In this paper we study the nonzero-sum Dynkin game in continuous time, which is a two-player noncooperative game on stopping times. We show that it has a Nash equilibrium point for general stochastic processes. As an application, we consider the problem of pricing American game contingent claims by the utility maximization approach.

We show that the following problem is EXP-complete: given a rational v and a two player, zero-sum Boolean gameG determine whether the value of G is at least v. The proof is via a translation of the proof of the same result for Boolean circuit games in [1]. 1 Preliminaries We will be using the encoding of [2] to replicate the proof of [1]. A familiarity with [2] will make the proof much easier t...

The zero-sum matrix game is one of the most classic game models, and it is widely used in many scientific and engineering fields. In the real world, due to the complexity of the decision-making environment, sometimes the payoffs received by players may be inexact or uncertain, which requires that the model of matrix games has the ability to represent and deal with imprecise payoffs. To meet suc...

We present a simple primal-dual algorithm for computing approximate Nash equilibria in two-person zero-sum sequential games with incomplete information and perfect recall (like Texas Hold’em poker). Our algorithm only performs basic iterations (i.e matvec multiplications, clipping, etc., and no calls to external first-order oracles, no matrix inversions, etc.) and is applicable to a broad class...

Abstract The objective of this paper is to study a class zero-sum optimal stopping games diffusions under so-called Poisson constraint: the players are allowed stop only at arrival times their respective Poissonian signal processes. These processes can have different intensities, which makes game setting asymmetric. We give weak and easily verifiable set sufficient condition we derive semi-expl...

A discretized game model of an anti-missile defense scenario is presented. Such an engagement is a pursuit of a "blind" evader, committed to satisfy a terminal constraint. It can be formulated as an incomplete information zero-sum pursuit-evasion game with state constraint. Such a game becomes non trivial if the evader has higher maneuverability than the pursuer. In this case the game admits a ...

The Internet revolution has resulted in increased competition among providers of goods and services to lure customers by tearing down the barriers of time and distance. For example, a home buyer shopping for a mortgage loan through the Internet is now a potential customer for a large number of lending institutions throughout the world. The lenders (players, in generic game theory nomenclature) ...

a {em roman dominating function} on a graph $g = (v ,e)$ is a function $f : vlongrightarrow {0, 1, 2}$ satisfying the condition that every vertex $v$ for which $f (v) = 0$ is adjacent to at least one vertex $u$ for which $f (u) = 2$. the {em weight} of a roman dominating function is the value $w(f)=sum_{vin v}f(v)$. the roman domination number of a graph $g$, denoted by $gamma_r(g)$, equals the...