Elsevier

Games and Economic Behavior

Volume 76, Issue 1, September 2012, Pages 349-353
Games and Economic Behavior

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Characterization of the von Neumann–Morgenstern stable set in a non-cooperative model of dynamic policy-making with a persistent agenda setter

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Abstract

We generalize the dynamic bargaining game of Diermeier and Fong (2011) to arbitrary quota rules to provide a non-cooperative characterization of the von Neumann–Morgenstern stable set. Assuming that players are sufficiently patient and have strict preferences, a pure-strategy stationary equilibrium exists and in any such equilibrium, a policy is a steady state if and only if it is in the stable set. The result provides a non-cooperative foundation of stable sets in settings with dynamic policy-making and a persistent agenda setter.

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    Stable sets have been found on several classes of games, such as assignment games (Núñez and Rafels, 2013), linear production games (Rosenmüller and Shitovitz, 2000, 2010), pillage games (MacKenzie et al., 2015), patent licensing games (Hirai and Watanabe, 2018), matching problems (Herings et al., 2017), tournaments (Brandt, 2011), voting games (Talamàs, 2018), and exchange economies (Graziano et al., 2015, 2017). Non-cooperative foundations of stable sets have been shown by Anesi (2010); Diermeier and Fong (2012). More farsighted notions of stable sets have been related to the core by Einy (1996); Bhattacharya and Brosi (2011); Ray and Vohra (2015); Hirai et al. (2019).

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    We apply our analysis of ergodic properties of equilibria to show that all equilibria are essentially pure, and we again obtain the equivalence between equilibrium absorbing points and von Neumann–Morgenstern solutions. Thus, we extend Theorem 1 of Diermeier and Fong (2012) by generalizing the quota rules to an arbitrary voting rule and by removing the restriction to pure strategy equilibria. Noncooperative foundations for von Neumann–Morgenstern solutions in political economy have been investigated in several different institutional settings, including electoral competition (Anesi, 2012) and committee voting (Anesi and Seidmann, 2014).

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We thank Roger Myerson for suggesting this line of inquiry. The work described in this paper was partially supported by a grant from City University of Hong Kong (Project No. 7200214). All errors are our own.

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