Game Theory about Traffic Overcrowding

Game Theory about Traffic Overcrowding

Game Theory about Traffic Overcrowding

The primary problems associated with urbanization involve traffic congestion and overcrowding. The demand-supply contradiction reinforces the issue. As such, traffic congestion can be considered as a game between travelers and urban transportation planners. Also, it can be viewed as a balance between the planners’ expectation to get minimal traffic congestion and the travelers’ expectation to get the most convenient and savings from a trip. This paper brings forward the concept of the prisoner’s dilemma and the game theory to study the correlation between travel decision-making and public resource utilization. The paper focuses on the underlying contradictions between traffic demand and traffic supply to find a solution to the traffic problem. The first section explores the relationship between travel decision-making and public resource utilization while the second one examines the conflict between traffic demand and traffic supply. The third section discusses the solution to the traffic problem.

Travel Decision-Making and Public Resource Utilization

Game theory studies show that people are naturally predisposed to over-exploit common-pool resources such as transportation systems even when doing so is detrimental to the society as a whole.  According to Emil, human beings are surrounded by complex systems requiring urban planners and engineers to come up with the most robust and secure structures. Xu and Yu add that without resource utilization, planners cannot make the most of the resources available to them to achieve the set objectives (89). The link between travel decision-making and public resource utilization occurs when engineers are expected to design transport systems that are not only aligned with what is best for the society but also provides the incentives necessary for people to use them. The current problem involves the contradiction between traffic demand and traffic supply, which results in congestion and overcrowding.

The primary theoretical framework employed to address this problem involves the game theory, which is concerned with analyzing the decisions made by multiple individuals whose incentives to make a decision is contingent on other people’s actions. At Nash equilibrium, the people making travel decision and those responsible for managing public resource utilization will selfishly select the options that yield the highest benefit for them, which is often to the detriment of their shared advantages (Daskalakis, Paul, and Christos 195). Consequently, understanding the relationship between travel decision-making and public resource utilization helps in identifying the things planners should take into consideration to ensure people responsibly utilize transport resources.

The Nash equilibrium is illustrated when the people making travel decision and those responsible for managing public resource utilization benefit by agreeing not to give into each other’s’ demands. The problem with this rational arrangement is that when party A knows that the party B will not carve into their demands, then A stands to benefit more, especially if B gives in to his demands and vice versa. Therefore, the only Nash equilibrium is for both A and B to give in to each other’s demand and reach a compromise. Understanding the behaviors of travelers and urban planners at the Nash equilibrium can be challenging because the outcomes are uncertain. Moreover, both parties have different risk preferences. The relationship between travel decision-making and public resource utilization reflects the fact that both parties decide how much of the transport resources to use by keeping in mind that if they consume a certain amount and the others utilize another amount, both will get some return, but the inherent risk is that the resource may fail.

The Contradiction between Traffic Demand and Traffic Supply

The key to solving the conflict between traffic demand and traffic supply involves considering how people perceive wins and losses. The prospect theory can be applied to help address the problem because it describes how people select probabilistic options that involve a certain amount of risk, especially when the probability of an outcome occurring remains uncertain. Although classical models ignore how people evaluate the likelihood of gaining and losing, this paper examines what happens at the Nash equilibrium by incorporating complicated risk preferences. The first step involves determining the failure probability that results in overcrowding and traffic congestion, which will be referred to as the fragility of the transport resource and a function of the travelers’ risk preferences (Daskalakis, Paul, and Christos 197). The assumption held is that failure is less likely to occur in a society that tightly controls the use of infrastructure resources.

As such, the concept of Nash equilibrium is essential in examining the contradiction between traffic demand and traffic supply because it captures the notion that neither the travelers nor the urban planners have been forced to do the right thing. Instead, they are doing what they need to optimize their utility and benefit (Palomar, Daniel, and Mung 1439). Moreover, the failure probability is lower because a central authority carefully manages infrastructural resources. However, at the Nash equilibrium, the prospect theory holds that resources have a higher likelihood of failure. Therefore, both travelers and urban planners are more likely to over-utilize resources. Furthermore, both parties are heterogeneous and have differing aversions to losing. The total exploitation of the transportation system is, however, higher since each party is allowed to make decisions based on their ability and willingness to avert a loss. Therefore, mere cooperation may not be in the parties’ best interests.

