Related papers: On the three-person game baccara banque
Game theory finds nowadays a broad range of applications in engineering and machine learning. However, in a derivative-free, expensive black-box context, very few algorithmic solutions are available to find game equilibria. Here, we propose…
We characterize Nash equilibrium by postulating coherent behavior across varying games. Nash equilibrium is the only solution concept that satisfies the following axioms: (i) strictly dominant actions are played with positive probability,…
We introduce a variant of the classic poker game blackjack -- the continuous blackjack. We study the Nash Equilibrium as well as the case where players deviate from it. We then pivot to the study of a large class of adaptive strategies and…
We investigate the degree of discontinuity of several solution concepts from non-cooperative game theory. While the consideration of Nash equilibria forms the core of our work, also pure and correlated equilibria are dealt with. Formally,…
This paper discusses a special type of multi-user communication scenario, in which users' utilities are linearly impacted by their competitors' actions. First, we explicitly characterize the Nash equilibrium and Pareto boundary of the…
Multiplayer games with selfish agents naturally occur in the design of distributed and embedded systems. As the goals of selfish agents are usually neither equivalent nor antagonistic to each other, such games are non zero-sum games. We…
We study pure-strategy Nash equilibria in multi-player concurrent deterministic games, for a variety of preference relations. We provide a novel construction, called the suspect game, which transforms a multi-player concurrent game into a…
We consider two player quadratic games in a cooperative framework known as social value orientation, motivated by the need to account for complex interactions between humans and autonomous agents in dynamical systems. Social value…
Noncooperative game theory provides a normative framework for analyzing strategic interactions. However, for the toolbox to be operational, the solutions it defines will have to be computed. In this paper, we provide a single reduction that…
We give an example of a three-person deterministic graphical game that has no Nash equilibrium in pure stationary strategies. The game has seven positions, four outcomes (a unique cycle and three terminal positions), and its normal form is…
We investigate the existence of certain types of equilibria (Nash, $\varepsilon$-Nash, subgame perfect, $\varepsilon$-subgame perfect, Pareto-optimal) in multi-player multi-outcome infinite sequential games. We use two fundamental…
This paper studies a 2-players zero-sum Dynkin game arising from pricing an option on an asset whose rate of return is unknown to both players. Using filtering techniques we first reduce the problem to a zero-sum Dynkin game on a…
Nash equilibrium is a solution concept in non-strictly competitive, non-cooperative game theory that finds applications in various scientific and engineering disciplines. A non-strictly competitive, non-cooperative game model is presented…
Nash equilibrium is the most commonly-used notion of equilibrium in game theory. However, it suffers from numerous problems. Some are well known in the game theory community; for example, the Nash equilibrium of repeated prisoner's dilemma…
Bayesian rationality in strategic games presumes that it is possible to translate strategic uncertainty into imperfect information. Correlated equilibrium is guided by the idea that players are Bayes rational, have a common prior, and…
Games with incomplete preferences are an important model for studying rational decision-making in scenarios where players face incomplete information about their preferences and must contend with incomparable outcomes. We study the problem…
There are two well-known sufficient conditions for Nash equilibrium in two-player games: mutual knowledge of rationality (MKR) and mutual knowledge of conjectures. MKR assumes that the concept of rationality is mutually known. In contrast,…
In this short note we give an example of a four-person finite positional game with perfect information that has no positions of chance and no Nash equilibria in pure stationary strategies. The corresponding directed graph has only one…
Learning in games discusses the processes where multiple players learn their optimal strategies through the repetition of game plays. The dynamics of learning between two players in zero-sum games, such as Matching Pennies, where their…
We study rational synthesis problems for concurrent games with omega-regular objectives. Our model of rationality considers only pure strategy Nash equilibria that satisfy either a social welfare or Pareto optimality condition with respect…