Outcome (game theory)

About: Outcome (game theory) is a research topic. Over the lifetime, 7416 publications have been published within this topic receiving 190495 citations.

Non-cooperative games

Abstract: we would call cooperative. This theory is based on an analysis of the interrelationships of the various coalitions which can be formed by the players of the game. Our theory, in contradistinction, is based on the absence of coalitions in that it is assumed that each participant acts independently, without collaboration or communication with any of the others. The notion of an equilibrium point is the basic ingredient in our theory. This notion yields a generalization of the concept of the solution of a two-person zerosum game. It turns out that the set of equilibrium points of a two-person zerosum game is simply the set of all pairs of opposing "good strategies." In the immediately following sections we shall define equilibrium points and prove that a finite non-cooperative game always has at least one equilibrium point. We shall also introduce the notions of solvability and strong solvability of a non-cooperative game and prove a theorem on the geometrical structure of the set of equilibrium points of a solvable game. As an example of the application of our theory we include a solution of a

The Nash bargaining solution in economic modelling

Abstract: This article establishes the relationship between the static axiomatic theory of bargaining and the sequential strategic approach to bargaining. We consider two strategic models of alternating offers. The models differ in the source of the incentive of the bargaining parties to reach agreement: the bargainers' time preference and the risk of breakdown of negotiations. Each of the models has a unique perfect equilibrium. When the motivation to reach agreement is made negligible, in each model the unique perfect equilibrium outcome approaches the Nash bargaining solution with utilities that reflect the incentive to settle and with the proper disagreement point chosen. The results provide a guide for the application of the Nash bargaining solution in economic modelling.

Other solutions to nash's bargaining problem

Abstract: A two-person bargaining problem is considered. It is shown that under four axioms that describe the behavior of players there is a unique solution to such a problem. The axioms and the solution presented are different from those suggested by Nash. Also, families of solutions which satisfy a more limited set of axioms and which are continuous are discussed. WE CONSIDER a two-person bargaining problem mathematically formulated as follows. To every two-person game we associate a pair (a, S), where a is a point in the plane and S is a subset of the plane. The pair (a, S) has the following intuitive interpretation: a = (a1, a2) where ai is the level of utility that player i receives if the two players do not cooperate with each other. Every point x = (x1, x2) e S represents levels of utility for players 1 and 2 that can be reached by an outcome of the game which is feasible for the two players when they do cooperate. We are interested in finding an outcome in S which will be agreeable to both players. This problem was considered by Nash [3] and his classical result was that under certain axioms there is a unique solution. However, one of his axioms of independence of irrelevant alternatives came under criticism (see [2, p. 128]). In this paper we suggest an alternative axiom which leads to another unique solution. Also, it was called to our attention by the referee that experiments conducted by H. W. Crott [1] led to the solution implied by our axioms rather than to Nash's solution. We also consider the class of continuous solutions which are required to satisfy only the axioms of Nash which are usually accepted. We give examples of families of such solutions.

A Social Equilibrium Existence Theorem.

Abstract: In a wide class of social systems each agent has a range of actions among which he selects one. His choice is not, however, entirely free and the actions of all the other agents determine the subset to which his selection is restricted. Once the action of every agent is given, the outcome of the social activity is known. The preferences of each agent yield his complete ordering of the outcomes and each one of them tries by choosing his action in his restricting subset to bring about the best outcome according to his own preferences. The existence theorem presented here gives general conditions under which there is for such a social system an equilibrium, i.e., a situation where the action of every agent belongs to his restricting subset and no agent has incentive to choose another action.