One of the most popular game theories, the prisoner’s dilemma, provides a framework for developing a better understanding of a balance reached between competition and cooperation, especially when making strategic decisions. Unlike most game theories, the prisoner’s dilemma suggests that mere cooperation is not always in the best interest of players (Doebeli and Christoph 748). For example, when travelers are seeking to elicit their governments to build a new road network or a bridge, calling for action through rallies may be the preferred course of action from the public’s perspectives. Otherwise, the government may adopt a policy of stubbornness in resource allocation in an attempt to maximize its utility, which in turn results in travelers not getting value for the taxes they pay.

            The primary basics in the prisoner’s dilemma that helps address the contradiction between traffic demand and traffic supply work by evaluating the best course of action using a payoff matrix. Table 1 shows the inherent payoffs in the prisoner’s dilemma which is depicted as the length of time each person is incarcerated, as symbolized by the negative sign. The assumption held is that the most desirable outcomes are those with a higher number (Doebeli, Michael, and Christoph 749). The terms cooperate have been used to refer to the suspects collaborating such as when none of them confesses while the term defect is used to indicate when they fail to cooperate such as when one party and the other does not.

Table 1.

The inherent payoffs in the prisoner’s dilemma (Source: Doebeli, Michael, and Christoph 751)

Prisoner’s Dilemma – Payoff MatrixSuspect B  
  CooperateDefect
Suspect ACooperate(a) -1, -1(c) -3, 0
 Defect(b) 0, -3(d) -2, -2

There are four possible outcomes in the prisoner’s dilemma. Firstly, if both suspects cooperate, they will each receive only one year in prison as seen in the cell (a). Secondly, when suspect A confesses and B cooperates, then the former will be released, and B will receive three years incarceration as seen in the cell (b). Thirdly, if suspect A fails to confess but B defects, then A will receive be incarcerated for three years while B will be set free as seen in the cell (c). Finally, if both suspects confess, then they all receive two years in prison as seen in the cell (d). The prisoner’s dilemma holds that the dominant strategy for each player is the one that yields the highest payoff irrespective of the strategy used by another player. Therefore, the dominant strategy in Table 1 is for each suspect to defect because it would help them minimize the amount of time they spend in prison. The prisoner’s dilemma can be applied to solve the contradiction between traffic demand and traffic supply because it shows that the outcome is often worse when each party pursues his or her self-interest than if they decide to cooperate (Doebeli, Michael, and Christoph 748). For example, by cooperating, both the travelers and urban planners will remain silent and maintain the status quo; therefore, the traffic confection will continue persisting.

The Solution to the Traffic Problem

Table 2.

The inherent payoffs between the travelers and urban planners

Travelers and Urban planners Payoff MatrixUrban planners  
 Travelers CollaborateDefect
Collaborate(a) 7, 7(c) 0,10
 Defect(b) 10, 0(d) 3, 3

            In reality, both the travelers and urban planners are rational people who are only interested in maximizing their utility and benefits. As such, each party would prefer to defect rather than cooperate. Table 2 shows the inherent payoffs between travelers and urban planners. The prisoner’s dilemma can be leveraged to assist in solving the traffic congestion problem by first identifying the utility whose payoff is a non-numerical attribute whereby the parties are satisfied with the deal (Doebeli, Michael, and Christoph 749). The primary assumption held is that the planners are seeking to get minimal traffic congestion while the travelers’ want to get the most convenient and savings from a trip. Consequently, if both parties agree to cooperate, there will be no negotiating which is much to the urban planners’ delight. On the contrary, defecting involves haggling with the urban planner using the least resources allocated to minimize traffic congestion while the travelers want to get the most sustainable and convenient infrastructure. By assigning numerical values to the individual levels of satisfaction for each party, the inherent payoffs between the travelers and the urban planners can be identified (Table 2). The numerical values assigned are 10, which mean one is fully satisfied with the deal and 0, which suggests that they are not satisfied.

