Related papers: Inverse maximum theorems and some consequences

We deal with the generalized Nash game proposed by Rosen, which is a game with strategy sets that are coupled across players through a shared constraint. A reduction to a classical game is shown, and as a consequence, Rosen's result can be…

Under what conditions do the behaviors of players, who play a game repeatedly, converge to a Nash equilibrium? If one assumes that the players' behavior is a discrete-time or continuous-time rule whereby the current mixed strategy profile…

In game theory, the concept of Nash equilibrium reflects the collective stability of some individual strategies chosen by selfish agents. The concept pertains to different classes of games, e.g. the sequential games, where the agents play…

This paper presents a general closed graph property for (randomized strategy) Nash equilibrium correspondence in large games. In particular, we show that for any large game with a convergent sequence of fiinite-player games, the limit of…

In this article, we consider generalized Nash games where the associated constraint map is not necessarily self. The classical Nash equilibrium may not exist for such games and therefore we introduce the notion of best approximate solution…

We show that under some general conditions the finite memory determinacy of a class of two-player win/lose games played on finite graphs implies the existence of a Nash equilibrium built from finite memory strategies for the corresponding…

The paper studies the convergence, as $N$ tends to infinity, of a system of $N$ coupled Hamilton-Jacobi equations, the Nash system. This system arises in differential game theory. We describe the limit problem in terms of the so-called…

We show that under some general conditions the finite memory determinacy of a class of two-player win/lose games played on finite graphs implies the existence of a Nash equilibrium built from finite memory strategies for the corresponding…

A fundamental problem with the Nash equilibrium concept is the existence of certain "structurally deficient" equilibria that (i) lack fundamental robustness properties, and (ii) are difficult to analyze. The notion of a "regular" Nash…

There are only limited classes of multi-player stochastic games in which independent learning is guaranteed to converge to a Nash equilibrium. Markov potential games are a key example of such classes. Prior work has outlined sets of…

Recently, invariant risk minimization (IRM) (Arjovsky et al.) was proposed as a promising solution to address out-of-distribution (OOD) generalization. In Ahuja et al., it was shown that solving for the Nash equilibria of a new class of…

In this short note we give some corollaries of the polynomial inverse function theorem for large fields. We prove inverse and implicit function theorems for Nash maps over large fields, characterize large fields as fields satisfying inverse…

A solution concept that is a refinement of Nash equilibria selects for each finite game a nonempty collection of closed and connected subsets of Nash equilibria as solutions. We impose three axioms for such solution concepts. The axiom of…

We characterize Nash equilibrium by postulating coherent behavior across varying games. Nash equilibrium is the only solution concept that satisfies the following axioms: (i) strictly dominant actions are played with positive probability,…

The fundamental laws of quantum world upsets the logical foundation of classic physics. They are completely counter-intuitive with many bizarre behaviors. However, this paper shows that they may make sense from the perspective of a general…

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…

Game theory is usually considered applied mathematics, but a few game-theoretic results, such as Borel determinacy, were developed by mathematicians for mathematics in a broad sense. These results usually state determinacy, i.e. the…

Finite objects and more specifically finite games are formalized using induction, whereas infinite objects are formalized using coinduction. In this article, after an introduction to the concept of coinduction, we revisit on infinite…

We study the convergence of Nash equilibria in a game of optimal stopping. If the associated mean field game has a unique equilibrium, any sequence of $n$-player equilibria converges to it as $n\to\infty$. However, both the finite and…

We pursue a general theory of quantum games. We show that quantum games are more efficient than classical games, and provide a saturated upper bound for this efficiency. We demonstrate that the set of finite classical games is a strict…