Institutions as a Solution Concept in a Game Theory Context

1986 ◽  
pp. 243-264 ◽  
Author(s):  
Philip Mirowski
Keyword(s):  
Game Theory ◽  
Solution Concept

scholarly journals Holding a group together: non-game-theory vs. game-theory

2021 ◽  
Author(s):  
Michael Richter ◽  
Ariel Rubinstein
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Competitive Equilibrium ◽  
Solution Concept ◽  
Equilibrium Concept

Abstract Each member of a group chooses a position and has preferences regarding his chosen position. The group’s harmony depends on the profile of chosen positions meeting a specific condition. We analyse a solution concept (Richter and Rubinstein, 2020) based on a permissible set of individual positions, which plays a role analogous to that of prices in competitive equilibrium. Given the permissible set, members choose their most preferred position. The set is tightened if the chosen positions are inharmonious and relaxed if the restrictions are unnecessary. This new equilibrium concept yields more attractive outcomes than does Nash equilibrium in the corresponding game.

scholarly journals A Cooperative Dual to the Nash Equilibrium for Two-Person Prescriptive Games

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
H. W. Corley ◽  
Phantipa Kwain
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Normal Form ◽  
Fundamental Solution ◽  
Solution Concept ◽  
Alternative Solution ◽  
Noncooperative Game ◽  
Noncooperative Game Theory ◽  
Best Interest

An alternative to the Nash equilibrium (NE) is presented for two-person, one-shot prescriptive games in normal form, where the outcome is determined by an arbiter. The NE is the fundamental solution concept in noncooperative game theory. It is based on the assumption that players are completely selfish. However, NEs are often not played in practice, so we present a cooperative dual as an alternative solution concept by which an arbiter can assign the players' actions. In this dual equilibrium (DE), each player acts in the other's best interest. We formally define prescriptive games and the DE, then summarize the duality relationships between the NE and DE for two players. We also apply the DE to some prescriptive games and compare it to other outcomes.

Learning Nash Equilibria in Non-Cooperative Games

2011 ◽  
pp. 1018-1023 ◽  
Author(s):  
Alfredo Garro
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Cooperative Games ◽  
Nash Equilibria ◽  
Applied Mathematics ◽  
Solution Concept ◽  
The Other ◽  
Political Sciences ◽  
Definition Of ◽  
Non Cooperative Games

Game Theory (Von Neumann & Morgenstern, 1944) is a branch of applied mathematics and economics that studies situations (games) where self-interested interacting players act for maximizing their returns; therefore, the return of each player depends on his behaviour and on the behaviours of the other players. Game Theory, which plays an important role in the social and political sciences, has recently drawn attention in new academic fields which go from algorithmic mechanism design to cybernetics. However, a fundamental problem to solve for effectively applying Game Theory in real word applications is the definition of well-founded solution concepts of a game and the design of efficient algorithms for their computation. A widely accepted solution concept of a game in which any cooperation among the players must be selfenforcing (non-cooperative game) is represented by the Nash Equilibrium. In particular, a Nash Equilibrium is a set of strategies, one for each player of the game, such that no player can benefit by changing his strategy unilaterally, i.e. while the other players keep their strategies unchanged (Nash, 1951). The problem of computing Nash Equilibria in non-cooperative games is considered one of the most important open problem in Complexity Theory (Papadimitriou, 2001). Daskalakis, Goldbergy, and Papadimitriou (2005), showed that the problem of computing a Nash equilibrium in a game with four or more players is complete for the complexity class PPAD-Polynomial Parity Argument Directed version (Papadimitriou, 1991), moreover, Chen and Deng extended this result for 2-player games (Chen & Deng, 2005). However, even in the two players case, the best algorithm known has an exponential worst-case running time (Savani & von Stengel, 2004); furthermore, if the computation of equilibria with simple additional properties is required, the problem immediately becomes NP-hard (Bonifaci, Di Iorio, & Laura, 2005) (Conitzer & Sandholm, 2003) (Gilboa & Zemel, 1989) (Gottlob, Greco, & Scarcello, 2003). Motivated by these results, recent studies have dealt with the problem of efficiently computing Nash Equilibria by exploiting approaches based on the concepts of learning and evolution (Fudenberg & Levine, 1998) (Maynard Smith, 1982). In these approaches the Nash Equilibria of a game are not statically computed but are the result of the evolution of a system composed by agents playing the game. In particular, each agent after different rounds will learn to play a strategy that, under the hypothesis of agent’s rationality, will be one of the Nash equilibria of the game (Benaim & Hirsch, 1999) (Carmel & Markovitch, 1996). This article presents SALENE, a Multi-Agent System (MAS) for learning Nash Equilibria in noncooperative games, which is based on the above mentioned concepts.