Table 2 shows that if the travelers are more likely to be satisfied with the deal if they drive a hard bargain and get substantial savings and convenience from the trips. However, the planners may not be satisfied due to the financial loss incurred in meeting all the traveler’s needs as seen in cell b. On the contrary, if the planners remain firm and refuse to budge, the travelers may be unsatisfied with the deal, but the planners will be fully satisfied with the minimal traffic congestion achieved as seen in cell c. Consequently, the travelers’ satisfaction level is likely to be less if they gave in to the planners demands as seen in cell (a). Moreover, the planners are likely to be less satisfied since the travelers’ willingness to get the most convenient trip that minimizes traffic congestion may leave them wondering if they could have influenced the deal to maximize their utility. Cell (d) indicates that both the planners and travelers will be less satisfied by the prolonged haggling, which can potentially result in a reluctant compromise on their expectation.

Similarly, assuming that the travelers realize that more value can be achieved given the amount of taxes collected, then they would be ill-advised if they decide to take the first proposition that the planners make to them during the negotiations relating to resource allocation. Although cooperating to take the first offer often seems like the best and easiest solution in a heated negotiation, it may result in one of the party getting less than they deserve. On the contrary, defecting and deciding to negotiate may get one of the parties or both a better deal. However, one may be dissatisfied with the final offer when the sponsor is unwilling to pay more. If the contradiction between traffic demand and traffic supply persists, it may result in a lower level of satisfaction for both parties. The traveler-planner payoff matrix (Tab.1) can be further extended to reveal the satisfaction level for the traveler versus the planners.

The prisoner’s dilemma is an essential game appraised in game theory that demonstrates why two completely rational parties (travelers and planners) may prefer not to cooperate, even when doing so may be in their best interests. The game theory analysis suggests that mere cooperation between the travelers and planners may not be in either party’s interests. Consequently, when striving to achieve a balance between the planners’ expectation to get the minimal traffic congestion and the travelers’ expectation to get the most convenient and savings from a trip, collective bargaining may be the most favored course of action from the travelers’ perspective. As such, a solution to the contradiction between traffic demand and traffic supply is found whereby each party understands the relative payoffs of cooperating as opposed to defecting. Therefore, the different options available help stimulate each party’s decision to engage in significant negotiations before finally settling for a deal.

Conclusion

The discussions developed leverage the principal of game theory to explore the correlation between travel decision-making and public resource utilization. The game theory helps in modeling the prisoner’s dilemma for a real-world situation involving travelers cooperating with planners to ensure their expectations are taken into consideration in the final decision. As such, the problem of traffic congestion and overcrowding is solved because the planners’ objectives of ensuring there is minimal traffic congestion will be aligned with travelers’ expectation of getting the most convenient and savings from a trip.

Works Cited

Emil, Venere. “Game Theory Research Reveals Fragility of Common Resources.” Purdue University. (2016): n.d.  

Xu, X. and Yu, H., 2014. A Game Theory Approach to Fair and Efficient Resource Allocation in Cloud Computing. Mathematical Problems in Engineering2014.

Daskalakis, Constantinos, Paul W. Goldberg, and Christos H. Papadimitriou. “The complexity of computing a Nash equilibrium.” SIAM Journal on Computing, vol. 39, no. 1 (2009), pp. 195-259.   

Palomar, Daniel Pérez, and Mung Chiang. “A Tutorial on Decomposition Methods for Network Utility Maximization.” IEEE Journal on Selected Areas in Communications, vol. 24, no. 8 (2006), pp. 1439-1451.   

Doebeli, Michael, and Christoph Hauert. “Models of Cooperation Based on the Prisoner’s Dilemma and the Snowdrift Game.” Ecology Letters, vol. 8, no. 7 (2005), pp. 748-766.   

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