scholarly journals COALITION FORMATION IN DYNAMIC MULTICRITERIA GAMES

2019 ◽  
Vol 10 (2) ◽  
pp. 40-61
Author(s):  
Анна Реттиева ◽  
Anna Rettieva
Keyword(s):  
Nash Equilibrium ◽  
Characteristic Function ◽  
Coalition Formation ◽  
Information Structure ◽  
Planning Horizon ◽  
Nash Bargaining ◽  
Management Problem ◽  
Multicriteria Games ◽  
Optimal Behavior ◽  
Bargaining Procedure

In this paper new approaches to obtain optimal behavior in dynamic multicriteria games are constructed. The multicriteria Nash equilibrium is obtained via the Nash bargaining design (Nash products), and the cooperative equilibrium is determined by the Nash bargaining procedure for the entire planning horizon. Coalition formation process in dynamic multicriteria games is investegated. To construct the characteristic function the Nash bargaining scheme is applied where the multicriteria Nash equilibrium plays the role of the status-quo points. Two variants of characteristic function's determination that take into account information structure of the game are presented (models without information and with informed players). Dynamic multicriteria bioresorce management problem is considered. The players' strategies and the size of the resource are compared under cooperative and noncooperative behavior and for different variants of characteristic function determination.

scholarly journals Dynamic Multicriteria Games with Finite Horizon

Mathematics ◽  
2018 ◽  
Vol 6 (9) ◽  
pp. 156 ◽  
Author(s):  
Anna Rettieva
Keyword(s):  
Nash Equilibrium ◽  
Finite Horizon ◽  
Nash Bargaining ◽  
Management Problem ◽  
Multicriteria Games ◽  
Optimal Behavior ◽  
Cooperative Equilibrium

The approaches to construct optimal behavior in dynamic multicriteria games with finite horizon are presented. To obtain a multicriteria Nash equilibrium, the bargaining construction (Nash product) is adopted. To construct a multicriteria cooperative equilibrium, a Nash bargaining scheme is applied. Dynamic multicriteria bioresource management problem with finite harvesting times is considered. The players’ strategies and the payoffs are obtained under cooperative and noncooperative behavior.

scholarly journals Dynamic multicriteria games' solutions: classical and untraditional approaches

2020 ◽  
Vol 12 (1) ◽  
pp. 19-32
Author(s):  
Анна Реттиева ◽  
Anna Rettieva
Keyword(s):  
Management Problem ◽  
Weighted Sum ◽  
Optimal Solutions ◽  
Multicriteria Games ◽  
Optimal Behavior ◽  
Classical Scheme

In this paper the approaches to obtain an optimal behavior in dynamic multicriteria games are constructed. Classical scheme with weighted sum of the criteria and new conceptions of optimal solutions' construction are presented. Dynamic multicriteria bioresorce management problem is considered. Parameters of the model where the equilibria obtained applying traditional or dynamic approaches coincide are obtained.

Equilibria in Dynamic Multicriteria Games

2017 ◽  
Vol 19 (01) ◽  
pp. 1750002 ◽  
Author(s):  
Anna Rettieva
Keyword(s):  
Nash Equilibrium ◽  
Discrete Time ◽  
Solution Concept ◽  
Status Quo ◽  
Nash Bargaining ◽  
Game Model ◽  
Multicriteria Games ◽  
Common Resource ◽  
Game Theoretic

Mathematical models involving more than one objective seem more adherent to real problems. Often players have more than one goal which are often not comparable. These situations are typical for game-theoretic models in economic and ecology. In this paper, new approaches to construct equilibria in dynamic multicriteria games are constructed. We consider a dynamic, discrete-time, game model where the players use a common resource and have different criteria to optimize. First, we construct the guaranteed payoffs in a several ways. Then, we find an equilibrium as a solution of a Nash bargaining scheme with the guaranteed payoffs playing the role of status quo points. The obtained equilibrium, called a multicriteria Nash equilibrium, gives a possible solution concept for dynamic multicriteria games.

R&D INVESTMENTS AS PREBARGAINING STRATEGIES

2014 ◽  
Vol 16 (03) ◽  
pp. 1450003 ◽  
Author(s):  
WILFRIED PAUWELS ◽  
PETER M. KORT ◽  
EVE VANHAECHT
Keyword(s):  
Nash Equilibrium ◽  
Low Cost ◽  
Unit Cost ◽  
The Other ◽  
Nash Bargaining ◽  
Unit Costs ◽  
Bargaining Outcome ◽  
Nash Bargaining Game ◽  
Output Market ◽  
The Difference

This paper analyzes a semicollusive, differentiated duopoly. Firms first compete in cost reducing R&D and then cooperate on the output market. The sharing of the joint profit on the output market is modeled as a Nash bargaining game. We study an asymmetric setting in which one firm has a lower unit cost of production than the other firm, before any R&D expenditures. If firms do not agree on how to share their joint profit, they play a noncooperative Nash equilibrium. Assuming linear demand functions, we show that the Nash bargaining outcome is independent of whether firms play a Cournot or a Bertrand Nash equilibrium, as long as both firms supply positive outputs in these equilibria. If the two products are sufficiently differentiated, there is a unique equilibrium in which both firms supply a positive output, and in which the low cost firm always invests more in R&D than the high cost firm. If the two products are not very differentiated, and if the difference in unit costs between the two firms is not too large, there exist two equilibria. In each of these equilibria only one firm supplies a positive output. This can be the low cost or the high cost firm. In the latter case, the initially high cost firm invests so much in R&D that its unit cost after R&D is lower than that of the other firm. This firm then leapfrogs the other firm. If the two products are very similar and if firms apply Bertrand strategies when disagreeing, there exist equilibria in which only one firm supplies a positive output, while in the noncooperative Nash equilibrium that same firm can prevent the other firm from entering the market. We show that, in the context of the Nash bargaining model, this latter firm still has the power to claim a share of the joint profit.

