Analyse de systèmes min-max
Analytic solutions of nonlinear Cournot duopoly game.
Bi-personal stochastic transient Markov games with stopping times and total reward criterion
The article is devoted to a class of Bi-personal (players 1 and 2), zero-sum Markov games evolving in discrete-time on Transient Markov reward chains. At each decision time the second player can stop the system by paying terminal reward to the first player. If the system is not stopped the first player selects a decision and two things will happen: The Markov chain reaches next state according to the known transition law, and the second player must pay a reward to the first player. The first player...
Complex dynamics in a nonlinear cobweb model for real estate market.
Deterministic Markov Nash equilibria for potential discrete-time stochastic games
In this paper, we study the problem of finding deterministic (also known as feedback or closed-loop) Markov Nash equilibria for a class of discrete-time stochastic games. In order to establish our results, we develop a potential game approach based on the dynamic programming technique. The identified potential stochastic games have Borel state and action spaces and possibly unbounded nondifferentiable cost-per-stage functions. In particular, the team (or coordination) stochastic games and the stochastic...
Nash -equilibria for stochastic games with total reward functions: an approach through Markov decision processes
The main objective of this paper is to find structural conditions under which a stochastic game between two players with total reward functions has an -equilibrium. To reach this goal, the results of Markov decision processes are used to find -optimal strategies for each player and then the correspondence of a better answer as well as a more general version of Kakutani’s Fixed Point Theorem to obtain the -equilibrium mentioned. Moreover, two examples to illustrate the theory developed are presented....
Note: The Smallest Nonevasive Graph Property
A property of n-vertex graphs is called evasive if every algorithm testing this property by asking questions of the form “is there an edge between vertices u and v” requires, in the worst case, to ask about all pairs of vertices. Most “natural” graph properties are either evasive or conjectured to be such, and of the few examples of nontrivial nonevasive properties scattered in the literature the smallest one has n = 6. We exhibit a nontrivial, nonevasive property of 5-vertex graphs and show that...
Permissive strategies : from parity games to safety games
It is proposed to compare strategies in a parity game by comparing the sets of behaviours they allow. For such a game, there may be no winning strategy that encompasses all the behaviours of all winning strategies. It is shown, however, that there always exists a permissive strategy that encompasses all the behaviours of all memoryless strategies. An algorithm for finding such a permissive strategy is presented. Its complexity matches currently known upper bounds for the simpler problem of finding...
Permissive strategies: from parity games to safety games
It is proposed to compare strategies in a parity game by comparing the sets of behaviours they allow. For such a game, there may be no winning strategy that encompasses all the behaviours of all winning strategies. It is shown, however, that there always exists a permissive strategy that encompasses all the behaviours of all memoryless strategies. An algorithm for finding such a permissive strategy is presented. Its complexity matches currently known upper bounds for the simpler problem...
Switched Stackelberg game analysis of false data injection attacks on networked control systems
This paper is concerned with a security problem for a discrete-time linear networked control system of switched dynamics. The control sequence generated by a remotely located controller is transmitted over a vulnerable communication network, where the control input may be corrupted by false data injection attacks launched by a malicious adversary. Two partially conflicted cost functions are constructed as the quantitative guidelines for both the controller and the attacker, after which a switched...
The turnpike property for dynamic discrete time zero-sum games.