Review of “A Non-Cooperative Equilibrium for Super games”
By: James W. Friedman
Nash has been useful in the generation of non-constant sum games. He came up with the non-cooperative solution and the non-cooperative equilibrium concept. The non-cooperative solution is a generalization of the minimax theorem for two persons zero sum games and Cournot solution (Friedman 1). The non-cooperative equilibrium concept is applicable to super game. This fits into the Nash (non-cooperative) definition and depicts some features that are similar to Nash cooperative solution. The purpose of this paper is to present the non-cooperative equilibrium concept and applicable concepts to supergames that fits into the non-cooperative definition and bears some of the characters that are similar to the Nash cooperative solution. The study also introduces associated solution as a proof of the existence of the concepts. The study argues that the common perceptions of threat in game theory are ineffective in non-cooperative supergames. The study proposes temptation as an analogous concept to threat and has intuitive appeal. The study further describes ordinary game, and non-cooperative equilibrium in addition to their establishment. There is a description of supergames and supergame strategies, definition and discussion of a non-cooperative equilibrium for supergames. The study concludes that a game is non-cooperative if the players cannot form coalitions or make agreements.
The study introduces non-cooperative equilibrium concept that are applicable to supergames and fit into the Nash definition, while bearing some features of Nash cooperative solution. According to the study, supergame refers to the activity of playing an infinite sequence of general games over a period. Oligopoly refers to a form of a supergame. Fried argues that general insights of threat in game theory are ineffective in non-cooperative supergames and goes on to propose that temptation as an analogous concept to threat and has intuitive appeal. The major objective of the study is to present the non-cooperative equilibrium concept, applicable concepts to supergames that fits into the non-cooperative definition and bears some of the characters that are similar to the Nash cooperative solution, and introduce associated solution as a proof of the existence of the concepts. The study is therefore useful in introducing completely innovative concepts of solution for non-cooperative supergames. The study defines an ordinary game as a game where every player posses a set of strategies that are compact and convex subset of Euclidean space of finite dimension. Fried proves the Mash game and establishes the continuation of the non-cooperative equilibrium for ordinary game.
Osborne mentions Fried when he introduces a varying definition of game as a strategic interaction that composes the constraints on the actions players can take and the interest of the players but fails to specify the actions of the players (Osborne, 2). He goes on to mention findings of Fried when he states that non-cooperative game captures a constant state of the play in a strategic game when every player holds the correct explanation of the behavior of other players and conduct themselves rationally.
Barros and Gordon mentions a contrary aspect that to the concept introduced by Fried when that state that natural-rate theories recommend that systematic components in monetary policy lack significant consequences for business cycle. The authors go on to mention that a high and variable rate of monetary growth is usually experienced with rational expectations equilibrium in discretionary surroundings where policymakers pursues reasonable objective.
Axelrod mentions Fried when he mentions problems of cooperation as being central in varied fields. Axelrod incorporates Fried’s Arguments when he questions whether unforced cooperation has ever been possible.
To examine the effectiveness of non-cooperative supergames, Fried discusses a proposition as a generalization of the Nash theorem without application of much data. In this discussion, he applies Si as a representation of finite sets of pure strategies. The proposition is a special case of a Debreu theorem, which is a general statement of existence of non-cooperative equilibria of finite strategy spaces. Econometric approaches are used to present the non-cooperative equilibrium concept, applicable concepts, and introduce associated solution as a proof of the existence of the concepts
No data is used as Fried sought to prove his concepts.
The major conclusion is that a non-cooperative game refers to the game where players fail to form coalitions or make agreements. In practical experiences, Cournot solution is felt since the mentioned equilibrium is a Pareto optimal and a non-cooperative equilibrium. Several basic game non-cooperative equilibriums are found in every point, which implies that numerous Pareto optimal points could form part of a supergame non-cooperative equilibrium. It is therefore impossible to select a supergame equilibrium as a natural game solution.
The article was written in a simplified manner that is easy to read and understand. It is short and hence covers only major details of the models while forgoing the minor details. Fried includes definition of all major terms used in the paper, which is useful for clear understanding of the basic concepts. He introduces a prospective application of the equilibrium concept in the theory of oligopoly. Game has been interpreted as an oligopoly, while the Cournot as varying from the Pareto optimal point. even though the concepts presented as useful, much dissatisfaction is experienced when applying it, since in practical areas such as in calculation of profit marginalization, firms experience profits only at the Cournot point. Such firms therefore experience what is known as the tacit collusion, which has mostly been presented as though the firms colluded. This point is mainly attained since the Cournot behavior is usually a common behavior.
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Friedman, W. James. “A Non-Cooperative Equilibrium for Supergames.” The Review of
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