 
Summary: Distributed Computing Meets Game Theory:
Combining Insights From Two Fields
Ittai Abraham Lorenzo Alvisi Joseph Y. Halpern
MSR Silicon Valley UT Austin Cornell University
ittaia@microsoft.com lorenzo@cs.utexas.edu halpern@cs.cornell.edu
Traditionally fault tolerance and security have divided processes into "good guys" and "bad guys". Work
on fault tolerance has focused on assuring that certain goals are met, as long as the number of "bad guys" is
bounded (e.g., less than one third or one half of the total number of players).
The viewpoint in game theory has been quite different. There are no good guys or bad guys, only rational
players who will make moves in their own selfinterest. Making this precise requires assigning payoffs
(or utilities) to outcomes. There are various solution concepts in game theorypredictions regarding the
outcome of a game with rational players. They all essentially involve players making best responses to their
beliefs, but differ in what players are assumed to know about what the other players are doing. Perhaps the
bestknown and most widelyused solution concept is Nash equilibrium (NE). A profile of strategiesthat
is, a collection of strategies consisting of one strategy i for each player iis a Nash equilibrium if no player
can improve his payoff by changing his strategy unilaterally, even assuming that he knows the strategies of
all the other players. In the notation traditionally used in game theory, is a Nash equilibrium if, for all i
and all strategies i for player i, ui(i, i) ui(): player i does not gain any utility by switching to i if
all the remaining players continue to play their component of . (See a standard game theory text, such as
[23], for an introduction to solution concepts, and more examples and intuition.)
