This paper studies how to compute optimal strategies to commit to under both commitment to pure strategies and commitment to mixed strategies, in both normal-form and Bayesian games.
This article characterize the exact number of candidates for which manipulation becomes hard for the plurality, Borda, STV, Copeland, maximin, veto, plurality with runoff, regular cup, and randomized cup protocols and shows that for simpler manipulation problems, manipulation cannot be hard with few candidates.
AWESOME is presented, the first algorithm that is guaranteed to have the two properties in games with arbitrary numbers of actions and players and it is still the only algorithm that does so while only relying on observing the other players' actual actions (not their mixed strategies).
Focusing-on settings where side payments are not possible, it is shown that the mechanism design problem is NP-complete for deterministic mechanisms and if the authors allow randomized mechanisms, the mechanisms design problem becomes tractable.
A single reduction demonstrates NP- hardness of determining whether Nash equilibria with certain natural properties exist, and demonstrates the NP-hardness of counting NashEquilibria (or connected sets of Nash Equilibria).
It is proved that for Copeland, maximin, Bucklin, and ranked pairs, the possible winner problem is NP-complete; also, a sufficient condition on scoring rules is given for the possiblewinner problem to be NP- complete (Borda satisfies this condition).
Improved bounding techniques are provided based on cycles in the pairwise majority graph, others are based on linear programs, and the relative strength of all of these bounds is characterized.
The communication complexity of the common voting rules is determined by giving a deterministic communication protocol and an upper bound on the number of bits communicated in it; then, a lower bound on (even the nondeterministic) communication requirements of the voting rule is given.
Voting is a very general method of preference aggregation that takes as input every voter's vote, and produces as output either just the winning alternative or a ranking of the alternatives.
It is shown that the Nash equilibria in security games are interchangeable, thus alleviating the equilibrium selection problem and proposed an extensive-form game model that makes the defender's uncertainty about the attacker's ability to observe explicit.