h i e v a b l eN a s he q u i l i b r i u m .I fg a m e participants follow the behavior logic of temptation-learnadapt-growth in decision, that is the concept of Evolutionary Stable Strategy (ESS) [ ].In the process of the game, players have limited information of individuals.According to their vested interests, players adjust their strategy to improve their own payo s on the marginal constantly.e limited rational users study and adjust to balance strategy in the sense of a group, the equilibrium strategies are called Evolutionary StableStrategy,andthegameprocessisdescribedasevolution of the game.
In the dynamic game model of car owners travel mode c h o i c e ,w ea s s u m et h a tt h e r ea r et w ot y p e so fp a r t i c i p a n t s in the game; pure strategy is used by all participation.e is de ned as the set of all pure strategies, function ( ) is represented by pure strategy set ∈ when all the participants can be adopted in phase ,thestatevariable ( ) is denoted by proportion vector in phase with pure strategy ,andthefunction ( , ) is denoted by the expected utility of participants group who adopt pure strategy when the other participants group is using pure strategy .V a r i a b l e is denoted by average expected utility of all participants.According to the certi cate in [ ], we can get the following conclusion: isisanimitatorreplicateddynamicequation,anditsatis es the following theorem: (Fudenberg, ) a stable state of imitator dynamic is a Nash equilibrium; more generally, any steady state originated from the limitative internal path is a Nash equilibrium.On the other hand, if there exists a >0 foranon-Nashequilibrium,allinternalpathwilleventually be cleared from the neighborhood of the steady state .

Establishing a Game Model
As stated earlier, in the future urban commute mode selection, part of the car owners will give up driving and commute by the public transit with the development of urban public transportation.All car owners were divided into two categories, group A and group B, in our game model.Each group selects commuter bus or driving according to certain proportion, the analysis about payo s being as follows: (1) when both group members choose public transit, payo s of both sides are ; (2) when one group chooses private cars and the other group chooses public transit, the game payo s are ( , ) and ( , ),respectively;(3) when both group members choose private cars, the payo s are both .e payo s matrix is shown in Table .Assumption of the proportion of car owners who choose to take public transit is , and the proportion of car owners who use cars is 1− .e game is randomly matched groups; then we apply the above analysis result; the participants payo s are denoted by ; the bene t of players who take public transit is ( ) e bene t of players who use car is For all players average bene t is Obviously in the general case, there are di erences benets between the two group participants.According to ( ),the dynamic changes of the proportion of the participants who take public transit can be represented as Equation ( ) is replicated dynamic equation which is described for the proportion of car owners who choose public transit mode.Substituting ( ) and ( ) into ( ),weget For the convenience, we assume that the pro t of all strategies under the combination is a constant, so derivative / is only the function of ;then( ) can be written as To discuss the evolutionary stable strategy of the game model, we can nd out the replication dynamic stable state rstly; a er that we can discuss the in uence of disturbance to the steady-state.
Let ( ) = 0; we can get three stable states from ( ): As the di erent values of payo s, 3 may be equal to 1 , 2 or does not exist ( 3 ∉ [0, 1]); then the game degenerates into only two stable states.
As an evolutionary stable strategy * must be a stable point, when it is given a small perturbation, it will still come back by replicated dynamic.According to the di erential equation of stability theorem, that derivative ( ) must be less than zero in place of * .It means when interference is below * , ( ) must be greater than ; when the interference is above * , ( ) must be less than .Re ected on the phase diagram, ( ) with horizontal axis intersection point tangent slopeisnegativeintheplace * ; * is the corresponding game replication dynamic evolutionary stable strategy at this time.

The Example of the Evolutionary Game
Model of the Commute Mode Choice under the Benefit Imbalance Situation We have described a general bene t structure under two symmetrical methods for analyzing the stability of the equilibrium of cooperative game.In fact in car owners group, people have di erent sensitivity for travel time and the cost of commute.We de ne group A as a low income group; they will tend to choose public transit commute under the condition of lower public transit fee or higher private car costs; at the same time we de ne group B with higher income level; even if the public transit fee is lower or private car travel cost is higher, they still incline to use private cars.In this setting, the game model of group A and group B is no longer the previous bene ts symmetric balanced game and changes into di erentiation level gaming revenue.For the sake of convenient calculation, we assume that the payo s are the dimensionless numbers; an evolutionary game model From Figure we can come to a conclusion: points (1, 0) and (0, 1) are the evolutionary stable strategy in game as shown in Table ; the system nally converges to the strategy decided by the initial state of the system.When the initial s t a t ef a l l si na r e aA ,t h es y s t e mw i l lc o n v e r g et o(0, 1),t h e group A will choose the strategy of cars commute, and group B will choose the public transit as commute mode.When initial state falls in area B, the system will converge to (1, 0), group A will adopt strategy of the public transit commute, and group B will adopt the strategy of cars commute.When t h ei n i t i a ls t a t ef a l l si na r e aCo rD ,t h ed i r e c t i o no fs y s t e m evolution is uncertain; it may enter into area A and converge to point (0, 1);i ti sa l s ol i k e l yt oe n t e ra r e aBa n dc o n v e r g e to point (1, 0); it re ects the diversity of competition strategy of reality.We can draw a conclusion from the above analysis that the system has the characteristics of the evolution of complex system; = 9/13 and =3 / 7are change threshold of system evolution characteristics.When the system's initial state is in the vicinity of the two values, the initial state of the smallchangeswilla ectthe nalresultofsystemevolution; this is the system sensitivity to initial conditions, when the system initial state in A, B, A nal state of system evolution is determined; it shows that the results of the system evolution depend on the initial conditions.

Conclusion
From the above analysis of evolutionary game model, we know the commute mode choice is mainly a ected by the factors of travel time, travel cost, and comfort level, and so forth.When the urban road tra c system cannot carry more and more private cars, commute by private cars is no longer the only optimal way.e commute mode of developed countries' change has shown this problem.
e commute mode choice of urban car owners is related to the public transport system development and private travel restriction game trend of car owners commutes mode choice.e two types of participants in the cooperative competition replication dynamic relationship graph are shown in Figure .