scholarly journals From Nash Equilibria to Chain Recurrent Sets: An Algorithmic Solution Concept for Game Theory

Entropy ◽  
2018 ◽  
Vol 20 (10) ◽  
pp. 782 ◽  
Author(s):  
Christos Papadimitriou ◽  
Georgios Piliouras
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Dynamical Systems ◽  
Nash Equilibria ◽  
Equilibrium Solution ◽  
Solution Concept ◽  
Constructive Proof ◽  
Specific Information ◽  
Potential Game ◽  
Chain Recurrence

In 1950, Nash proposed a natural equilibrium solution concept for games hence called Nash equilibrium, and proved that all finite games have at least one. The proof is through a simple yet ingenious application of Brouwer’s (or, in another version Kakutani’s) fixed point theorem, the most sophisticated result in his era’s topology—in fact, recent algorithmic work has established that Nash equilibria are computationally equivalent to fixed points. In this paper, we propose a new class of universal non-equilibrium solution concepts arising from an important theorem in the topology of dynamical systems that was unavailable to Nash. This approach starts with both a game and a learning dynamics, defined over mixed strategies. The Nash equilibria are fixpoints of the dynamics, but the system behavior is captured by an object far more general than the Nash equilibrium that is known in dynamical systems theory as chain recurrent set. Informally, once we focus on this solution concept—this notion of “the outcome of the game”—every game behaves like a potential game with the dynamics converging to these states. In other words, unlike Nash equilibria, this solution concept is algorithmic in the sense that it has a constructive proof of existence. We characterize this solution for simple benchmark games under replicator dynamics, arguably the best known evolutionary dynamics in game theory. For (weighted) potential games, the new concept coincides with the fixpoints/equilibria of the dynamics. However, in (variants of) zero-sum games with fully mixed (i.e., interior) Nash equilibria, it covers the whole state space, as the dynamics satisfy specific information theoretic constants of motion. We discuss numerous novel computational, as well as structural, combinatorial questions raised by this chain recurrence conception of games.

Legal Disputes Resolved via Game Theoretic Methods

2015 ◽  
Vol 17 (02) ◽  
pp. 1540015 ◽  
Author(s):  
T. E. S. Raghavan
Keyword(s):  
Game Theory ◽  
Solution Concept ◽  
Hourly Wage ◽  
Old Babylonian ◽  
Solution Methods ◽  
Game Theoretic ◽  
Person Game ◽  
Zero Sum ◽  
Mathematical Foundations ◽  
Non Cooperative Games

Mathematical foundations of conflict resolutions are deeply rooted in the theory of cooperative and non-cooperative games. While many elementary models of conflicts are formalized, one often raises the question whether game theory and its mathematically developed tools are applicable to actual legal disputes in practice. We choose an example from union management conflict on hourly wage dispute and how zero sum two person game theory can be used by a judge to bring about the need for realistic compromises between the two parties. We choose another example from the 2000-year old Babylonian Talmud to describe how a certain debt problem was resolved. While they may be unaware of cooperative game theory, their solution methods are fully consistent with the solution concept called the nucleolus of a TU game.

