ISSN 0253-2778

CN 34-1054/N

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Open AccessOpen Access JUSTC Original Paper

Optimal pricing based on customers perceived values of products

  • School of Management, University of Science and Technology of China, Hefei 230026, China

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2015.06.012
  • Received Date: 31 March 2015
  • Accepted Date: 27 May 2015
  • Rev Recd Date: 27 May 2015
  • Publish Date: 30 June 2015
    Abstract

  • Abstract

    Different customers attach different perceived values to the same products. And a customer chooses a firm based on such a difference in perceived values and his rational expectation of the firms product availability. In a monopoly market, a firms optimal quantity and product availability increase with its optimal price. Due to the non-monotonicity of distribution density from customers perceived values, a firms local optimal price is not necessarily equal to its global optimal price. In a competitive market with n firms, the pure Nash equilibrium result was solved and its uniqueness proved. When n is finite, firms may adopt different optimal prices, and all firms achieve the same optimal profit expect in two special conditions. However, when n is infinite, all firms share a same optimal profit in equilibrium.

    Abstract

    Different customers attach different perceived values to the same products. And a customer chooses a firm based on such a difference in perceived values and his rational expectation of the firms product availability. In a monopoly market, a firms optimal quantity and product availability increase with its optimal price. Due to the non-monotonicity of distribution density from customers perceived values, a firms local optimal price is not necessarily equal to its global optimal price. In a competitive market with n firms, the pure Nash equilibrium result was solved and its uniqueness proved. When n is finite, firms may adopt different optimal prices, and all firms achieve the same optimal profit expect in two special conditions. However, when n is infinite, all firms share a same optimal profit in equilibrium.
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    • References(15)
  • [1]
    Hammons A R, Kumar P V, Calderbank A R, et al. The Z4-linearity of Kerdock, Preparata, Goethals, and related codes[J]. IEEE Trans Inform Theory, 1994, 40(2): 301-319.
    [2]
    Bonnecaze A, Udaya P. Cyclic codes and self-dual codes over F2+uF2 [J]. IEEE Trans Inform Theory, 1999, 45(4): 1 250-1 255.
    [3]
    Qian J F, Zhang L N, Zhu S X. Cyclic codes over Fp+uFp+…+uk－1Fp[J]. IEICE Transaction on Foundamentals of Electronics, Communications and Computer Sciences, 2005, 88(3): 795-797.
    [4]
    Abualrub T, Siap I. Cyclic codes over the rings Z2+uZ2 and Z2+uZ2+u2Z2 [J]. Des Codes Cryptogr, 2007, 42: 273-287.
    [5]
    Qian J F, Zhang L N, Zhu S X. (1+u)-constacyclic and cyclic codes over F2+uF2 [J]. Appl Math Lett, 2006, 19: 820-823.
    [6]
    Abualrub T, Siap I. Constayclic codes over F2+uF2 [J]. J Franklin Inst, 2009, 346: 520-529.
    [7]
    Kai X S, Zhu S X, Li P. (1+λu)-constacyclic codes over Fp[u]/〈uk〉[J]. J Franklin Inst, 2010, 347: 751-762.
    [8]
    Dinh H Q, Nguyen H D T. On some classes of constacyclic codes over polynomial residue rings[J]. Advances in Mathematics of Communications, 2012, 6(2):175-191.
    [9]
    Shi Minjia, Zhu Shixin. Constacyclic codes over ring Fp+uFp+…+us－1Fp [J]. Journal of University of Science and Technology of China, 2009,39(6):583-587.
    施敏加,朱士信. 环Fp+uFp+…+us－1Fp上的常循环码[J]. 中国科学技术大学学报, 2009,39(6):583-587.
    [10]
    Guenda K, Gulliver T A. Repeated root constacyclic codes of length mps over Fpr+uFpr+…+ue－1Fpr[J]. J Algebra Appl, 2015, 14(1):1450081.
