Semi-markov strategies in stochastic games

Structural approximations in discounted semi-Markov games

We consider the problem of approximating the values and the equilibria in two-person zero-sum discounted semi-Markov games with in nite horizon and compact action spaces, when several uncertainties are present about the parameters of the model. Speci cally: on the one hand, we study approximations made on the transition probabilities, the discount factor and the reward functions when the state ...

Markov Perfect Equilibria in Stochastic Bequest Games

In many real-life situations, the preferences of an economic agent change over time. Rational behaviour of such agents was studied by many authors (Strotz, Pollak, Bernheim and Ray) who considered so-called “consistent plans”. Phelps and Pollak [10] introduced the notion of “quasi-hyperbolic discounting”, which is a modification of the classical discounting proposed in 1937 by Samuelson. Within...

Cyclic Markov equilibria in stochastic games

We examine a three-person stochastic game where the only existing equi-libria consist of cyclic Markov strategies. Unlike in two-person games of a similar type, stationary "-equilibria (" > 0) do not exist for this game. Besides we characterize the set of feasible equilibrium rewards.

Semi-algebraic Tools in Stochastic Games

In this thesis we consider two-person zero-sum stochastic games with a special focus on how tools from the mathematical field of semi-algebraic geometry have been applied to these games. In the first of two parts of the thesis we introduce stochastic games and prove a complexity result about computing the value of a type of stochastic games called concurrent reachability games. We show that the...

Stochastic Games and Stationary Strategies