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A positional game for an overlapping generation economy


  • Ahmad Naimzada
  • Marina Pireddu


We develop a model with intra-generational consumption externalities, based on the overlapping generation version of Diamond (1965) model. More specifically, we consider a two-period lived overlapping generation economy, assuming that the utility of each consumer depends also on the average level of consumption by other consumers in the same generation. In this way we obtain a positional game embedded in an overlapping generation economy. We characterize the consumption and saving choices for the two periods in the Nash equilibrium path and we determine a dynamic equation for capital accumulation coherent with the agents' choices in the Nash equilibrium. Hence, also the behavior, both static and dynamic, described by the equation for the capital accumulation is coherent with the Nash equilibrium. For the associated dynamical system we find a unique positive steady state for capital, which is globally stable. Its position is decreasing with respect to positive variations in the degree of interaction in the first period, while the opposite relation holds in the second period. We then compare the steady states for capital with and without social interaction. In this respect we show that the steady state with social interaction is larger than the steady state in the absence of social interaction if and only if the degree of interaction in the second period exceeds the degree of interaction in the first period. In particular, if the degrees of interaction in the two periods coincide, the dynamical system is equivalent to the one without social interaction.

Suggested Citation

  • Ahmad Naimzada & Marina Pireddu, 2013. "A positional game for an overlapping generation economy," Working Papers 247, University of Milano-Bicocca, Department of Economics, revised Jun 2013.
  • Handle: RePEc:mib:wpaper:247

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    References listed on IDEAS

    1. Lahiri, Amartya & Puhakka, Mikko, 1998. "Habit Persistence in Overlapping Generations Economies under Pure Exchange," Journal of Economic Theory, Elsevier, vol. 78(1), pages 176-186, January.
    2. de la Croix, David, 1996. "The dynamics of bequeathed tastes," Economics Letters, Elsevier, vol. 53(1), pages 89-96, October.
    3. Bunzel, Helle, 2006. "Habit persistence, money, and overlapping generations," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2425-2445, December.
    4. Carole Uhlaner, 1989. "“Relational goods” and participation: Incorporating sociability into a theory of rational action," Public Choice, Springer, vol. 62(3), pages 253-285, September.
    5. H. Leibenstein, 1950. "Bandwagon, Snob, and Veblen Effects in the Theory of Consumers' Demand," The Quarterly Journal of Economics, Oxford University Press, vol. 64(2), pages 183-207.
    6. Rauscher, Michael, 1993. "Demand for social status and the dynamics of consumer behavior," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 22(2), pages 105-113.
    7. Rauscher, Michael, 1992. "Keeping up with the Joneses : Chaotic patterns in a status game," Economics Letters, Elsevier, vol. 40(3), pages 287-290, November.
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    More about this item


    Positional game; overlapping generations; consumption externalities;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D91 - Microeconomics - - Micro-Based Behavioral Economics - - - Role and Effects of Psychological, Emotional, Social, and Cognitive Factors on Decision Making
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth
    • O41 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - One, Two, and Multisector Growth Models

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