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Some problems of measure theory which are related to economic theory.

Heinz J. Skala (1982)

Stochastica

After a short discussion of the first application of measure theoretic tools to economics we show that it is consistent relative to the usual axioms of set theory that there exists no nonatomic probability space of power less than the continuum. This together with other results shows that Aumann's continuum-of-agents methodology provides a sound framework at least for the cooperative theory. There are, however, other problems in economics where, without further assumptions, the continuum may be...

Some remarks on equilibria in semi-Markov games

Andrzej Nowak (2000)

Applicationes Mathematicae

This paper is a first study of correlated equilibria in nonzero-sum semi-Markov stochastic games. We consider the expected average payoff criterion under a strong ergodicity assumption on the transition structure of the games. The main result is an extension of the correlated equilibrium theorem proven for discounted (discrete-time) Markov games in our joint paper with Raghavan. We also provide an existence result for stationary Nash equilibria in the limiting average payoff semi-Markov games with...

Some short elements on hedging credit derivatives

Philippe Durand, Jean-Frédéric Jouanin (2007)

ESAIM: Probability and Statistics

In practice, it is well known that hedging a derivative instrument can never be perfect. In the case of credit derivatives (e.g. synthetic CDO tranche products), a trader will have to face some specific difficulties. The first one is the inconsistence between most of the existing pricing models, where the risk is the occurrence of defaults, and the real hedging strategy, where the trader will protect his portfolio against small CDS spread movements. The second one, which is the main subject of...

Some values for constant-sum and bilateral cooperative games

Andrzej Młodak (2007)

Applicationes Mathematicae

We prove new axiomatizations of the Shapley value and the Banzhaf value, defined on the class of nonnegative constant-sum games with nonzero worth of the grand coalition as well as on nonnegative bilateral games with nonzero worth of the grand coalition. A characteristic feature of the latter class of cooperative games is that for such a game any coalition and its complement in the set of all players have the same worth. The axiomatizations are then generalized to the entire class of constant-sum...

Some weak covering properties and infinite games

Masami Sakai (2014)

Open Mathematics

We show that (I) there is a Lindelöf space which is not weakly Menger, (II) there is a Menger space for which TWO does not have a winning strategy in the game Gfin(O,Do). These affirmatively answer questions posed in Babinkostova, Pansera and Scheepers [Babinkostova L., Pansera B.A., Scheepers M., Weak covering properties and infinite games, Topology Appl., 2012, 159(17), 3644–3657]. The result (I) automatically gives an affirmative answer of Wingers’ problem [Wingers L., Box products and Hurewicz...

Split of an Optimization Variable in Game Theory

R. Aboulaich, A. Habbal, N. Moussaid (2010)

Mathematical Modelling of Natural Phenomena

In the present paper, a general multiobjective optimization problem is stated as a Nash game. In the nonrestrictive case of two objectives, we address the problem of the splitting of the design variable between the two players. The so-called territory splitting problem is solved by means of an allocative approach. We propose two algorithms in order to find fair allocation tables

Spreading mechanisms of cooperation for the evolutionary Prisoner's Dilemma games

György Szabó (2008)

Banach Center Publications

We survey several mechanisms supporting the maintenance of cooperation for evolutionary Prisoner's Dilemma games. In these models players are located on the sites of a lattice or graph and they can follow one of the pure strategies: cooperation (C) or defection (D). Their total income comes from Prisoner's Dilemma games with their neighbors. We discuss the consequences of different evolutionary rules determining the time-dependence of the strategy distribution and compare the results of spreading...

Stability estimates of generalized geometric sums and their applications

Evgueni I. Gordienko (2004)

Kybernetika

The upper bounds of the uniform distance ρ ∑ k = 1 ν X k , ∑ k = 1 ν X ˜ k between two sums of a random number ν of independent random variables are given. The application of these bounds is illustrated by stability (continuity) estimating in models in queueing and risk theory.

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