On positionality of trigger strategies Nash Equilibria in SCAR

10/25/2019

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by   George Konstantinidis, et al.

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We study the positionality of trigger strategies Nash equilibria σ for the N-player SCAR games Γ_N(G|s_0,γ,ε) (with N≥3). Our study is exhaustive with respect to types of graphs G, initial states s_0 and values of N,γ,ε. We conclude that in the majority of cases, profiles σ are nonpositional. Whenever σ are positional a key role is played by paths and the ε, γ values (especially whether ε>0 or not). A crucial concept in our analysis is the state cop number, which is first introduced in the current paper.