For the problem of route choice in taxi carpooling detour, considering the uncertainty of traffic and the characteristic of passengers’ noncomplete rationality, an evolutionary game model of taxi carpooling detour route is built, in which prospect theory is introduced and revenue of strategy is replaced by prospect value. The model reflects more really decisionmaking psychology of passengers. Then the stable strategies of the model are studied, and the influences of detour distance and traffic congestion on detour carpooling success are analyzed, respectively. The results show that when at least one route of which prospect values for two passenger sides are both positive exists, carpooling route can reach an agreement. The route is stable strategy of evolutionary game, and the passengers requiring short travel time tend to select the nondetour route. With the increase of detour distance and traffic congestion rate, the possibility of reaching an agreement decreases gradually; that is, possibility of carpooling failure increases. So taxi carpooling detour is possible under the certain condition, but some measures must be carried out such as constraints of detour distance and mitigation of traffic congestion to improve carpooling success probability. These conclusions have a certain guiding significance to the formulation of taxi carpooling policy.
Taxi carpooling mode is the behavior pattern in which passengers agree to take the same taxi after consultation. The mode can effectively improve the transportation efficiency and ease the traffic pressure, which is an effective solution to solve the urban traffic problem [
Many scholars have carried out researches on the problem of carpooling [
This paper aims at the problem of taxi carpooling detour route choice. Detour is a common phenomenon in taxi carpooling. Detour may occur when destinations of passengers who ride the same taxi are different. There must be one side passenger who agrees to drive detour route in order to realize carpooling successfully. Taxi carpooling detour route is the route through which passengers reach an agreement to drive after consultation. Of course, the final route is not the best route for passengers selecting detour from the point of travel distance only, but it is the best strategy after comprehensive consideration. Whether passengers will reach an agreement or not is the key of carpooling success. The regulations of carpooling detour route choice have important significance to the formulation of traffic policy.
This paper considers the situation of carpooling route strategy of two passengers whose destinations are different. One of passengers has to choose detour route if the two passengers ride the same taxi successfully. Each passenger faces the two route strategies: detour route and nondetour route. The nondetour route is the shortest route for passenger, and the detour route is the shortest route for the other side. How to decide route for passengers is the key of the research. The two factors including individual psychology and choice of the other passenger will affect decision of passenger. On the one hand passenger tends to select the route closer to his psychological expectation. Moreover the decisionmaking environment is uncertain because the phenomenon of traffic congestion is common in reality and traffic condition is uncertain, which brings trouble to study passenger’s decision. And human being always shows nonfullrationality in decisionmaking [
In summary, game of taxi carpooling detour route is studied based on prospect theory and evolution game theory. Firstly, passenger psychology decision model is built considering travel time and cost, in which comprehensive prospect value of each route is obtained. Secondly, carpooling detour route game model is established, in which comprehensive prospect values revealing passengers’ real psychological gains and losses are used as revenue. Then evolutionary strategy and its regularity are analyzed further. At last an example is given to show application of the model; meanwhile influence of detour distance and traffic congestion on stable strategy are analyzed in this paper.
Suppose two passengers start from the same location
Travel routes of carpooling passengers.
Passenger will consider individual psychological expectation and traffic congestion condition when he makes route choice. Individual psychological expectations about travel time and cost are regarded as the reference points called time reference point and cost reference point, respectively.
Set
Suppose taxi charging standard stipulates that initiate fee is
Cost gain of possible cost
According to value function form of prospect theory, define value function of scenes
The probability of traffic congestion passenger perceived is not actual probability according to prospect theory. Set
Time prospect value
Considering comprehensively travel time and cost, comprehensive prospect value of passenger
Time prospect value
Comprehensive prospect value of strategy reflects actually psychology gain of passenger. The greater
The two passengers both face two route strategies: strategy 1 (route
Revenue matrix of passengers.
Passenger 1  Passenger 2  

Strategy 
Strategy 

Strategy 

0, 0 
Strategy 
0, 0 

Suppose the proportion of passengers selecting strategy 1 of passenger 1 type is
Average expectation gain is
Replication dynamic equation of proportion of passenger 1 type is
Subject expectation gains of strategy 1 and strategy 2 for passenger 2, respectively, are
Average expectation gain is
Replication dynamic equation of proportion of passenger 2 type is
The equilibrium points of evolution system are (0, 0), (0, 1), (1, 0), (1, 1), and
Jacobian matrix is
Next we analyze stability of equilibrium points based on Jacobian matrix, as shown in Table
Stability analysis.
Equilibrium point  Det 
Tr 

(0, 0) 


(0, 1) 


(1, 0) 


(1, 1) 


( 

0 
Based on above analysis, there are four possible stable points in system: (0, 0), (0, 1), (1, 0), and (1, 1). Figure
Replication dynamic relationship and stability of two passengers.
Among them, Figures
Taking taxi charging standard of a city as example, initiate fee is 10¥/3 km, 1.4¥ per kilometer more than 3 kilometers, and waiting fee is 1.2¥/2.5 min. Two passengers ride the same taxi from the same location
Compute prospect values of each strategy for the two passengers based on the method proposed in this paper in the above four scenes. Tables
Prospect value of scene 1.
Time prospect value  Cost prospect value 










