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Sunspot equilibrium in positive recursive general quitting games

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Abstract

We prove that positive recursive general quitting games, which are quitting games in which (a) each player has a single quitting action and possibly several continue actions, (b) the stage payoff as long as quitting does not occur is 0, and (c) the payoff when quitting occurs is non-negative, admit a sunspot \(\varepsilon \)-equilibrium, for every \(\varepsilon > 0\).

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Notes

  1. Note that since \(\mathrm{\mathbf{P}}_{{\widehat{\xi }}}(t_* < \infty ) = 1\), the payoff \(\gamma _{\alpha ,r}^E({\widehat{\xi }})\) is independent of r, the payoff if quitting does not occur.

  2. The fact that the auxiliary quitting game \(\Gamma _{s,r}\) admits stationary 0-equilibria for every \(s \in [0,1]\) is due to a careful choice of the payoff function. In general, stationary 0-equilibria need not exist in all auxiliary quitting games.

  3. For the definition of Q-matrices see Remark 3.

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Acknowledgements

The authors thank Hari Govindan, Ehud Lehrer, John Levy, and Eugenii Shustin for valuable discussions, and the anonymous referees for comments that improved the presentation. E. Solan acknowledges the support of the Israel Science Foundation, grant #217/17.

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  1. The School of Mathematical Sciences, Tel Aviv University, 6997800, Tel Aviv, Israel

    Eilon Solan & Omri N. Solan

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  1. Eilon Solan
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  2. Omri N. Solan
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Correspondence to Eilon Solan.

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Solan, E., Solan, O.N. Sunspot equilibrium in positive recursive general quitting games. Int J Game Theory 50, 891–909 (2021). https://doi.org/10.1007/s00182-021-00773-1

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