    [11]
    Dinh H Q, Wang L Q, Zhu S X. Negacyclic codes of length 2psover Fpm+uFpm[J]. Finite Fields Appl, 2015, 31:178-201.
    [12]
    Shi Minjia, Yang Shanlin, Zhu Shixin. The distributions of distances of (1+u)-constacyclic codes of length 2s over ring F2+uF2+…+uk－1F2[J]. Journal of Electronics & Information Technology, 2010, 32(1):112-116.
    施敏加, 杨善林, 朱士信. 环F2+uF2+…+uk－1F2上长为2s的(1+u)常循环码的距离分布[J]. 电子与信息学报, 2010, 32(1):112-116.
    [13]
    Shi Minjia, Yang Shanlin, Zhu Shixin. The distance of cyclic codes of length 2s over ring F2+uF2 [J]. Acta Electronic Sinica, 2011, 39(1):29-34.
    施敏加, 杨善林, 朱士信. 环F2+uF2上长度为2s的循环码的距离[J]. 电子学报, 2011, 39(1):29-34.
    [14]
    Huang Lei, Zhu Shixin. Negacyclic codes of arbitrary lengths over the ring Fq+uFq+u2Fq[J]. Journal of University of Science and Technology of China, 2014, 44(12):991-995.
    黄磊,朱士信. 环Fq+uFq+u2Fq上任意长度的负循环码[J]. 中国科学技术大学学报, 2014,44(12):991-995.
    [15]
    Abhay K S, Pramod K K. On cyclic codes over the ring Zp[u]/〈uk〉[J]. Des Codes Cryptogr, 2015, 74(1): 1-13.
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    [1]
    Hammons A R, Kumar P V, Calderbank A R, et al. The Z4-linearity of Kerdock, Preparata, Goethals, and related codes[J]. IEEE Trans Inform Theory, 1994, 40(2): 301-319.
    [2]
    Bonnecaze A, Udaya P. Cyclic codes and self-dual codes over F2+uF2 [J]. IEEE Trans Inform Theory, 1999, 45(4): 1 250-1 255.
    [3]
    Qian J F, Zhang L N, Zhu S X. Cyclic codes over Fp+uFp+…+uk－1Fp[J]. IEICE Transaction on Foundamentals of Electronics, Communications and Computer Sciences, 2005, 88(3): 795-797.
    [4]
    Abualrub T, Siap I. Cyclic codes over the rings Z2+uZ2 and Z2+uZ2+u2Z2 [J]. Des Codes Cryptogr, 2007, 42: 273-287.
    [5]
    Qian J F, Zhang L N, Zhu S X. (1+u)-constacyclic and cyclic codes over F2+uF2 [J]. Appl Math Lett, 2006, 19: 820-823.
    [6]
    Abualrub T, Siap I. Constayclic codes over F2+uF2 [J]. J Franklin Inst, 2009, 346: 520-529.
    [7]
    Kai X S, Zhu S X, Li P. (1+λu)-constacyclic codes over Fp[u]/〈uk〉[J]. J Franklin Inst, 2010, 347: 751-762.
    [8]
    Dinh H Q, Nguyen H D T. On some classes of constacyclic codes over polynomial residue rings[J]. Advances in Mathematics of Communications, 2012, 6(2):175-191.
    [9]
    Shi Minjia, Zhu Shixin. Constacyclic codes over ring Fp+uFp+…+us－1Fp [J]. Journal of University of Science and Technology of China, 2009,39(6):583-587.
    施敏加,朱士信. 环Fp+uFp+…+us－1Fp上的常循环码[J]. 中国科学技术大学学报, 2009,39(6):583-587.
    [10]
    Guenda K, Gulliver T A. Repeated root constacyclic codes of length mps over Fpr+uFpr+…+ue－1Fpr[J]. J Algebra Appl, 2015, 14(1):1450081.
    [11]
    Dinh H Q, Wang L Q, Zhu S X. Negacyclic codes of length 2psover Fpm+uFpm[J]. Finite Fields Appl, 2015, 31:178-201.
    [12]
    Shi Minjia, Yang Shanlin, Zhu Shixin. The distributions of distances of (1+u)-constacyclic codes of length 2s over ring F2+uF2+…+uk－1F2[J]. Journal of Electronics & Information Technology, 2010, 32(1):112-116.
    施敏加, 杨善林, 朱士信. 环F2+uF2+…+uk－1F2上长为2s的(1+u)常循环码的距离分布[J]. 电子与信息学报, 2010, 32(1):112-116.
    [13]
    Shi Minjia, Yang Shanlin, Zhu Shixin. The distance of cyclic codes of length 2s over ring F2+uF2 [J]. Acta Electronic Sinica, 2011, 39(1):29-34.
    施敏加, 杨善林, 朱士信. 环F2+uF2上长度为2s的循环码的距离[J]. 电子学报, 2011, 39(1):29-34.
    [14]
    Huang Lei, Zhu Shixin. Negacyclic codes of arbitrary lengths over the ring Fq+uFq+u2Fq[J]. Journal of University of Science and Technology of China, 2014, 44(12):991-995.
    黄磊,朱士信. 环Fq+uFq+u2Fq上任意长度的负循环码[J]. 中国科学技术大学学报, 2014,44(12):991-995.
    [15]
    Abhay K S, Pramod K K. On cyclic codes over the ring Zp[u]/〈uk〉[J]. Des Codes Cryptogr, 2015, 74(1): 1-13.
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