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Multiple Attribute Decision Making (MADM) problem is a management science technique, which is popularly used to rank the priority of alternatives with respect to their competing attributes. It is popularly used in diverse fields such as engineering management, portfolio selection, transportation planning, and performance evaluation. Weights form the core of MADM: it is obvious that different weights lead to various evaluation results and decisions. Several approaches have been developed for assessing the weights of MADM problems, e.g., the eigenvector method, ELECTRE, and TOPSIS. However, an assessment approach of weights in MADM, which meets both the need of simplicity interface for practitioners and concrete theory for scholars is not easy, and balancing these two aspects is a challenging and tough task. Since the pay-off matrix in game theory could be regarded as a simple interface for data input/output, and very few scholars had ever explored the two-person zero-sum game on MADM problems. In this paper, the weights of a MADM problem are obtained by formulating it as a two-person zero-sum game with multiple decision makers. The group equilibrium solution, i.e., consensus of weights and the resolution steps for such a group MADM game has also been originally developed and validated in this study. Finally, an actual case of selecting the appropriate portfolio decision for a paper company is illustrated.

In this paper, we consider a scheduling problem with $m$ uniform parallel-batching machines $\{M_1,M_2,\dots ,M_m\}$ under game situation. There are $n$ jobs, each of which is associated with a load. Each machine $M_i(1\le i\le m)$ has a speed $s_i$ and can handle up to $b$ jobs simultaneously as a batch. The load of a batch is the load of the longest job in the batch. All the jobs in a batch start and complete at the same time. Each job is owned by an agent and its individual cost is the completion time of the job. The social cost is the largest completion time over all jobs, i.e., the makespan. We design a coordination mechanism for the scheduling game problem. We discuss the existence of Nash Equilibrium and offer an upper bound on the price of anarchy (POA) of the coordination mechanism. We present a greedy algorithm and show that: (i) under the coordination mechanism, any instance of the scheduling game problem has a unique Nash Equilibrium and it is precisely the schedule returned by the greedy algorithm; (ii) the mechanism has a POA no more than $1+\frac{s_{max}}{\bar{s}}\left(\right.1-\frac{1}{max\{m,b\}}\left)\right.+\delta$, where $s_{max}=max\{s_1,s_2,\dots ,s_m\}$, $\bar{s}=(s_1+s_2+\cdots +s_m)/m$, and $\delta$ is a small positive number that tends to 0.

We provide a survey of recent developments about capacities (or fuzzy measures) and cooperative games in characteristic form, when they are defined on more general structures than the usual power set of the universal set, namely lattices. In a first part, we give various possible interpretations and applications of these general concepts, and then we elaborate about the possible definitions of usual tools in these theories, such as the Choquet integral, the Möbius transform, and the Shapley value.

A new product can be produced and sold in a market thanks to the entrance of a patent holder into the market. This market is divided into submarkets controlled by only some firms and the profit attainable in each submarket is uncertain. In this paper, this situation is studied by means of cooperative games under interval uncertainty. We consider different ways of allocating the interval profit among the firms. One of these is the interval $\mathcal{T}$-value, which is defined for interval games satisfying some conditions. Efficient interval solutions in terms of the market data are provided.

Infinite multistage games G with games Γ(·) played on each stage are considered. The definition of path and trajectory in graph tree are introduced. For infinite multistage games G a regularization procedure is introduced and in the regularizied game a strong Nash Equilibrium (coalition proof) is constructed. The approach considered in this paper is similar to one used in the proof of Folk theorems for infinitely repeated games. The repeated n-person "Prisoner's Dilemma" game is considered, as a special case. For this game a strong Nash Equilibrium is found.

We analyze the pre- and post-election processes as a two-period game between an incumbent and a challenger. Before the election, in period 1, an incumbent allocates resources into production, fighting with the challenger, and providing public goods, which impact the probability of winning an election. After the election, in period 2 the incumbent may accept the election result, or a coalition or standoff may follow. Six outcomes are that the incumbent wins, the challenger wins, and that a standoff or coalition arises after one of the players wins. We analyze the incumbent’s and challenger’s strategic choices, how these choices depend on a variety of parameters, and the impact of the choices. The analysis is mapped to and tested against empirics of 48 African elections during 2009–2015 which are classified into the six outcomes. To test the model empirically, the correlations between three variables (the incumbent’s fighting and public goods provision and the challenger’s fighting, in period 1) and the six election outcomes are determined for 48 African elections.

