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Social Dilemma Analysis for Modeling Traffic Flow

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Evolutionary Games with Sociophysics

Part of the book series: Evolutionary Economics and Social Complexity Science ((EESCS,volume 17))

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Abstract

In this chapter, we concern ourselves with traffic flow as an example of an intrinsically dynamical system to which evolutionary game theory can be applied. The study of traffic flow was originally thought to be best explained using fluid dynamics in the mid-twentieth century, mainly in the field of civil engineering, owing to the recognition of traffic jams as a pressing urban problem. In the 1990s, complexity science, strongly supported by the rapid growth of computational resources, re-highlighted traffic-flow analysis with the concept of multi-agent simulation (MAS), allowing researchers to incorporate microscopic events, such as merging and branching lanes, lane-changing, and drivers’ decision-making characteristics, into simulations to better reproduce real traffic flows.

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Notes

  1. 1.

    Precisely speaking, it should be called “ultra-discrete”, as shown in Fig. 3.1. According to the convention in the fields of mathematics and physics, the term “discrete” has been used for digitalization for either ‘time’ or ‘space’. In the current discussion, the object to be digitalized is the body to be transferred.

  2. 2.

    With respect to the macroscopic concept, readers can consult the following text book: Haberman (1977).

  3. 3.

    Tanimoto et al. (2015).

  4. 4.

    Kerner called this plot the chattered area, with the region sandwiched between the free-flow phase and jam phase called the ‘synchronized phase’ He insisted that a real traffic-flow field must contain those three phases, and a phase transition from free to jam takes place via the synchronized phase (not F- > J directly but F- > S- > J). This is called Kerner’s three-phase theory; for details, readers can consult. Kerner (2009).

  5. 5.

    Payne (1971).

  6. 6.

    Jiang et al. (2002).

  7. 7.

    Bando et al. (1995).

  8. 8.

    Xue (2002).

  9. 9.

    There have been many works on this subject; a representative one is: Peng et al. (2011).

  10. 10.

    Wolfram (1983).

  11. 11.

    Takayasu and Takayasu (1993).

  12. 12.

    Nishinari and Takahashim (2000).

  13. 13.

    We suggest the following references: Nishinari and Takahashim (1998), Nishinari (2001), Tokihiro et al. (1996).

  14. 14.

    A reader can consult the following literature concerning ZRP and its exact solution. O’Loan et al. (1998).

  15. 15.

    Fukui and Ishibashi (1996).

  16. 16.

    Nagel and Chreckenberg (1992).

  17. 17.

    Kokubo et al. (2011).

  18. 18.

    Sakai et al. (2006).

  19. 19.

    Fukuda et al. (2016).

  20. 20.

    Many previous works have examined this question, including: Gundaliya et al. (2008), Tanaka et al. (2008), Lan et al. (2009).

  21. 21.

    Kerner and Klenov (2009).

  22. 22.

    Kukida et al. (2011).

  23. 23.

    Tadaki et al. (2013).

  24. 24.

    Whale et al. (2000).

  25. 25.

    Xiang and Xiong (2013).

  26. 26.

    Although we have not discussed the case of three alternative routes, we have confirmed that the general conclusion that can be drawn is basically the same as in the case of two routes, as reported herein.

  27. 27.

    Although not reported, we can extend the model for three or more alternative routes as mentioned in the text. In those cases, this part of our model was modified as in the text. If a defective vehicle chooses one route, but cannot enter it owing to a jam within five time-steps ahead, it instead takes the second-best route. Likewise, if a cooperative vehicle chooses one route but cannot enter it due to a jam ahead with five time-steps, it randomly takes one of the remaining alternative routes.

  28. 28.

    Tanimoto et al. (2014a).

  29. 29.

    Yamauchi et al. (2009).

  30. 30.

    Nakata et al. (2010).

  31. 31.

    Tanimoto et al. (2014b).

  32. 32.

    Arthur (1994).

  33. 33.

    Tanimoto and Sagara (2007a).

  34. 34.

    Wang et al. (2015).

  35. 35.

    Tanimoto and Sagara (2007b).

  36. 36.

    Wakiyama and Tanimoto (2011).

  37. 37.

    A set of Chicken-type games satisfying T + S > 2R, such as Leader and Hero games, have a feature that is different from the PD, where mixing of S and T shared by focal and opposing players can obtain a higher payoff than mutual Cs (or R), which is the best cooperative solution in PD (R-reciprocity). This unique feature of obtaining a high payoff by sharing S and T is called ST-reciprocity. In terms of direct reciprocity, ST-reciprocity seems to be as important as mutual cooperation in PD.

  38. 38.

    There have been many related works, one of which has been discussed in the previous section. Here, let us suggest another: Zhang and Chen (2012).

  39. 39.

    With respect to “sanction” in an evolutionary game, there has been a rich stock of previous works. A representative work is: Schoenmakers et al. (2014).

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  1. Graduate School of Engineering Sciences, Kyushu University, Fukuoka, Japan

    Jun Tanimoto

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Tanimoto, J. (2018). Social Dilemma Analysis for Modeling Traffic Flow. In: Evolutionary Games with Sociophysics. Evolutionary Economics and Social Complexity Science, vol 17. Springer, Singapore. https://doi.org/10.1007/978-981-13-2769-8_3

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  • DOI: https://doi.org/10.1007/978-981-13-2769-8_3

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