Related papers: EF equivalent not isomorphic models

For a family of multidimensional gambler models we provide formulas for the winning probabilities (in terms of parameters of the system) and for the distribution of game duration (in terms of eigenvalues of underlying one-dimensional…

In this paper, we use a unified framework introduced in [3] to study two classes of nonconforming immersed finite element (IFE) spaces with integral value degrees of freedom. The shape functions on interface elements are piecewise…

Wide machine learning tasks can be formulated as non-convex multi-player games, where Nash equilibrium (NE) is an acceptable solution to all players, since no one can benefit from changing its strategy unilaterally. Attributed to the…

We examine two isomorphisms between affine Hecke algebras of type $A$ associated with parameters $q^{-1}$, $t^{-1}$ and $q$, $t$. One of them maps the non-symmetric Macdonald polynomials $E_{\eta}(x;q^{-1},t^{-1})$ onto $E_{\eta}(x;q,t)$,…

Mean-field games have been studied under the assumption of very large number of players. For such large systems, the basic idea consists to approximate large games by a stylized game model with a continuum of players. The approach has been…

We adapt the classical notion of building models by games to the setting of continuous model theory. As an application, we study to what extent canonical operator algebras are enforceable models. For example, we show that the hyperfinite…

We introduce two new iteration games: the game G, which is a strengthening of the weak iteration game, and the game G+, which is somewhat stronger than G but weaker than the full iteration game of length omega_1. For a countable M…

Following the work of Lloyd Shapley on the Shapley value, and tangentially the work of Guillermo Owen, we offer an alternative non-probabilistic formulation of part of the work of Robert J. Weber in his 1978 paper "Probabilistic values for…

We discuss the back and forth technique in the context of presheaf model theory. The essence of the back and forth technique lies in showing the relationship between various hierarchies which calibrate similarity between two models and,…

We construct two abelian varieties over $\mathbb{Q}$ which are not isomorphic, but have isomorphic Mordell--Weil groups over every number field, isomorphic Tate modules and equal values for several other invariants.

Interesting connection has been established between two apparently unrelated concepts, namely, quantum nonlocality and Bayesian game theory. It has been shown that nonlocal correlations in the form of advice can outperform classical…

We show that it is not provable in ZFC that any two countable elementarily equivalent structures have isomorphic ultrapowers relative to some ultrafilter on omega .

We investigate Maker-Breaker games on graphs of size $\aleph_1$ in which Maker's goal is to build a copy of the host graph. We establish a firm dependence of the outcome of the game on the axiomatic framework. Relating to this, we prove…

We initiate the study of the phantom version of Maker-Breaker positional games. In a phantom game, the moves of one of the players are hidden from the other player, who still has the complete information. We look at the biased $(a:b)$…

Let $\mathcal{M}$ be a von Neumann algebra equipped with a faithful semifinite normal weight $\phi$ and $\mathcal{N}$ be a von Neumann subalgebra of $\mathcal{M}$ such that the restriction of $\phi$ to $\mathcal{N}$ is semifinite and such…

While fictitious play is guaranteed to converge to Nash equilibrium in certain game classes, such as two-player zero-sum games, it is not guaranteed to converge in non-zero-sum and multiplayer games. We show that fictitious play in fact…

Energy parity games are infinite two-player turn-based games played on weighted graphs. The objective of the game combines a (qualitative) parity condition with the (quantitative) requirement that the sum of the weights (i.e., the level of…

We develop methods to formally describe and compare games, in order to probe questions of game structure and design, and as a stepping stone to predicting player behavior from design patterns. We define a grammar-like formalism to describe…

Ehrenfeucht-Fra\"iss\'e games provide a fundamental method for proving elementary equivalence (and equivalence up to a certain quantifier rank) of relational structures. We investigate the soundness and completeness of this method in the…

We present an example of symmetric ergodic $N$-players differential games, played in memory strategies on the position of the players, for which the limit set, as $N\to +\infty$, of Nash equilibrium payoffs is large, although the game has a…