Trembling Hand Equilibria of Plurality Voting

Trembling hand (TH) equilibria were introduced by Selten in 1975. Intuitively, these are Nash equilibria that remain stable when players assume that there is a small probability that other players will choose off-equilibrium strategies. This concept is useful for equilibrium refinement, i.e., selecting the most plausible Nash equilibria when the set of all Nash equilibria can be very large, as is the case, for instance, for Plurality voting with strategic voters. In this paper, we analyze TH equilibria of Plurality voting. We provide an efficient algorithm for computing a TH best response and establish many useful properties of TH equilibria in Plurality voting games. On the negative side, we provide an example of a Plurality voting game with no TH equilibria, and show that it is NP-hard to check whether a given Plurality voting game admits a TH equilibrium where a specific candidate is among the election winners.

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