Related papers: Two Person zero-sum fuzzy matrix games and extensi…
In this paper, we study the egalitarian solution for games with discrete side payment, where the characteristic function is integer-valued and payoffs of players are integral vectors. The egalitarian solution, introduced by Dutta and Ray in…
In this work, we consider the problem of a two-player zero-sum game. In the literature, the successive over-relaxation Q-learning algorithm has been developed and implemented, and it is seen to result in a lower contraction factor for the…
Two player zero sum simultaneous action games are common in video games, financial markets, war, business competition, and many other settings. We first introduce the fundamental concepts of reinforcement learning in two player zero sum…
This paper concerns two-player alternating play combinatorial games (Conway 1976) in the normal-play convention, i.e. last move wins. Specifically, we study impartial vector subtraction games on tuples of nonnegative integers (Golomb 1966),…
Despite recent advancements in AI and NLP, negotiation remains a difficult domain for AI agents. Traditional game theoretic approaches that have worked well for two-player zero-sum games struggle in the context of negotiation due to their…
The theory of fuzzy sets has a wide range of applications, one of which is that of fuzzy groups . The fuzzy sets were introduced by Zadeh. Even though, the story of fuzzy logic started much earlier, it was specially designed mathematically…
In this paper, we study nonzero-sum separable games, which are continuous games whose payoffs take a sum-of-products form. Included in this subclass are all finite games and polynomial games. We investigate the structure of equilibria in…
Consider a linear programming problem with n primal and m dual variables paired with n dual and m primal slack variables respectively, and aggregately denote these variables and slack variables as a vector z of length 2(n+m). Unlike…
Recently the matcher game was introduced. In this game, two players create a maximal matching by one player repeatedly choosing a vertex and the other player choosing a $K_2$ containing that vertex. One player tries to minimize the result…
Recent work by Atserias and Dawar (J. Log. Comp 2019) and Tucker-Foltz (LMCS 2024) has established undefinability results in fixed-point logic with counting (FPC) corresponding to many classical complexity results from the hardness of…
A new class of multi-player competitive stochastic games in discrete-time with an affine specification of the redistribution of payoffs at exercise is proposed and examined. Our games cover as a very special case the classic two-person…
We study binary coordination games with random utility played in networks. A typical equilibrium is fuzzy -- it has positive fractions of agents playing each action. The set of average behaviors that may arise in an equilibrium typically…
The works of (Daskalakis et al., 2009, 2022; Jin et al., 2022; Deng et al., 2023) indicate that computing Nash equilibria in multi-player Markov games is a computationally hard task. This fact raises the question of whether or not…
This paper extends the notion of learning equilibrium in game theory from matrix games to stochastic games. We introduce Foolproof Cooperative Learning (FCL), an algorithm that converges to a Tit-for-Tat behavior. It allows cooperative…
A naive way to solve the model-checking problem of the mu-calculus uses fixpoint iteration. Traditionally however mu-calculus model-checking is solved by a reduction in linear time to a parity game, which is then solved using one of the…
This paper proposes a new method for finding closed-loop saddle points in zero-sum linear-quadratic stochastic differential games by decoupling their inherent structure. Specifically, we develop a nested iterative scheme that constructs a…
We consider extensive games with perfect information with well-founded game trees and study the problems of existence and of characterization of the sets of subgame perfect equilibria in these games. We also provide such characterizations…
In recent years, the problem of fuzzy clustering has been widely concerned. The membership iteration of existing methods is mostly considered globally, which has considerable problems in noisy environments, and iterative calculations for…
Two-player zero-sum games are a well-established model for synthesising controllers that optimise some performance criterion. In such games one player represents the controller, while the other describes the (adversarial) environment, and…
Many models from a variety of areas involve the computation of an equilibrium or fixed point of some kind. Examples include Nash equilibria in games; market equilibria; computing optimal strategies and the values of competitive games…