A Formal Separation Between Strategic and Nonstrategic Behavior - PowerPoint PPT Presentation


 A Formal Separation Between Strategic and Nonstrategic Behavior James R. Wright 
 Alberta Machine Intelligence Institute 
 University of Alberta 
 Joint work with Kevin Leyton-Brown (UBC) Contributions: 1. A formal definition of strategic behavior that is not equivalent to perfect rationality 2. A constructive characterization that precisely distinguishes between strategic and nonstrategic behavior

Strategic vs. Nonstrategic Agents • Behavioral game theorists often model boundedly rational agents (e.g., humans) using iterative models such as the level- k model : ⏟ • Level-0 agents: behave uniformly at random Nonstrategic • Level-1 agents: best respond to level-0 agents • Level-2 agents: best respond to level-1 agents Strategic ⋮ Uniform a i ∈ A i randomization Question: What kinds of other behavior "count" as nonstrategic? i [ min u i ( a i , a − i ) ] Maxmin a i ∈ arg max a ′ � a − i i [ max u i ( a i , a − i ) ] Maxmax a i ∈ arg max • Most work argues heuristically for certain rules a ′ � a − i Max total payoffs a − i ∑ a i ∈ arg max max u j ( a i , a − i ) a ′ � i j • (truthful reporting, largest number, etc.) i , a − i ) ] i [ min Min unfairness* a i ∈ arg min u − i ( a ′ � i , a − i ) − u i ( a ′ � a ′ � a − i Nash equilibrium { a i ∣ ∃ a − i : ( a i , a − i ) is Nash equilibrium }

Strategic Agents Definition: A behavioral model is strategic if it is both other responsive and dominance responsive . Definition: 
 A behavioral model is dominance responsive if, for every pair of games where some action is strictly dominant in one game and strictly dominated in the other, the model does not behave identically: f i ( G ) ≠ f i ( G ′ � ) ∀ G , G ′ � with a * i dominant in G and dominated in G ′ � Definition: 
 A behavioral model is other responsive if there exists any pair of games that differ only in the payoffs of the other agents in which the model predicts different behavior: ∃ G , G ′ � : f i ( G ) ≠ f i ( G ′ � ) ∧ ∀ a ∈ A : u i ( a ) = u ′ � i ( a ) Theorem: All of QRE , Nash equilibrium , correlated equilibrium, cognitive hierarchy , and level-k (*) are (profiles of) strategic behavioral models.

Elementary Behavioral Models Definition: 
 h ( Φ ) G a,b c,d e,f A behavioral model is elementary if it can be f i represented as , where: f i ( G ) = h ( Φ ( G )) g,h i,j k,l • for all games , for all , G = ( N , A , u ) a ∈ A m,n o,p q,r , Φ ( G ) a = φ ( u ( a )) satisfies no smuggling , and • (a,b) (c,d) (e,f) φ Φ φ φ φ ℝ A → Δ ( A i ) is an arbitrary function that maps h • (g,h) (i,j) (k,l) φ φ φ (m,n) (o,p) (q,r) φ φ φ Main Theorem: No elementary behavioral model f ( G ) is strategic . f i same φ