Related papers: Absorbing games with irrational values

We introduce a simple class of mean field games with absorbing boundary over a finite time horizon. In the corresponding $N$-player games, the evolution of players' states is described by a system of weakly interacting It\^o equations with…

Iterated admissibility is a well-known and important concept in classical game theory, e.g. to determine rational behaviors in multi-player matrix games. As recently shown by Berwanger, this concept can be soundly extended to infinite games…

An integer program (IP) with a finite number of feasible solutions may have an unbounded linear programming relaxation if it contains irrational parameters, due to implicit constraints enforced by the irrational numbers. We show that those…

An absorbing game is a stochastic game with a single nonabsorbing state. Such a game is called recursive if all players receive a payoff of 0 in the nonabsorbing state, and positive if all payoffs in absorbing states are positive. An action…

We consider zero sum stochastic games. For every discount factor $\lambda$, a time normalization allows to represent the game as being played on the interval [0, 1]. We introduce the trajectories of cumulated expected payoff and of…

We study a class of deterministic mean field games on finite and infinite time horizons arising in models of optimal exploitation of exhaustible resources. The main characteristic of our game is an absorption constraint on the players'…

It was shown in Flesch and Solan (2022) with a rather involved proof that all two-player stochastic games with finite state and action spaces and shift-invariant payoffs admit an $\epsilon$-equilibrium, for every $\epsilon>0$. Their proof…

The Nakamura number of a simple game plays a critical role in preference aggregation (or multi-criterion ranking): the number of alternatives that the players can always deal with rationally is less than this number. We comprehensively…

Past efforts to classify impartial three-player combinatorial games (the theories of Li and Straffin) have made various restrictive assumptions about the rationality of one's opponents and the formation and behavior of coalitions. One may…

Admissibility has been studied for games of infinite duration with Boolean objectives. We extend here this study to games of infinite duration with quantitative objectives. First, we show that, un- der the assumption that optimal worst-case…

In a zero-sum stochastic game with signals, at each stage, two adversary players take decisions and receive a stage payoff determined by these decisions and a variable called state. The state follows a Markov chain, that is controlled by…

We are interested in the convergence of the value of n-stage games as n goes to infinity and the existence of the uniform value in stochastic games with a general set of states and finite sets of actions where the transition is commutative.…

For a family of multidimensional gambler models we provide formulas for the winning probabilities (in terms of parameters of the system) and for the distribution of game duration (in terms of eigenvalues of underlying one-dimensional…

We propose an interpretation of the infinite sum of combinatorial games. In such an interpretation, plays involve infinite runs, but without loops. The notion of a run is quite natural, but different possibilities arises for the notion of…

The value of a finite-state two-player zero-sum stochastic game with limit-average payoff can be approximated to within $\epsilon$ in time exponential in a polynomial in the size of the game times polynomial in logarithmic in…

We develop the fictitious play algorithm in the context of the linear programming approach for mean field games of optimal stopping and mean field games with regular control and absorption. This algorithm allows to approximate the mean…

We study quitting games and define the concept of absorption paths, which is an alternative definition to strategy profiles that accomodates both discrete time aspects and continuous time aspects, and is parameterized by the total…

We consider the general model of zero-sum repeated games (or stochastic games with signals), and assume that one of the players is fully informed and controls the transitions of the state variable. We prove the existence of the uniform…

We consider average-energy games, where the goal is to minimize the long-run average of the accumulated energy. While several results have been obtained on these games recently, decidability of average-energy games with a lower-bound…

Combinatorial Game Theory has also been called `additive game theory', whenever the analysis involves sums of independent game components. Such {\em disjunctive sums} invoke comparison between games, which allows abstract values to be…