Game Development Reference
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fraction of players in a system to be 'good' and follow the recommended
protocol, even if it is not a best reply. In general, it may be hard to figure
out what the best reply is, so if following the recommended protocol is
not unreasonable, they will do that. (Note that this can be captured in a
computational model of equilibrium, by charging for switching from the
recommended strategy.)
There may be other standard ways that players act irrationally. For
example, Kash, Friedman, and I [2007] consider scrip systems , where
players perform work in exchange for scrip. There is a Nash equilibrium
where everyone uses a threshold strategy , performing work only when
they have less scrip than some threshold amount. Two standard ways of
acting 'irrationally' in such a system are to (a) hoard scrip and (b) provide
service for free (this is the analogue of posting music on Kazaa). A robust
solution should take into account these more standard types of irrational
behaviour, without perhaps worrying as much about arbitrary irrational
behaviour.
The definitions of computational Nash equilibrium considered only Bayes-
ian games. What would appropriate solution concepts be for extensive-
form games? Some ideas from the work on awareness seem relevant here,
especially if we think of 'lack of awareness' as 'unable to compute'.
Where do the beliefs come from in an equilibrium with awareness? That
is, if I suddenly become aware that you can make a certain move, what
probability should I assign to you making that move? Ozbay [2007]
proposes a solution concept where the beliefs are part of the solution
concept. He considers only a simple setting, where one player is aware
of everything (so that revealing information is purely strategic). Can
his ideas be extended to a more general setting?
Agents playing a game can be viewed participating in a concurrent,
distributed protocol. Game theory does not take the asynchrony into
account, but it can make a big difference. For example, all the results
from [Abraham et al., 2006, 2008] mentioned in Section 8.2 depend on the
system being synchronous. Things are more complicated in asynchronous
settings. Getting solution concepts that deal well with asynchrony is
clearly important.
Another issue that plays a major role in computer science but has thus
far not been viewed as significant in game theory, but will, I believe,
turn out to be important to the problem of defining appropriate solution
concepts, is the analogue of specifying and verifying programs. Games
are typically designed to solve certain problems. Thus, for example,
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