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In nature and society problems arise when different interests are difficult to reconcile, which are modeled in game theory. While most applications assume uncorrelated games, a more detailed modeling is necessary to consider the…
We consider finite $n$-person deterministic graphical (DG) games. These games are modelled by finite directed graphs (digraphs) $G$ which may have directed cycles and, hence, infinite plays. Yet, it is assumed that all these plays are…
We investigate stochastic differential games of optimal trading comprising a finite population. There are market frictions in the present framework, which take the form of stochastic permanent and temporary price impacts. Moreover,…
In many cases the Nash equilibria are not predictive of the experimental players' behaviour. For some games of Game Theory it is proposed here a method to estimate the probabilities with which the different options will be actually chosen…
This paper investigates the impact of perturbations on the best-response-based algorithms approximating Nash equilibria in zero-sum games, namely Double Oracle and Fictitious Play. More precisely, we assume that the oracle computing the…
A strategy profile in a multi-player game is a Nash equilibrium if no player can unilaterally deviate to achieve a strictly better payoff. A profile is an $\epsilon$-Nash equilibrium if no player can gain more than $\epsilon$ by…
We study equilibrium concepts in non-cooperative games under uncertainty where both beliefs and mixed strategies are represented by non-additive measures (capacities). In contrast to the classical Nash framework based on additive…
Generating payoff matrices of normal-form games at random, we calculate the frequency of games with a unique pure strategy Nash equilibrium in the ensemble of $n$-player, $m$-strategy games. These are perfectly predictable as they must…
In game theory, the concept of Nash equilibrium reflects the collective stability of some individual strategies chosen by selfish agents. The concept pertains to different classes of games, e.g. the sequential games, where the agents play…
We define solution concepts appropriate for computationally bounded players playing a fixed finite game. To do so, we need to define what it means for a \emph{computational game}, which is a sequence of games that get larger in some…
This paper aims to design a distributed coordination algorithm for solving a multi-agent decision problem with a hierarchical structure. The primary goal is to search the Nash equilibrium of a noncooperative game such that each player has…
We consider a dynamical approach to game in extensive forms. By restricting the convertibility relation over strategy profiles, we obtain a semi-potential (in the sense of Kukushkin), and we show that in finite games the corresponding…
Pseudo-games are a natural and well-known generalization of normal-form games, in which the actions taken by each player affect not only the other players' payoffs, as in games, but also the other players' strategy sets. The solution…
Optimizing strategic decisions (a.k.a. computing equilibrium) is key to the success of many non-cooperative multi-agent applications. However, in many real-world situations, we may face the exact opposite of this game-theoretic problem --…
Successful algorithms have been developed for computing Nash equilibrium in a variety of finite game classes. However, solving continuous games -- in which the pure strategy space is (potentially uncountably) infinite -- is far more…
We consider bargaining problems which involve two participants, with a nonempty closed, bounded convex bargaining set of points in the real plane representing all realizable bargains. We also assume that there is no definite threat or…
When designing optimal controllers for any system, it is often the case that the true state of the system is unknown to the controller, for example due to noisy measurements or partially observable states. Incomplete state information must…
While game theory has been transformative for decision-making, the assumptions made can be overly restrictive in certain instances. In this work, we investigate some of the underlying assumptions of rationality, such as mutual consistency…
We investigate optimal decision making under imperfect recall, that is, when an agent forgets information it once held before. An example is the absentminded driver game, as well as team games in which the members have limited communication…
In the ultimatum game, the challenge is to explain why responders reject non-zero offers thereby defying classical rationality. Fairness and related notions have been the main explanations so far. We explain this rejection behavior via the…