We study a nonzero-sum game in which two players label the N vertices of a path as being either Knights (i.e., truth-tellers) or Knaves (i.e., liars). Each vertex utters the sentence “An even number of my neighbors are Knights” and can be consistent (the truth value of its sentence agrees with its type) or inconsistent. The Knight player favors consistent vertices and the Knave player inconsistent ones. After characterizing the pure Nash equilibria of the game, we concentrate on the study of best-response dynamics. It turns out that these are the dynamics of a Rule 90 affine cellular automaton: x(t+1)=ANx(t)+dN, where AN is the adjacency matrix of the N-path and the arithmetic is performed in the Galois field F2. Using the characteristic polynomial of AN, we study the properties of the best response dynamics with special emphasis on its periodic behavior.
This work introduces an independently randomized formulation in which each stopping rule is represented by an adapted, nondecreasing cumulative stopping process, and identifies an exact-potential subclass with a closed-form threshold equilibrium.
We introduce an uncoupled learning algorithm which, when employed by all players of an arbitrary $N$-player normal form game with up to $K$ actions per player, guarantees $O(N^3\log^2 K)$ individual regret, uniformly over the horizon of play. The proposed algorithm - which we call higher-order optimism with discounting...
Omar Abbadi, R. Laraki, P. Mertikopoulos· 4 citations· ⚡4
Let f be a labeling of the edges of a finite graph G by positive integers, and let the weight of a path be the sum of the labels of its edges. The labeling is a geodesic Leech labeling if the weights of the geodesics are exactly 1, 2, ..., t_gp(G), each occurring once, where t_gp(G) is the geodesic path number of G. Le...
The complexity of IVF(C)CEs in succinct games, which model more realistic strategic interactions that feature either many players or exponentially many pure strategies, is examined, showing that it is at least as hard as the P-matrix linear complementarity problem, and hence as hard as simple stochastic games.
In the study of Nash equilibria of finite-player games, one often seeks equilibria that are compatible with predetermined constraints, either determined by the players or by an external agent. We discuss the algebraic loci, called Nash loci, of games whose Nash equilibrium scheme intersects a fixed algebraic variety in...
Luca Sodomaco, Julian Weigert· 0 citations
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