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 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' 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.

scholarly journals Rational Behavior in Dynamic Multicriteria Games

Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1485
Author(s):  
Anna Rettieva
Keyword(s):  
Game Model ◽  
Bargaining Solution ◽  
Rational Behavior ◽  
Management Problem ◽  
Multicriteria Games ◽  
Cooperative Solution ◽  
Cooperative Equilibrium ◽  
Irrational Behavior ◽  
Common Resource ◽  
Behavior Condition

We consider a dynamic, discrete-time, game model where n players use a common resource and have different criteria to optimize. To construct a multicriteria Nash equilibrium the bargaining solution is adopted. To design a multicriteria cooperative equilibrium, a modified bargaining scheme that guarantees the fulfillment of rationality conditions is applied. The concept of dynamic stability is adopted for dynamic multicriteria games. To stabilize the multicriteria cooperative solution a time-consistent payoff distribution procedure is constructed. The conditions for rational behavior, namely irrational-behavior-proofness condition and each step rational behavior condition are defined for dynamic multicriteria games. To illustrate the presented approaches, a dynamic bi-criteria bioresource management problem with many players is investigated.

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.

A REFINEMENT CONCEPT FOR EQUILIBRIA IN MULTICRITERIA GAMES VIA STABLE SCALARIZATIONS

2007 ◽  
Vol 09 (02) ◽  
pp. 169-181 ◽  
Author(s):  
GIUSEPPE DE MARCO ◽  
JACQUELINE MORGAN
Keyword(s):  
Nash Equilibrium ◽  
Existence Theorem ◽  
Stable Equilibrium ◽  
Multicriteria Games ◽  
Trade Off ◽  
Multicriteria Game

In a finite multicriteria game, one or more systems of weights might be implicitly used by the agents by playing a Nash equilibrium of the corresponding trade-off scalar games. In this paper, we present a refinement concept for equilibria in finite multicriteria games, called scalarization-stable equilibrium, that selects equilibria stable with respect to perturbations on the scalarization. An existence theorem is provided together with some illustrative examples and connections with some other refinement concepts are investigated.

scholarly journals A note on ideal Nash equilibrium in multicriteria games

2008 ◽  
Vol 21 (11) ◽  
pp. 1105-1111 ◽  
Author(s):  
M.S. Radjef ◽  
K. Fahem
Keyword(s):  
Nash Equilibrium ◽  
Multicriteria Games
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