Algorithm for Evolutionarily Stable Strategies against Pure Mutations

2018 ◽  
Author(s):  
Sam Ganzfried
Keyword(s):  
Game Theory ◽  
Positive Result ◽  
Evolutionarily Stable Strategy ◽  
Solution Concept ◽  
Evolutionarily Stable Strategies ◽  
Stable Strategy ◽  
Mutation Strategy ◽  
Important Solution ◽  
Pure Strategies ◽  
Evolutionarily Stable

Evolutionarily stable strategy (ESS) is an important solution concept in game theory which has been applied frequently to biology and even cancer. Finding such a strategy has been shown to be difficult from a theoretical complexity perspective. Informally an ESS is a strategy that if followed by the population cannot be taken over by a mutation strategy. We present an algorithm for the case where mutations are restricted to pure strategies. This is the first positive result for computation of ESS, as all prior results are computational hardness and no prior algorithms have been presented.

scholarly journals A reply to Mueller (2018) Supply chain collaboration: Further insights into incentive alignment in the Beer Game scenario

2018 ◽  
Vol 11 (3) ◽  
pp. 535
Author(s):  
Borja Ponte ◽  
Isabel Fernández ◽  
Rafael Rosillo ◽  
José Parreño ◽  
Nazario García
Keyword(s):  
Game Theory ◽  
Bargaining Power ◽  
Solution Concept ◽  
Supply Chain Collaboration ◽  
Incentive Alignment ◽  
For Profit ◽  
Profit Allocation ◽  
Previous Discussion ◽  
Beer Game

Purpose: We expand a previous discussion in this journal by proposing a new solution concept, based on game theory, for profit allocation with the aim of aligning incentives in collaborative supply chains.Design/methodology/approach: Through the Gately’s notion of propensity to disrupt, we minimize the desire of the nodes to leave the grand coalition in the search of a self-enforcing allocation mechanism.Findings: We discuss the benefits and limitations of this solution in comparison with more established alternatives (e.g. nucleolus and Shapley value). We show that it considers the bargaining power of the nodes, but it may not belong to the core.Originality/value: Finding a fair and self-enforcing scheme for incentive alignment, and specifically profit allocation, is essential to ensure the long-term sustainability of collaborative supply chains.

Computing Nash Equilibria in Non-Cooperative Games

2013 ◽  
Vol 3 (3) ◽  
pp. 29-42
Author(s):  
Alfredo Garro
Keyword(s):  
Game Theory ◽  
Cooperative Games ◽  
Nash Equilibria ◽  
Fundamental Problem ◽  
Solution Concept ◽  
Worst Case ◽  
Interacting Agents ◽  
Definition Of ◽  
Non Cooperative Games ◽  
Computation Of Equilibria

Game Theory has recently drawn attention in new fields which go from algorithmic mechanism design to cybernetics. However, a fundamental problem to solve for effectively applying Game Theory in real word applications is the definition of well-founded solution concepts of a game and the design of efficient algorithms for their computation. A widely accepted solution concept for games in which any cooperation among the players must be self-enforcing (non-cooperative games) is represented by the Nash equilibrium. However, even in the two players case, the best algorithm known for computing Nash equilibria has an exponential worst-case running time; furthermore, if the computation of equilibria with simple additional properties is required, the problem becomes NP-hard. The paper aims to provide a solution for efficiently computing the Nash equilibria of a game as the result of the evolution of a system composed by interacting agents playing the game.

scholarly journals Action Being Character: A Promising Perspective on the Solution Concept of Game Theory

PLoS ONE ◽  
2011 ◽  
Vol 6 (5) ◽  
pp. e19014 ◽  
Author(s):  
Kuiying Deng ◽  
Tianguang Chu
Keyword(s):  
Game Theory ◽  
Solution Concept ◽  
Promising Perspective
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