A Logical Multidemand Bargaining Model with Integrity Constraints

Jiang

2017

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In real life, sometimes multicriteria decision making (MCDM) problems are dealt with inevitably under cognitive limitations of human's minds. However, few existing models can directly solve MCDM problems of this kind. Thus, to address the issue, this paper proposes a novel approach, which can: (i) handle the cognitive limitations in MCDM problems by distinguishing the case of complete criteria (i.e., there are no hidden cognitive factors that can deviate rational decisions) from the case of incomplete criteria (i.e., there are some hidden cognitive factors that can deviate rational decisions); (ii) differentiate incomplete and complete relative ranking of the groups of decision alternatives (DAs) over a criterion; and (iii) solve the imprecise and uncertain evaluation of criterion weight as well as the ambiguous evaluations of the groups of DAs regarding a given criterion. Hence, we give a measure to consider the influence of cognitive limitations and give two methods to reduce the influence of cognitive limitations when a decision making needs more rational. Moreover, we illustrate our approach by solving a real‐life problem of estate investment. Finally, we give some experimental results about the reduction of the required number of knowledge judgments in our method compared with the previous methods.

Section: Discussionmentioning

confidence: 99%

Multicriteria Decision Making with Cognitive Limitations: A DS/AHP-Based Approach

Jiang

2017

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“…Thereby, the order of magnitude for the payoff function is 0.1, which means that for any two payoffs 1 and 2 , if | 1 − 2 | < 0.1, then 1 and 2 are indifferent for Ada. Taking Bell's strategy reasonable price as an example, the frame of discernment is a payoff set as • For ( , ), ( ) = [4,7] (by formulas (20)). And by formulas (21), we have ( , ) = log ( − + 1) = log 100 (90 − 60 + 1) = 0.75.…”

Section: Illustrationmentioning

confidence: 99%

“…Generally speaking, decision making involved multiple self‐interested agents is more complicated than that of only one agent. This is because when multiple agents make decisions, they have to consider how other agents choose their strategies . The most fundamental solution concept in multi‐agents decision making (i.e., game theory) is Nash equilibrium, which is widely used for predicting the outcome of a strategic interaction in different research areas .…”

Section: Introductionmentioning

confidence: 99%

“…other agents choose their strategies. [1][2][3][4] The most fundamental solution concept in multi-agents decision making (i.e., game theory) is Nash equilibrium, 5 which is widely used for predicting the outcome of a strategic interaction in different research areas. 2,[6][7][8] Informally, a Nash equilibrium corresponds to a steady state of a matrix game (i.e., each player has no incentive to deviate the state).…”

mentioning

confidence: 99%

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Matrix games with missing, interval, and ambiguous lottery payoffs of pure strategy profiles and compound strategy profiles

Jiang

2017

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In a matrix game, the interactions among players are based on the assumption that each player has accurate information about the payoffs of their interactions and the other players are rationally self‐interested. As a result, the players should definitely take Nash equilibrium strategies. However, in real‐life, when choosing their optimal strategies, sometimes the players have to face missing, imprecise (i.e., interval), ambiguous lottery payoffs of pure strategy profiles and even compound strategy profile, which means that it is hard to determine a Nash equilibrium. To address this issue, in this paper we introduce a new solution concept, called ambiguous Nash equilibrium, which extends the concept of Nash equilibrium to the one that can handle these types of ambiguous payoff. Moreover, we will reveal some properties of matrix games of this kind. In particular, we show that a Nash equilibrium is a special case of ambiguous Nash equilibrium if the players have accurate information of each player's payoff sets. Finally, we give an example to illustrate how our approach deals with real‐life game theory problems.

“…[1][2][3] The research on negotiation is carried out mainly in three domains: game theory, [4][5][6] business and management science, 7,8 and computer science. 3,[9][10][11] The focus of game theoretic approaches is on finding the best strategy for each player in a bargaining game. However, the main assumption of game theoretic analysis and modeling of negotiation is that in a game each player knows everything about each other (at least to some extent).…”

Section: Introductionmentioning

confidence: 99%

Reward and Penalty Functions in Automated Negotiation

Yang

Leung

2015

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Automated negotiation is very important for organizing decentralized systems such as e-business, p2p systems, cloud computing, and so on. During the course of a negotiation, reward and penalty can be used to increase the chance of reaching agreements between negotiating agents, but have not been applied into automated negotiation systems well, especially integrating both in a single negotiation system. Thus, in this work we make an effort to reveal how the reward increases the acceptability of an offer and how the penalty decreases the deniability of an offer. More specifically, our study shows that the degree, to which a reward and a penalty influence the outcome, depends on the greedy degree for the reward and the creditable degree on the penalty. Therefore, if we know an offeree's utilities of accepting and denying an offer, the greedy degree for reward and the creditable degree on penalty, we can calculate how much reward and penalty the offerer agent needs to change the offeree's mind (i.e., from denying to accepting). C 2015 Wiley Periodicals, Inc.