Abstract
This paper investigates absorption and global accessibility under perfect foresight dynamics in games with linear incentives. An action distribution in the society is absorbing if there is no equilibrium path escaping from the distribution, and globally accessible if, from every initial distribution, there exists an equilibrium path which converges to the distribution. Using time symmetry of the dynamics, we show that every absorbing strict Nash equilibrium, if it exists, is globally accessible under zero rate of time preference. With the additional assumption of supermodularity, we prove that there generically exists an absorbing strict Nash equilibrium. Relations with a global game and a reaction-diffusion model also become clear.
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The definition of absorption used in this paper is slightly different from the original one in Matsui and Matsuyama (1995). This difference is neglected in Sect. 1, and will be discussed in Sect. 2.2.
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Takahashi, S. Perfect foresight dynamics in games with linear incentives and time symmetry. Int J Game Theory 37, 15–38 (2008). https://doi.org/10.1007/s00182-007-0101-6
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DOI: https://doi.org/10.1007/s00182-007-0101-6