Nondominated equilibrium solutions of a multiobjective two-person nonzero-sum game in extensive form and corresponding mathematical programming problem

Ichiro Nishizaki; Takuma Notsu
October 2008
Journal of Global Optimization;Oct2008, Vol. 42 Issue 2, p201
Academic Journal
Abstract  In most of studies on multiobjective noncooperative games, games are represented in normal form and a solution concept of Pareto equilibrium solutions which is an extension of Nash equilibrium solutions has been focused on. However, for analyzing economic situations and modeling real world applications, we often see cases where the extensive form representation of games is more appropriate than the normal form representation. In this paper, in a multiobjective two-person nonzero-sum game in extensive form, we employ the sequence form of strategy representation to define a nondominated equilibrium solution which is an extension of a Pareto equilibrium solution, and provide a necessary and sufficient condition that a pair of realization plans, which are strategies of players in sequence form, is a nondominated equilibrium solution. Using the necessary and sufficient condition, we formulate a mathematical programming problem yielding nondominated equilibrium solutions. Finally, giving a numerical example, we demonstrate that nondominated equilibrium solutions can be obtained by solving the formulated mathematical programming problem.


Related Articles

  • Efficiency in the trust game: an experimental study of precommitment. Bracht, Juergen; Feltovich, Nick // International Journal of Game Theory;2008, Vol. 37 Issue 1, p39 

    We experimentally test a precommitment mechanism for the trust game. Before the investor’s decision, the allocator places an amount into escrow, to be forfeited if he keeps the proceeds of investment for himself. We vary the available escrow amounts—in particular, whether there is...

  • Equilibria of the Games in Choice Form. Stefanescu, Anton; Ferrara, Massimiliano; Stefanescu, Maria // Journal of Optimization Theory & Applications;Dec2012, Vol. 155 Issue 3, p1060 

    Equilibrium in choice is a solution-concept for noncooperative games defined in a general framework-the game in choice form. There are two leading ideas of the new definition. One is that the players' preferences need not be explicitly represented, but earlier accepted solution concepts should...

  • Perfect foresight dynamics in games with linear incentives and time symmetry. Takahashi, Satoru // International Journal of Game Theory;2008, Vol. 37 Issue 1, p15 

    This paper investigates absorption and global accessibility under perfect foresight dynamics in games with linear incentives. An action distribution in the society is absorbing if there is no equilibrium path escaping from the distribution, and globally accessible if, from every initial...

  • Research on combinatorial auction. Liu Xin-ming // Proceedings of the International Symposium on Electronic Commerc;Jun2010, p288 

    Since the mid-20th century, with the Nash equilibrium theory formulation and development, game theory has gradually become a new subject. It involves economics, management, computer science, sociology and other fields, which has played a significant role in promoting the development of society....

  • Order-Driven Markets are Almost Competitive. RITZBERGER, KLAUS // Review of Economic Studies;Jan2016, Vol. 83 Issue 1, p338 

    This article studies a market game under uncertainty in which agents may submit multiple limit and market orders. When agents know their preferences at all states, the competitive equilibrium can be supported as a Nash equilibrium of the market game, that is, agents behave as if they were price...

  • Polymatrix games and optimization problems. Strekalovskii, A.; Enkhbat, R. // Automation & Remote Control;Apr2014, Vol. 75 Issue 4, p632 

    Consideration was given to the properties of the polymatrix game, a finite noncooperative game of N players ( N ⩾ 3). A theorem of reduction of the search for Nash equilibria to an optimization problem was proved. This clears the way to the numerical search of equilibria. Additionally, a...

  • An application of optimization theory to the study of equilibria for games: a survey. Mallozzi, Lina // Central European Journal of Operations Research;Sep2013, Vol. 21 Issue 3, p523 

    This contribution is a survey about potential games and their applications. In a potential game the information that is sufficient to determine Nash equilibria can be summarized in a single function on the strategy space: the potential function. We show that the potential function enable the...

  • Potential Games Are Necessary to Ensure Pure Nash Equilibria in Cost Sharing Games. Gopalakrishnan, Ragavendran; Marden, Jason R.; Wierman, Adam // Mathematics of Operations Research;Nov2014, Vol. 39 Issue 4, p1252 

    We consider the problem of designing distribution rules to share "welfare" (cost or revenue) among individually strategic agents. There are many known distribution rules that guarantee the existence of a (pure) Nash equilibrium in this setting, e.g., the Shapley value and its weighted variants;...

  • Loss of skills in coordination games. Flesch, J.; Schoenmakers, G.; Vrieze, O. // International Journal of Game Theory;Oct2011, Vol. 40 Issue 4, p769 

    This paper deals with 2-player coordination games with vanishing actions, which are repeated games where all diagonal payoffs are strictly positive and all non-diagonal payoffs are zero with the following additional property: At any stage beyond r, if a player has not played a certain action for...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics