Related papers: On Farkas' Lemma and Related Propositions in BISH
We provide a unified variational inequality framework for the study of fundamental properties of the Nash equilibrium in network games. We identify several conditions on the underlying network (in terms of spectral norm, infinity norm and…
In Stackelberg v/s Stackelberg games a collection of leaders compete in a Nash game constrained by the equilibrium conditions of another Nash game amongst the followers. The resulting equilibrium problems are plagued by the nonuniqueness of…
This paper is concerned with a Stackelberg stochastic differential game on a finite horizon in feedback information pattern. A system of parabolic partial differential equations is obtained at the level of Hamiltonian to give the…
{\AA}qvist's logics (E, F, F+(CM), and G) are among the best-known systems in the long tradition of preference-based approaches for modeling conditional obligation. While the general semantics of preference models align well with…
We consider the relation between Sion's minimax theorem for a continuous function and a Nash equilibrium in a five-players game with two groups which is zero-sum and symmetric in each group. We will show the following results. 1. The…
We present new criteria on the existence of fixed points that combine some monotonicity assumptions with the classical fixed point index theory. As an illustrative application, we use our theoretical results to prove the existence of…
The theory of combinatorial game (like board games) and the theory of social games (where one looks for Nash equilibria) are normally considered as two separate theories. Here we shall see what comes out of combining the ideas. The central…
Game Logic is an excellent setting to study proofs-about-programs via the interpretation of those proofs as programs, because constructive proofs for games correspond to effective winning strategies to follow in response to the opponent's…
Min-max optimization problems, also known as saddle point problems, have attracted significant attention due to their applications in various fields, such as fair beamforming, generative adversarial networks (GANs), and adversarial…
We design and analyze minimax-optimal algorithms for online linear optimization games where the player's choice is unconstrained. The player strives to minimize regret, the difference between his loss and the loss of a post-hoc benchmark…
In previous papers on this project a general static logical framework for formalizing and mechanizing set theories of different strength was suggested, and the power of some predicatively acceptable theories in that framework was explored.…
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…
We present a new duality theory for non-convex variational problems, under possibly mixed Dirichlet and Neumann boundary conditions. The dual problem reads nicely as a linear programming problem, and our main result states that there is no…
We give a sharpened form of Siegel Lemma's w. r. t. the maximum norm. This implies a new lower bound on the greatest element of a sum-distinct set of positive integers (Erd\"os-Moser problem). The main tools are Minkowski's theorem on…
The literature on ranking from ordinal data is vast, and there are several ways to aggregate overall preferences from pairwise comparisons between objects. In particular, it is well known that any Nash equilibrium of the zero sum game…
We introduce a new unified framework for modelling both decision problems and finite games based on quantifiers and selection functions. We show that the canonical utility maximisation is one special case of a quantifier and that our more…
In this paper, a gentle introduction to Game Theory is presented in the form of basic concepts and examples. Minimax and Nash's theorem are introduced as the formal definitions for optimal strategies and equilibria in zero-sum and…
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 real-valued game has the finite improvement property (FIP), if starting from an arbitrary strategy profile and letting the players change strategies to increase their individual payoffs in a sequential but non-deterministic order always…
This paper studies parameterized stochastic optimization problems in finite discrete time that arise in many applications in operations research and mathematical finance. We prove the existence of solutions and the absence of a duality gap…