Related papers: Minimax theorem and Nash equilibrium of symmetric …
We consider a partially asymmetric multi-players zero-sum game with two strategic variables. All but one players have the same payoff functions, and one player (Player $n$) does not. Two strategic variables are $t_i$'s and $s_i$'s for each…
We consider a partially asymmetric three-players zero-sum game with two strategic variables. Two players (A and B) have the same payoff functions, and Player C does not. Two strategic variables are $t_i$'s and $s_i$'s for $i=A, B, C$.…
We consider the relation between Sion's minimax theorem for a continuous function and a Nash equilibrium in a multi-players game with two groups which is zero-sum and symmetric in each group. We will show the following results. 1. The…
We consider the relation between Sion's minimax theorem for a continuous function and a Nash equilibrium in an asymmetric multi-players zero-sum game in which only one player is different from other players, and the game is symmetric for…
We consider the relation between Sion's minimax theorem for a continuous function and a Nash equilibrium in a five-players game with two groups which is zero-sum and symmetric in each group. We will show the following results. 1. The…
We consider a formulation of a non zero-sum n players game by an n+1 players zero-sum game. We suppose the existence of the n+1-th player in addition to n players in the main game, and virtual subsidies to the n players which is provided by…
We consider two classes of constrained finite state-action stochastic games. First, we consider a two player nonzero sum single controller constrained stochastic game with both average and discounted cost criterion. We consider the same…
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…
In this paper, I prove that existence of pure-strategy Nash equilibrium in games with infinitely many players is equivalent to the axiom of choice.
Creating strong agents for games with more than two players is a major open problem in AI. Common approaches are based on approximating game-theoretic solution concepts such as Nash equilibrium, which have strong theoretical guarantees in…
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 consider a general nonzero-sum impulse game with two players. The main mathematical contribution of the paper is a verification theorem which provides, under some regularity conditions, a suitable system of quasi-variational inequalities…
We study a two-player nonzero-sum stochastic differential game where one player controls the state variable via additive impulses while the other player can stop the game at any time. The main goal of this work is characterize Nash…
We consider a game in which each player must find a compromise between more daring strategies that carry a high risk for him to be eliminated, and more cautious ones that, however, reduce his final score. For two symmetric players this game…
Due to the lack of coordination, it is unlikely that the selfish players of a strategic game reach a socially good state. A possible way to cope with selfishness is to compute a desired outcome (if it is tractable) and impose it. However…
We propose a toy model for a stochastic description of the competition between two athletes of unequal strength, whose average strength difference is represented by a parameter $d$. The athletes interact through the choice of their…
In this paper, we first devise two algorithms to determine whether or not a bimatrix game has a strategically equivalent zero-sum game. If so, we propose an algorithm that computes the strategically equivalent zero-sum game. If a given…
For any two-by-two game $\G$, we define a new two-player game $\G^Q$. The definition is motivated by a vision of players in game $\G$ communicating via quantum technology according to a certain standard protocol originally introduced by…
We consider the problem of computing stationary points in min-max optimization, with a particular focus on the special case of computing Nash equilibria in (two-)team zero-sum games. We first show that computing $\epsilon$-Nash equilibria…
We consider a class of N-player stochastic games of multi-dimensional singular control, in which each player faces a minimization problem of monotone-follower type with submodular costs. We call these games "monotone-follower games". In a…