Two adversarial actors interact controversially. Early incomplete evidence emerges about which actor is at fault. In period 1 of a two-period game, two media organizations identify ideologically with each of the two actors who are the players exerting manipulation efforts to support the actor they represent. In period 2, the full evidence emerges. Again, the two players exert efforts to support their preferred actor. This paper illustrates the players’ strategic dilemmas for the typical event that actor 1 is considerably at fault based on the early evidence, and much less at fault based on the full evidence. The model assumes that exerting effort in period 1 implies reward or punishment in period 2 depending on whether the full evidence exceeds the early evidence. Twelve parameters in the model are varied individually relative to a benchmark. For example, the players’ efforts are inverse U shaped to an extent in which the actors they identify with are at fault in the two periods. Increasing the evidence ratio intensity causes lower efforts since the players become more unequally matched.

Parrondo's Paradox has pointed out that combined losing strategies can win. In Parrondo's Paradox games, the design of game B is critical. Currently there are mainly three versions, which depend on capital, history and space. We devise a new version of game B which depends on the capital parity and draw on the structure of the benefit matrix in the Prisoner's Dilemma game model. Theoretical analysis and computer simulation results both demonstrate the establishment of this paradox version.

We propose the use of a quantum algorithm to deal with the problem of searching with errors in the framework of two-person games. Specifically, we present a solution to the Ulam's problem that polynomially reduces its query complexity and makes it independent of the dimension of the search space.

We consider the bin packing problem with cardinality constraints in a non-cooperative game setting. In the game, there are a set of items with sizes between 0 and 1, and a number of bins each of which has a capacity of 1. Each bin can pack at most $k$ items, for a given integer parameter $k\ge 2$. The social cost is the number of bins used in the packing. Each item tries to be packed into one of the bins so as to minimize its cost. The selfish behaviors of the items result in some kind of equilibrium, which greatly depends on the cost rule in the game. We say a cost rule encourages sharing if for an item, compared with sharing a bin with some other items, staying in a bin alone does not decrease its cost. In this paper, we first show that for any bin packing game with cardinality constraints under an encourage-sharing cost rule, the price of anarchy of it is at least $2-\frac{2}{k}$. We then propose a cost rule and show that the price of anarchy of the bin packing game under the rule is $2-\frac{2}{k}$ when $k\ge 7$.

The article shows the role of a scientific toy in the methodology of teaching physics and describes graphic examples in various sections. The significance of homemade toys is highlighted, examples of such toys are also given.

Organizations stumble and fail for many reasons. One is that a dominant narrative, in the form of a story a company tells itself, one it shares with its audience/ market, or both, does not jibe with the lived experiences of a significant number of its employees and/or customers. This chapter is predicated on the idea that co-created stories are a way communities, organizations, and individuals can ease or eliminate the negative outcomes of dominant narratives. I propose that a basis for the structured co-creation of stories is what I call “game,” and that a definition of the game that can be applied to any co-created story is ERGO, an acronym for environment/roles/guidelines/objective. To explain the concept and its genesis, I take the reader through a community storytelling workshop I conducted in 2013, in which participants practiced applying the ERGO game structures to co-created community stories of drug abuse prevention.

A paradox of self-reference in beliefs in games is identified, which yields a game-theoretic impossibility theorem akin to Russell's Paradox. An informal version of the paradox is that the following configuration of beliefs is impossible:Ann believes that Bob assumes thatAnn believes that Bob's assumption is wrongThis is formalized to show that any belief model of a certain kind must have a “hole.” An interpretation of the result is that if the analyst's tools are available to the players in a game, then there are statements that the players can think about but cannot assume. Connections are made to some questions in the foundations of game theory.