  Significant controversy remains about what constitute correct self-locating
beliefs in scenarios such as the Sleeping Beauty problem, with proponents on
both the "halfer" and "thirder" sides. To attempt to settle the issue, one
natural approach consists in creating decision variants of the problem,
determining what actions the various candidate beliefs prescribe, and assessing
whether these actions are reasonable when we step back. Dutch book arguments
are a special case of this approach, but other Sleeping Beauty games have also
been constructed to make similar points. Building on a recent article (James
R.~Shaw. {\em De se} belief and rational choice. {\em Synthese},
190(3):491-508, 2013), I show that in general we should be wary of such
arguments, because unintuitive actions may result for reasons that are
unrelated to the beliefs. On the other hand, I show that, when we restrict our
attention to {\em additive} games, then a thirder will necessarily maximize her
{\em ex ante} expected payout, but a halfer in some cases will not (assuming
causal decision theory). I conclude that this does not necessarily settle the
issue and speculate about what might.

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