Solymosi and Raghavan (2001) characterize the stability of the core of the assignment game by means of a property of the valuation matrix. They show that the core of an assignment game is a von Neumann-Morgenstern stable set if and only if its valuation matrix has a dominant diagonal. Their proof makes use of some graphtheoretical tools, while the present proof relies on the notion of buyer-sel...

The function that assigns to each matrix game (i.e., the mixed extension of a finite zero-sum two-player game) its value is axiomatized by a number of intuitive properties.

We consider a repeated 2-person 0-sum game with incomplete information about the pay-off matrix. Player I (maximizer) knows the real pay-off matrix but he is uncertain about the beliefs of his opponent. We show that in this case the Aumann-Maschler results on incomplete information on one side no longer hold. In particular such a game will not have a value in general, in spite of the fact that ...

In this paper we propose a new method to associate a coalitional game with each strategic game. The method is based on the lower value of matrix games. We axiomatically characterize this new method, as well as the method that was described in von Neumann and Morgenstern (1944). As an intermediate step, we provide some axiomatic characterizations of the value and the lower value of matrix games.

In this paper, we have discussed the results of sensitivity analysis in a payoff matrix of the Matching Pennies game. After representing the game as a LPmodel, the sensitivity analysis of the elements of the payoffmatrix is presented. The game value and the optimal strategies for different values of parameters are determined and compared. Published by Elsevier Ltd

In the paper we compare well known numerical methods of finding PageRank vector. We propose Markov Chain Monte Carlo method and obtain a new estimation for this method. We also propose a new method for PageRank problem based on the reduction of this problem to the matrix game. We solve this (sparse) matrix game with randomized mirror descent. It should be mentioned that we used non-standard ran...

game theory is an approach based on mathematics to study social interactions and modeling strategic situations. this theory focuses on decision situations where preferences of decision makers are disputed. existence of strategic position in city also with a conflict of interest or competition makes using game theory to describe the urban management issues, attractive. one of the important contr...

Assuming that cards are dealt with replacement from a single deck and that each of Player and Banker sees the total of his own two-card hand but not its composition, baccara is a 2 × 2 matrix game, which was solved by Kemeny and Snell in 1957. Assuming that cards are dealt without replacement from a d-deck shoe and that Banker sees the composition of his own two-card hand while Player sees only...

In this paper, some new criteria for detecting whether a finite game is potential are proposed by solving potential equations. The verification equations with the minimal number for checking a potential game are obtained for the first time. Some connections between the potential equations and the existing characterizations of potential games are established. It is revealed that a finite game is...

In this paper, we consider a two persons zero sum game with imprecise values in payoff matrix. All the imprecise values are assumed to be octagonal fuzzy numbers. An approach for solving problems by using ranking of the fuzzy numbers has been considered to solve the fuzzy game problem. By using ranking to the payoffs we convert the fuzzy valued game problem to crisp valued game problem, which c...