A Laplace's principle based approach for solving fuzzy matrix games

We introduce a solution for matrix games with fuzzy payoffs via the α -cuts and the introduction of Nature as a third player expressing the uncertainty involved in the game. The beliefs of players about the behavior of Nature are based on the Laplace’s principle of “insufficient reason”. Moreover, we provide a procedure for computing the introduced solution

Strong Berge and Pareto Equilibrium Existence for a Noncooperative Game

In this paper, we study the main properties of the strong Berge equilibrium which is also a Pareto efficient (SBPE) and the strong Nash equilibrium (SNE). We prove that any SBPE is also a SNE, we prove also existence theorem of SBPE based on the KyFan inequality. Finally, we also provide a method for computing SPBE.Strong Berge equilibrium, Pareto efficiency, strong Nash equilibrium, Ky Fan inequality

Nonlinear Inequality, Fixed Point and NashEquilibrium

In this paper, we give new sufficient conditions for the existence of a solution of theg-maximum equality. As a consequence, we prove a new fixed point theorem. We also prove a new theorem of existence of Nash equilibrium.Ky Fan inequality, g-maximum equality, fixed point, Nash equilibrium

ON BERGE EQUILIBRIUM

Based on the notion of equilibrium of a coalition P relatively to a coalition K, of Berge, Zhukovskii has introduced Berge equilibrium as an alternative solution to Nash equilibrium for non cooperative games in normal form. The essential advantage of this equilibrium is that it does not require negotiation of any player with the remaining players, which is not the case when a game has more than one Nashequilibrium. The problem of existence of Berge equilibrium is more difficult (compared to that of Nash). This paper is a contribution to the problem of existence and computation of Berge equilibrium of a non cooperative game. Indeed, using the g-maximum equality, we establish the existence of a Berge equilibrium of a non-cooperative game in normal form. In addition, we give sufficient conditions for theexistence of a Berge equilibrium which is also a Nash equilibrium. This allows us to get equilibria enjoying the properties of both concepts of solution. Finally, using these results, we provide two methods for the computation of Berge equilibria: the first one computes Berge equilibria; the second one computes Berge equilibria which are also Nash equilibria

Strong Berge and Pareto Equilibrium Existence for a Noncooperative Game

In this paper, we study the main properties of the strong Berge equilibrium which is also a Pareto efficient (SBPE) and the strong Nash equilibrium (SNE). We prove that any SBPE is also a SNE, we prove also existence theorem of SBPE based on the KyFan inequality. Finally, we also provide a method for computing SPBE

New Sufficient Conditions for the g-maximum<br />Inequality

In this paper, we give new sufficient conditions for the existence of a solution of theg-maximum equality. As an application, we prove a new fixed point theorem

Seigniorage of fiat money and the maqasid al-shari'ah: the compatibility of the gold dinar with the maqasid

Part I of the paper argued that fiat money is counterproductive to the attainment of the maqasid al-Shari’ah. In the present interest-based fiat monetary system one of the maqasid, namely, the protection of wealth (mal) cannot be realized, which in turn causes the other maqasid to be affected too. In this Part II paper we argue for commodity monies, like the gold dinar and silver dirham, as being compatible with the maqasid. Basically the paper concludes that the Islamic economic system is fundamentally a ‘barter’ system, i.e. an exchange economy where goods and services are exchanged value for value; but avoids the problems associated with barter by taking some of the commodities exchanged in the economy, that have the characteristics of money, as money; and gold is here argued as the best Shari’ah mone

New Sufficient Conditions for the g-maximumInequality

In this paper, we give new sufficient conditions for the existence of a solution of theg-maximum equality. As an application, we prove a new fixed point theorem.Ky Fan inequality, g-maximum equality, fixed point.