Geography played on an -cycle times a 4-cycle.
Grapho-analytic method of solving 2 × n bi-matrix games
Greatly increased practical usefulness of two-person game theory by adoption of median criterion
Growth versus environment in dynamic models of capital accumulation.
Growth-optimal portfolios under transaction costs
This paper studies a portfolio optimization problem in a discrete-time Markovian model of a financial market, in which asset price dynamics depends on an external process of economic factors. There are transaction costs with a structure that covers, in particular, the case of fixed plus proportional costs. We prove that there exists a self-financing trading strategy maximizing the average growth rate of the portfolio wealth. We show that this strategy has a Markovian form. Our result is obtained...
GTES : une méthode de simulation par jeux et apprentissage pour l'analyse des systèmes d'acteurs
Cet article décrit une approche de la modélisation d'un système d'acteurs, particulièrement adaptée à la modélisation des entreprises, fondée sur la théorie des jeux [11] et sur l'optimisation par apprentissage du comportement de ces acteurs. Cette méthode repose sur la combinaison de trois techniques : la simulation par échantillonnage (Monte-Carlo), la théorie des jeux pour ce qui concerne la recherche d'équilibre entre les stratégies, et les méthodes heuristiques d'optimisation locale,...
Guessing secrets.
Gδ -sets in topological spaces and games
Players ONE and TWO play the following game: In the nth inning ONE chooses a set from a prescribed family ℱ of subsets of a space X; TWO responds by choosing an open subset of X. The players must obey the rule that for each n. TWO wins if the intersection of TWO’s sets is equal to the union of ONE’s sets. If ONE has no winning strategy, then each element of ℱ is a -set. To what extent is the converse true? We show that: (A) For ℱ the collection of countable subsets of X: 1. There are subsets...
Hamilton–Jacobi equations and two-person zero-sum differential games with unbounded controls
A two-person zero-sum differential game with unbounded controls is considered. Under proper coercivity conditions, the upper and lower value functions are characterized as the unique viscosity solutions to the corresponding upper and lower Hamilton–Jacobi–Isaacs equations, respectively. Consequently, when the Isaacs’ condition is satisfied, the upper and lower value functions coincide, leading to the existence of the value function of the differential game. Due to the unboundedness of the controls,...
Handling a Kullback-Leibler divergence random walk for scheduling effective patrol strategies in Stackelberg security games
This paper presents a new model for computing optimal randomized security policies in non-cooperative Stackelberg Security Games (SSGs) for multiple players. Our framework rests upon the extraproximal method and its extension to Markov chains, within which we explicitly compute the unique Stackelberg/Nash equilibrium of the game by employing the Lagrange method and introducing the Tikhonov regularization method. We also consider a game-theory realization of the problem that involves defenders and...
Hercules and Hydra
Hercules and Hydra, a game on rooted finite trees
Hercules versus Hidden Hydra Helper
L. Kirby and J. Paris introduced the Hercules and Hydra game on rooted trees as a natural example of an undecidable statement in Peano Arithmetic. One can show that Hercules has a “short” strategy (he wins in a primitively recursive number of moves) and also a “long” strategy (the finiteness of the game cannot be proved in Peano Arithmetic). We investigate the conflict of the “short” and “long” intentions (a problem suggested by J. Nešetřil). After each move of Hercules (trying to kill Hydra fast)...
Hierarchical solution concept for static and multistage decision problems with two objectives
How long can a graph be kept planar?
How Long Can One Bluff in the Domination Game?
The domination game is played on an arbitrary graph G by two players, Dominator and Staller. The game is called Game 1 when Dominator starts it, and Game 2 otherwise. In this paper bluff graphs are introduced as the graphs in which every vertex is an optimal start vertex in Game 1 as well as in Game 2. It is proved that every minus graph (a graph in which Game 2 finishes faster than Game 1) is a bluff graph. A non-trivial infinite family of minus (and hence bluff) graphs is established. minus graphs...
How to play MetaSquares
Identitäten bei den Stirling-Zahlen 2.Art aus kombinatorischen Überlegungen beim Würfelspiel.
Incomplete information and risk sensitive analysis of sequential games without a predetermined order of turns
The authors introduce risk sensitivity to a model of sequential games where players don't know beforehand which of them will make a choice at each stage of the game. It is shown that every sequential game without a predetermined order of turns with risk sensitivity has a Nash equilibrium, as well as in the case in which players have types that are chosen for them before the game starts and that are kept from the other players. There are also a couple of examples that show how the equilibria might...
Infinite asymptotic games
We study infinite asymptotic games in Banach spaces with a finite-dimensional decomposition (F.D.D.) and prove that analytic games are determined by characterising precisely the conditions for the players to have winning strategies. These results are applied to characterise spaces embeddable into sums of finite dimensional spaces, extending results of Odell and Schlumprecht, and to study various notions of homogeneity of bases and Banach spaces. The results are related to questions of rapidity...