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Static and dynamic equilibria in noisy binary choice (Ising) games on complete and random graphs in the annealed approximation are analysed. Two versions, an Ising game with interaction term defined in accordance with the Ising model in statistical physics and a reduced Ising game with a customary definition of interaction term in game theory on graphs, are considered. A detailed analysis of hysteresis phenomenon shaping the pattern of static equilibria based on consideration of elasticity with respect to external influence is conducted. Fokker-Planck equations describing dynamic versions of the games under consideration are written and their asymptotic stationary solutions derived. It is shown that domains of parameters corresponding to the maxima of these probability distributions are identical with the corresponding hysteresis ranges for static equilibria. Same result holds for domains defining local stability of solutions of the evolution equations for the moments. In all the cases considered it is shown that the results for the reduced Ising game coincide with those obtained for the Ising game on complete graphs. It is shown that for s special case of logistic noise the results obtained for static equilibria for the Ising game reproduce those in the Ising model on graphs in statistical physics., Comment: arXiv admin note: substantial text overlap with arXiv:1912.09584

Static and dynamic equilibria in noisy binary choice games on graphs are considered. Equations defining static quantal response equilibria (QRE) for binary choice games on graphs with arbitrary topology and noise distribution are written. It is shown that in the special cases of complete graph and arbitrary noise distribution, and circular and star topology and logistic noise distribution the resulting equations can be cast in the form coinciding with that derived in the earlier literature. Explicit equations QRE for non-directed graphs in the annealed approximation are derived. It is shown that the resulting effect on the phase transition is the same as found in the literature on phase transition in the Ising model on graphs in the same approximation.Evolutionary noisy binary choice game having the earlier described QRE as its stationary equilibria in the mean field approximation is constructed using the formalism of master equation., Comment: 15 pages and no figures

The paper provides consistent mathematical framework for seminal Tiebout free-mobility model (1956). Our setting supports continuum of consumers with multidimensional preferences and finite number of strategic public good providers. We accommodate the most general assumptions: providers' production function may have variable returns to scale, our framework is rich enough to incorporate possible externalities, spillovers, scale economies, network effects, etc.; consumers utility may depend on choice of other agents in almost arbitrary way. We focus on equilibrium existence, however the questions of efficiency and stability are not left behind. The model can also be applied in several related fields, most notably in political economy., Comment: 25 pages, 1 figure