This paper deals with the problem of designing a rapid transit network that reacts as well as possible to link failures. It is assumed that when a link fails, another path or another transportation mode is provided to transport passengers between the endpoints of the affected link. The goal is to build a network that attracts as many passengers as possible when a failure occurs. The problem is ...

for all mixed strategies Al, . ., ,, and i = 1, . . ., n in an n-person game r for all possible assignments of the pay-offfunction h is that r have total recall. Theorem 1 generalizes the theorem of von Neumann which asserts that a zero-sum two-person game with perfect information is strictly determined. It is proved by the same inductive device with a slight variation due to the absence of the...

Two-person zero-sum stochastic games with finite state and action spaces are considered. The expected average payoff criterion is used for multichain structures. In the special caae that only one player controls the transitions, it is shown that the optimal stationary policies and the value of the game can be obtained from the optimal solutions to a pair of dual linear programs. A decomposition...

A finite-horizon two-person non-zero-sum differential game is considered. The dynamics of the linear. Each players has a quadratic functional on its own disposal, which should be minimized. case where weight matrices in control costs one player are singular both functionals studied. Hence, under consideration singular. novel definition Nash equilibrium this (a sequence) proposed. solved by appl...

Algorithms for pruning game trees generally rely on a game being zero-sum, in the case of alpha-beta pruning, or constant-sum, in the case of multi-player pruning algorithms such as speculative pruning. While existing algorithms can prune non-zero-sum games, pruning is much less effective than in constant-sum games. We introduce the idea of leaf-value tables, which store an enumeration of the p...

Let G = 〈I, J, g〉 be a two-person zero-sum game. We examine the two-person zero-sum repeated game G(k, m) in which player 1 and 2 place down finite state automata with k, m states respectively and the payoff is the average per stage payoff when the two automata face off. We are interested in the cases in which player 1 is “smart” in the sense that k is large but player 2 is “much smarter” in th...

We propose a theory of mixed strategies in zero-sum two-person games. Given a finite zero-sum two-person game g, we extend it to collective games g∞ and g∞,S, which are infinite repetitions of the game g. Players in the collective games are restricted to use computable strategies only, but each has a complex sequence that can be used in the computation. We adopt kolmogorov complexity to define ...

We show that a symmetric two-player zero-sum game has a pure strategy equilibrium if and only if it is not a generalized rock-paper-scissors matrix. Moreover, we show that every finite symmetric quasiconcave two-player zero-sum game has a pure equilibrium. Further sufficient conditions for existence are provided. We point out that the class of symmetric two-player zero-sum games coincides with ...

While the idea of a matching pennies game may seem contrived, it is merely the simplest example of a general class of zero-sum games, where the total payoff of the players is constant regardless of the outcome. Consequently gains for one player can only come from losses of the other. For this reason, zero-sum games will rarely have a pure strategy Nash equilibrium. Examples would be chess, or m...