Multiagent Systems: Course Reader Errata

·        p. 105 It states that every behavioural strategy is also a mixed strategy. This is not true in general, as example on p. 106 shows. In general, for games of imperfect recall, there may exist mixed strategies that are not equivalent to any behavioural strategies, and vice versa, behavioural strategies not equivalent to any mixed strategy. That cannot happen in games of perfect recall.

·        p. 107 In the last paragraph, it should read "R dominates C", instead of "L dominates C". Also, it should read "player 1 should go R" instead of "player 1 should go D".

·        p. 111 The statement of the folk theorem is slightly wrong. The "only if" direction is fine. The "if" direction should be supplemented with: "(r₁,r₂) is a feasible payoff profile of G". A feasible payoff profile is a rational convex combination of outcome payoffs of G (That is a linear combination where coefficients are rational, non-negative, and sum to 1). Note that (r₁,r₂) is not necessarily a payoff profile of any strategy profile of G. Also, the folk theorem is not restricted to 2-player games. See handout #7 for the proof.

·        p. 112 Definition 3.5.3 should read "A Markov strategy...". Conversely, definition 3.5.4 should read "A stationary strategy s_i is a Markov strategy...".

·        p. 150 In the definition 5.1.3 of monotonic function, the part "(but leaving the orderings otherwise unchanged)" should not be there. All that matters for the condition of monotonicity is that o only moves up in preferences.

·        p. 150 Below Muller-Satterthwaite theorem, the sentence "This means it must not be non-monotonic" should read "This means it must be non-monotonic".