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We present a few techniques for proving $L^p$ estimates for martingales. Basic applications to It\^o integration and rough paths are included.
This article introduces differential hybrid games, which combine differential games with hybrid games. In both kinds of games, two players interact with continuous dynamics. The difference is that hybrid games also provide all the features…
We formulate and analyze game-theoretic problems for systems governed by integral equations. For Volterra integral equations, we obtain and prove necessary and sufficient conditions for linear-quadratic problems, and for problems that are…
In this paper we define the canonical mixed extension of a decision form game. We motivate the necessity to introduce this concept and we show several examples about the new concept. In particular we focus our study upon the mixed…
An equation containing a fractional power of an elliptic operator of second order is studied for Dirichlet boundary conditions. Finite difference approximations in space are employed. The proposed numerical algorithm is based on solving an…
The pricing, hedging, optimal exercise and optimal cancellation of game or Israeli options are considered in a multi-currency model with proportional transaction costs. Efficient constructions for optimal hedging, cancellation and exercise…
We investigate the existence of certain types of equilibria (Nash, $\varepsilon$-Nash, subgame perfect, $\varepsilon$-subgame perfect, Pareto-optimal) in multi-player multi-outcome infinite sequential games. We use two fundamental…
We study 2-player impartial games of the form take-away which produce P-positions (second player winning positions) corresponding to complementary Beatty sequences, given by the continued fractions (1;k,1,k,1,...) and (k+1;k,1,k,1,...). Our…
Gradient-based techniques are becoming increasingly critical in quantitative fields, notably in statistics and computer science. The utility of these techniques, however, ultimately depends on how efficiently we can evaluate the derivatives…
Berlekamp proposed a class of impartial combinatorial games based on the moves of chess pieces on rectangular boards. We generalize impartial chess games by playing them on Young diagrams and obtain results about winning and losing…
We first prove some weighted inequalities for compositions of functions on time scales which are in turn applied to establish some new dynamic Opial-type inequalities in several variables. Some generalizations and applications to partial…
Results about existence and uniqueness of solutions of initial value problem for certain types of partial differential equations are recalled as well as iterative scheme and an error estimate for approximate solutions obtained using this…
We provide, to the best of our knowledge, the first computational study of extensive-form adversarial team games. These games are sequential, zero-sum games in which a team of players, sharing the same utility function, faces an adversary.…
The purpose of this paper is to introduce the idea of triangular Ramsey numbers and provide values as well as upper and lower bounds for them. To do this, the combinatorial game Mines is introduced; after some necessary theorems about…
An open problem posed by the first author is the complexity to decide whether a sequence of nonnegative integer numbers can be the final score of a football tournament. In this paper we propose polynomial time approximate and exponential…
Poset games have been the object of mathematical study for over a century, but little has been written on the computational complexity of determining important properties of these games. In this introduction we develop the fundamentals of…
The numerical solution methods for partial differential equation (PDE) solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods…
Several conjectural continued fractions found with the help of various algorithms are published in this paper.
Parity games have been broadly studied in recent years for their applications to controller synthesis and verification. In practice, partial solvers for parity games that execute in polynomial time, while incomplete, can solve most games in…
A variety of practical problems can be modeled by the decision-making process in multi-player games where a group of self-interested players aim at optimizing their own local objectives, while the objectives depend on the actions taken by…