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Game-theoretic upper expectations are joint (global) probability models that mathematically describe the behaviour of uncertain processes in terms of supermartingales; capital processes corresponding to available betting strategies.…
We study financial systems from a game-theoretic standpoint. A financial system is represented by a network, where nodes correspond to firms, and directed labeled edges correspond to debt contracts between them. The existence of cycles in…
Tasks and objects are two predominant ways of specifying distributed problems. A task is specified by an input/output relation, defining for each set of processes that may run concurrently, and each assignment of inputs to the processes in…
In this paper, we present theorems specifying the critical values for series associated with debts arranged in the order of their duration.
Using martingale theory, we compute, in very few lines, exact analytical expressions for various first-exit-time statistics associated with one-dimensional biased diffusion. Examples include the distribution for the first-exit time from an…
We consider optimal stopping problems for a Brownian motion and a geometric Brownian motion with a "disorder", assuming that the moment of a disorder is uniformly distributed on a finite interval. Optimal stopping rules are found as the…
In this paper we review some of the main results obtained in the field of truels. A "truel" is a generalization of a duel involving three players. Depending on the rules used for chosing the players, we may distinguish between the random,…
Practitioners making decisions based on causal effects typically ignore structural uncertainty. We analyze when this uncertainty is consequential enough to warrant methodological solutions (Bayesian model averaging over competing causal…
We derive confidence intervals and confidence sequences for causal effects in situations where the back-door or front-door criteria are applicable. Our tightest confidence intervals hold in the standard setting where the training data…
We consider graph games of infinite duration with winning conditions in parameterized linear temporal logic, where the temporal operators are equipped with variables for time bounds. In model checking such specifications were introduced as…
This essay looks at decision-making with interval-valued probability measures. Existing decision methods have either supplemented expected utility methods with additional criteria of optimality, or have attempted to supplement the…
In a discrete-time setting, we study arbitrage concepts in the presence of convex trading constraints. We show that solvability of portfolio optimization problems is equivalent to absence of arbitrage of the first kind, a condition weaker…
For the iterated Prisoner's Dilemma, there exist Markov strategies which solve the problem when we restrict attention to the long term average payoff. When used by both players these assure the cooperative payoff for each of them. Neither…
The work [8] established memory loss in the time-dependent (non-random) case of uniformly expanding maps of the interval. Here we find conditions under which we have convergence to the normal distribution of the appropriately scaled…
We present a simple game model where agents with different memory lengths compete for finite resources. We show by simulation and analytically that an instability exists at a critical memory length, and as a result, different memory lengths…
We consider a problem of dispersing points on disjoint intervals on a line. Given n pairwise disjoint intervals sorted on a line, we want to find a point in each interval such that the minimum pairwise distance of these points is maximized.…
We consider the interim core of normal form cooperative games and exchange economies with incomplete information based on the partition model. We develop a solution concept that we can situate roughly between Wilson's coarse core and…
Classical game theory addresses decision problems in multi-agent environment where one rational agent's decision affects other agents' payoffs. Game theory has widespread application in economic, social and biological sciences. In recent…
This paper considers time-inconsistent problems when control and stopping strategies are required to be made simultaneously (called stopping control problems by us). We first formulate the timeinconsistent stopping control problems under…
This work is concerned with the existence and uniqueness of boundary value problems defined on semi-infinite intervals. These kinds of problems seldom admit exactly known solutions and, therefore, the theoretical information on their…