Algorithmic Game Theory Summer 2015 , Week 1 Game Theory

• Si is the set of (pure) strategies of player i, • S = ∏ i∈N Si is the set of states, • ci : S → R is the cost function of player i ∈ N . In state s ∈ S, player i has a cost of ci(s). We denote by s−i = (s1, ..., si−1, si+1, ..., sn) a state s without the strategy si. This notation allows us to concisely define a unilateral deviation of a player. For i ∈ N , let s ∈ S and si ∈ Si, then (si, s−i) = (s1, . . . , si−1, si, si+1, . . . , sn).