9 problems

In the fictitious-play setting, let $A\in\mathbb{R}^{n\times n}$ be the identity matrix, and consider the convergence rate measured by the relevant gap function. Karlin's conjectur…

Let a finite game be a weighted potential game, and consider a fictitious-play process in that game. Harris's conjecture. The rate of convergence of fictitious play is exponential…

Let $\{f_t\}_{t\geq 1}$ be the sequence of joint empirical frequencies generated by decentralized fictitious play (DFP) in a near-potential game, and let $C_{N\delta}$ denote the s…

A mean field game (MFG) is called monotone when it satisfies the monotonicity assumption used in the paper. In discrete time, let $t$ denote the iteration count and let the converg…

A finite potential game is a game admitting a potential function whose unilateral payoff changes agree with the corresponding changes in the potential; fictitious play (FP) is the…

Consider bimatrix games with a unique, completely mixed Nash equilibrium and their typical fictitious-play orbits. Average-payoff dominance conjecture. For most such games, typical…

Ostrovski's conjecture. Under these conditions, the Nash equilibrium does not Pareto dominate typical fictitious-play orbits. This conjecture gives a sufficient transition-combinat…

Consider the space of $n\times n$ bimatrix games with entries in $[0,1]$. Restrict attention to games with a unique, completely mixed Nash equilibrium and to typical fictitious-pla…

Let $(A,B)$ be a bimatrix game with a unique Nash equilibrium in the interior of the mixed-strategy space, and consider its continuous-time fictitious-play dynamics. Two bimatrix g…