In this paper we present a preliminary investigation of modelling spatial aspects of security games within the context of Markov games. Reinforcement learning is a powerful tool for adaptation in unknown environments, however the basic singleagent RL algorithms are unfit to be applied in adversarial scenarios. Therefore, we profit from Adversarial Multi-Armed Bandit (AMAB) methods which are des...

The existence of a value and optimal strategies is proved for the class of twoperson repeated games where the state follows a Markov chain independently of players’ actions and at the beginning of each stage only player one is informed about the state. The results apply to the case of standard signaling where players’ stage actions are observable, as well as to the model with general signals pr...

This paper deals with an extension of the concept of correlated strategies to Markov stopping games. The Nash equilibrium approach to solving nonzero-sum stopping games may give multiple solutions. An arbitrator can suggest to each player the decision to be applied at each stage based on a joint distribution over the players’ decisions. This is a form of equilibrium selection. Examples of corre...

The potential double exponential blow-up for the generation of deterministic ω-automata for linear temporal logic formulas motivates research on weaker forms of determinism. One of these notions is the goodfor-games property that has been introduced by Henzinger and Piterman together with an algorithm for generating good-for-games automata from nondeterministic Büchi automata. The contribution ...

We consider a class of two-player dynamic stochastic nonzero-sum games where the state transition and observation equations are linear, and the primitive random variables are Gaussian. Each controller acquires possibly different dynamic information about the state process and the other controller’s past actions and observations. This leads to a dynamic game of asymmetric information among the c...

Rapoport and Budescu (1992) showed that despite subjects’ failure to generate random sequences under explicit instructions, they were able to generate more random sequences when engaging in competitive games like Matching Pennies. Why people were able to correct their distorted sense of randomness in competitive games remains unclear. Therefore, I explored two probabilistic models to answer thi...

This note investigates the noncooperative foundations of von Neumann-Morgenstern (vN-M) stable sets in voting games. To do so, we study subgame perfect equilibria of a noncooperative legislative bargaining game, based on underlying simple games. The following results emerge from such an exercise: Every stable set of the underlying simple game is the limit set of undominated pure-strategy Markov...

We study a class of discounted, infinite horizon stochastic games with public and private signals and strategic complementarities. Using monotone operators defined on the function space of values and strategies (equipped with a product order), we prove existence of a stationary Markov–Nash equilibrium via constructive methods. In addition, we provide monotone comparative statics results for ord...

Partially observable stochastic games (POSGs) are an attractive model for many multi-agent domains, but are computationally extremely difficult to solve. We present a new model, Markov games of incomplete information (MGII) which imposes a mild restriction on POSGs while overcoming their primary computational bottleneck. Finally we show how to convert a MGII into a continuous but bounded fully ...