scholarly journals Forest management for optimizing soil protection: a landscape-level approach

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Ana Raquel Rodrigues ◽  
Susete Marques ◽  
Brigite Botequim ◽  
Marco Marto ◽  
José G. Borges
Keyword(s):  
Forest Management ◽  
Soil Erosion ◽  
Planning Horizon ◽  
Programming Approach ◽  
Soil Protection ◽  
Planning Problem ◽  
Management Problem ◽  
Critical Periods ◽  
Trade Offs ◽  
Landscape Level

Abstract Background Soil erosion is still identified as the main cause of land degradation worldwide, threatening soil functions and driving several research and policy efforts to reverse it. Trees are commonly associated to some of the most successful land-use systems to achieve soil protection goals, but the extent to which forest ecosystems reduce erosion risks can largely depend on management decisions and associated silvicultural practices. Optimization tools can assist foresters in solving the complex planning problem they face, concerning the demand for different, and often conflicting, ecosystem services. A resource capability model (RCM), based on a linear programming approach, was built and solved for a forest landscape management problem in Northwest Portugal, over a 90-years planning horizon, divided in 10-years periods. Results Timber provision and soil erosion were found to be in trade-off. The management alternatives included in the model were proven to be sufficiently flexible to obtain the desired level of timber yield, both in volume and even distribution along the planning horizon, while ensuring lower levels of soil loss estimates (below 35 Mg∙ha− 1∙year− 1). However, under climate change conditions, compatible with an increasing greenhouse gases emission scenario, potential landscape soil erosion may be enhanced up to 46 Mg∙ha− 1∙year− 1 in critical periods. Conclusions Soil conservation concerns in landscape-level forest management planning can be addressed by LP-based optimization methods. Besides providing an optimal management solution at landscape level, this approach enables a comprehensive analysis of the RCM, possible trade-offs and potential changes towards uncertainties.

The Core of Aggregative Cooperative Games with Externalities

2016 ◽  
Vol 16 (1) ◽  
pp. 389-410 ◽  
Author(s):  
Giorgos Stamatopoulos
Keyword(s):  
Normal Form ◽  
Characteristic Function ◽  
Coalition Formation ◽  
Cooperative Games ◽  
Grand Coalition ◽  
Normal Form Games ◽  
The Core ◽  
Aggregative Games ◽  
Games With Externalities

AbstractThis paper analyzes cooperative games with externalities generated by aggregative normal form games. We construct the characteristic function of a coalition S for various coalition formation rules and we examine the corresponding cores. We first show that the $$\gamma $$-core is non-empty provided each player’s payoff decreases in the sum of all players’ strategies. We generalize this result by showing that if S believes that the outside players form at least $$l(s) = n - s - (s - 1)$$ coalitions, then S has no incentive to deviate from the grand coalition and the corresponding core is non-empty (where n is the number of players in the game and s the number of members of S). We finally consider the class of linear aggregative games (Martimort and Stole 2010). In this case, if S believes that the outsiders form at least $$\widehat l(s) = {n \over s} - 1$$ coalitions [where $$\widehat l(s) \le l(s)$$] a core non-emptiness result holds again.

Titik Setimbang Nash pada Permainan Linear Kuadratik Non-kooperatif dengan Asumsi Keseluruhan Pemain dapat Menstabilkan Sistem

2017 ◽  
Vol 1 (2) ◽  
pp. 211-224
Author(s):  
Ezhari Asfa’ani
Keyword(s):  
Quadratic Differential ◽  
Information Structure ◽  
Nash Equilibria ◽  
Sufficient Conditions ◽  
Planning Horizon ◽  
Open Loop ◽  
Linear Quadratic ◽  
Linear Quadratic Differential Games ◽  
Necessary And Sufficient ◽  
Infinite Planning Horizon

We discuss about Nash equilibria for the linear quadratic differential game for an infinite planning horizon. We consider an open-loop information structure. In the standard literature this problem is solved under the assumption and provide both necessary and sufficient conditions for existence of Nash equilibria for this game under the assumption that the system as a whole is stabilizable.      Keywords: linear quadratic differential games, open-loop information structure

USING THE ASPIRATION CORE TO PREDICT COALITION FORMATION

2012 ◽  
Vol 14 (01) ◽  
pp. 1250004 ◽  
Author(s):  
CAMELIA BEJAN ◽  
JUAN CAMILO GÓMEZ
Keyword(s):  
Nash Equilibrium ◽  
Coalition Formation ◽  
Solution Concept ◽  
Transferable Utility ◽  
Tu Game ◽  
Subgame Perfect Nash Equilibrium ◽  
The Core ◽  
Core Solution ◽  
Aspiration Core ◽  
Overlapping Coalitions

This work uses the defining principles of the core solution concept to determine not only payoffs but also coalition formation. Given a cooperative transferable utility (TU) game, we propose two noncooperative procedures that in equilibrium deliver a natural and nonempty core extension, the aspiration core, together with the supporting coalitions it implies. As expected, if the cooperative game is balanced, the grand coalition forms. However, if the core is empty, other coalitions arise. Following the aspiration literature, not only partitions but also overlapping coalition configurations are allowed. Our procedures interpret this fact in different ways. The first game allows players to participate with a fraction of their time in more than one coalition, while the second assigns probabilities to the formation of potentially overlapping coalitions. We use the strong Nash and subgame perfect Nash equilibrium concepts.

Sign in / Sign up

Export Citation Format

Share Document