Jason J. Wang

Between controlling the virus and boosting the economy, it has become a “President’s Dilemma”, in which determining the optimal time to open-up the economy while still being able to contain the virus is the president’s top priority. In this study, we utilize game theory examples to illustrate various scenarios of the President’s Dilemma and provide possible game theory tools to obtain the optimal solutions. For the normal simultaneous game, the Nash equilibrium is at (Open-up, Lock-down). For the GDP vs mortality game, Open-up is a more cost-effective option. In the Bayesian game, if the proportion of the governors siding with the president q>=1/3, the President would choose Open-up while if q<1/3, he would choose Lock-down. The Stackelberg game point out the possible study path to figure out the leader-follower roles and related factors.

]]>Shahd H. Alkaraz, Essam El-Seidy, Neveen S. Morcos

]]>Hassan El Kady, Essam El-Seidy

We introduce a class of impartial combinatorial game which is the multi-player Last Nim game, denoted by in which there are N piles of counters which are linearly ordered, the move will be, the n-player will remove any positive integer of counters from the last pile, we will introduce this with Shifted Standard alliance system by 1, denoted by in which each player will prefer winning for another player over himself. The Aim is to determine the game value of the positions of where is the number of piles and is the number of players and we will present the possible and determine the game value in this case.

]]>Wesam B. Zorik, Essam EL-Seidy, Entisarat M. Elshobaky

Zero Determinant (ZD) strategies is a new class of probabilistic and conditional strategies discovered by Press and Dyson which has been applied on two players. ZD strategies for multiple players will be explored where the application of ZD has been taken on Iterated three-player Prisoner’s Dilemma Game (IPDG) with two actions C or D. It is assumed that the results in the case of the three players correspond to what was obtained in the case of two players with different calculation methods. It is interesting, although the player who adopts ZD strategies can determine the opponent’s payoffs in a unilateral way. And with an extortion strategy, he can impose a linear relationship between the expected return for him and the expected payoff of other players, but he cannot determine his own score. Also, the yield matrix was determined in the case of three players.

]]>Essam El_Seidy, Hassan El Kady, Dieaa I. Nassr

The Last Nim game is an impartial combinatorial game studied only in the case of the standard alliance matrix. In this paper, we consider the Last Nim game with N linearly ordered nonempty piles containing counters, and n players for any alliance matrix. For this, we give an algorithm to get the winner, the tree of all possibilities of the game, and the best strategy for the winner. For the practical result, we implement this algorithm using C++ language and give some examples.

]]>Yeremia Maroutian

In this paper for fuzzy cooperative games we generalize the classical Shapley value through using one of the known approaches for its redefinition. For fuzzy cooperative games formalized as well the Shapley axioms. For the fuzzy pre-value of Shapley we research certain of known properties that hold true for classical Shapley value.

]]>Zhao Rui-juan, Zhou Jian-heng

This study investigated signaling strategy of a dual-channel supply chain, which contains a manufacturer (he), who owns a direct online channel and tries to convince his retailer (she) of the high-demand potential of his products, considering channel competition and free riding across channels. In this paper we incorporated retailer’s value-added services into the model, to analyze how the manufacturer uses wholesale price and slotting allowance to practice his signaling strategy under asymmetric information. Our results suggest that: compared with the situation when information is symmetric, under information asymmetry, the high-demand manufacturer needs to distort the wholesale price upward under some conditions, and pays lower slotting allowance to the retailer. However, in some situation, he can also realize separation by using the information-symmetry contract. Moreover, the fiercer of the competition is, or the greater the free-riding effect is, it is more possible that the manufacturer needs to choose the distorted wholesale price for signaling.

]]>Alexander Munson

We consider the question whether a pillage game can have infinitely many stable sets under certain regularity and dominance conditions. We establish a rigidity result in continuous pillage games. This property implies that in any continuous pillage game, an allocation's dominance structure is essentially determined by local regularity behaviours of the power function. Using this property, we derive a weak convergence theorem on the power set of the n-players near any point in the allocation space by passing any sequence of allocations through specially constructed filters subject to geometric, parity, and unidirectionality conditions. Combining these results, a sufficient condition for the theoretical existence of an infinite set of stable sets is proposed. We also discuss the extension of our results in the wider scope where some of the conditions are lifted.

]]>Qing Hu

We consider a firm which sells one product in a monopolistic market and sells another product in an oligopolistic market. The leverage theory states that bundling the two products is always profitable. We investigate whether the leverage theory still holds in network industries. We find that this conventional wisdom reverses and bundling is not always preferred. In addition, we find that the profitable bundling can increase the consumer surplus when the network effect is relatively intense.

]]>Irinel Dragan

In earlier works, we discussed the Inverse Problem for Binomial Semivalues, with coalitional rationality, and the use of Flow Games in the Gas Routing Problem. In the present paper, we apply the techniques shown in connection with the first problems, to the second class of practical problems of cooperation in the gas routing activity.

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