Passenger 1  3.265  −0.980  −8.117  −1.153  5/6  −2.943  −1.074 
Passenger 2  −10.048  −6.140  2.851  −1.512  5/2  −6.362  −4.818 
Prospect value of scene 2.
Time prospect value  Cost prospect value 










Passenger 1  5.850  3.840  −4.678  1.445  35/36  0.512  2.626 
Passenger 2  1.332  4.620  0.097  −6.423  10/11  0.685  −1.164 
Prospect value of scene 3.
Time prospect value  Cost prospect value 










Passenger 1  5.850  3.840  −4.678  1.445  35/36  0.512  2.626 
Passenger 2  −4.358  −0.429  4.122  1.118  110/51  −1.672  0.061 
Prospect value of scene 4.
Time prospect value  Cost prospect value 










Passenger 1  5.850  3.840  −4.678  1.445  35/36  0.512  2.626 
Passenger 2  −0.979  3.265  3.495  −0.242  5/3  0.698  1.950 
Strategies dynamic evolution of different initial probabilities.
Considering the difference of different passengers’ psychology reference points, comprehensive prospect values of each strategy for different psychology reference points are obtained by simulation. The range of time reference point is from 10 min to 24 min, and the range of cost reference point is from 3¥ to 11¥ based on the condition of the above example. Comprehensive prospect values of nondetour strategy are shown as in Figure
Comprehensive prospect values of different reference points for nondetour strategy.
Comprehensive prospect values of different reference points for detour strategy.
Figure
Possible reference points of carpooling success.
Above simulation results are obtained under the condition of detour distance and traffic congestion rate given. Detour distance and traffic congestion rate will affect the decisionmaking of passengers in the reality. Next the influences of detour distance and traffic congestion rate on carpooling route decision are analyzed, respectively.
Detour distance
Possible reference points of carpooling success with detour distance 1.5 km.
When detour distance increases to
Possible reference points of carpooling success with detour distance 2 km.
Possible reference points of carpooling success with detour distance 2.5 km.
The traffic congestion rate also has effect on route decision of passengers. Change traffic congestion rate and keep other references unchanged to analyze the influence of traffic congestion on carpooling route strategy. Figures
Possible reference points of carpooling success with traffic congestion rate 0.
Possible reference points of carpooling success with traffic congestion rate 0.25.
Possible reference points of carpooling success with traffic congestion rate 0.5.
Possible reference points of carpooling success with traffic congestion rate 0.75.
Possible reference points of carpooling success with traffic congestion rate 1.
This paper studies the problem of carpooling detour route choice based on prospect theory and evolutionary game theory, considering the uncertainty of traffic and the characteristic of human noncomplete ration. Passenger’s decision psychology is analyzed well, and evolutionary game model is established. The comprehensive prospect value which can describe psychology gain of passenger is used as revenue of evolutionary game. Stable strategies of detour route and influence regulations of carpooling success are obtained. Conclusions obtained are the following:
There are four stable strategies in taxi carpooling detour system: (detour route, nondetour route), (nondetour route, detour route), (detour route, detour route), and (nondetour route, nondetour route), in which the first two stable strategies mean reaching an agreement and carpooling success. If the two carpooling passengers both feel gain to the same route, the route is stable strategy. If they both feel gain to the two routes, stable strategy depends on the initial probability of strategy choice of the two types of passengers.
The passengers requiring shorter travel time tend to nondetour strategy; the probability of the passengers who do not require shorter travel time selecting detour strategy is larger. The possibility of passengers selecting detour strategy must be increased in order to improve the probability of detour carpooling success. Decreasing cost of the passenger selecting detour strategy is one of effective measures.
Detour distance and traffic congestion rate have large influence on passengers’ decision. The possibility of carpooling success decreases with detour distance increase. Carpooling route cannot reach an agreement and carpooling fails when detour distance adds to a certain degree. Moreover, the possibility of carpooling success decreases with traffic congestion rate increase. So limit of detour distance and ease traffic congestion are effective method of improving the probability of carpooling success.
In fact, there are some intangible factors affecting passenger’s decision, for example, trust in the other party, sex, age of the other party, and day or night. People usually tend to choose detour route in order to take care of old man or child, and people will not choose detour at night. Moreover, information technology also affects passenger’s decision. If passenger obtains exact road condition information by intelligent equipment, time and cost are certain. Passenger’s decision is not affected by route condition, and decision result is closer to optimization. So development of technology can reduce to a certain extent uncertainty of decision and optimize route choice.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This research was funded by National Natural Science Foundation of China (61364026, 51408288) and Youth Science Foundation of Lanzhou Jiaotong University (2015032). The authors express their thanks to all who participated in this research for their cooperation.