THE FORGIVING TRIGGER STRATEGY: AN ALTERNATIVE TO THE TRIGGER STRATEGY

2004 ◽  
Vol 06 (02) ◽  
pp. 247-264
Author(s):  
M. ARAMENDIA ◽  
L. RUIZ ◽  
F. VALENCIANO
Keyword(s):  
Nash Equilibrium ◽  
Subgame Perfect Equilibrium ◽  
Economic Models ◽  
Perfect Equilibrium ◽  
Oligopoly Model ◽  
Trigger Strategy ◽  
Subgame Perfection

The grim-trigger strategy introduced by Friedman is often used in economic models, mainly because of its simplicity, to show that collusion can be sustained by means of a subgame perfect equilibrium. In this work we show that, under simple conditions, it is possible to improve on the grim-trigger strategy while retaining subgame perfection and in some cases adding weak renegotiation proofness (in the sense of Farrell and Maskin). The basic idea is that, following a deviation, the cheater, instead of continuing in the Nash equilibrium forever, chooses an autopenalty which signals, in a very strong way, that he/she would not deviate any more if cooperation were reestablished. We check the nice working of this strategy in the Cournot's oligopoly model.

Quantifying Commitment in Nash Equilibria

2019 ◽  
Vol 21 (02) ◽  
pp. 1940011
Author(s):  
Thomas A. Weber
Keyword(s):  
Nash Equilibrium ◽  
Normal Form ◽  
Nash Equilibria ◽  
Dynamic Game ◽  
Subgame Perfect Equilibrium ◽  
Canonical Extension ◽  
Perfect Equilibrium ◽  
Form Game ◽  
Normal Form Game ◽  
The Given

To quantify a player’s commitment in a given Nash equilibrium of a finite dynamic game, we map the corresponding normal-form game to a “canonical extension,” which allows each player to adjust his or her move with a certain probability. The commitment measure relates to the average overall adjustment probabilities for which the given Nash equilibrium can be implemented as a subgame-perfect equilibrium in the canonical extension.

Synthesis of equilibria in infinite-duration

2021 ◽  
Vol 8 (2) ◽  
pp. 4-29
Author(s):  
Véronique Bruyère
Keyword(s):  
Game Theory ◽  
Nash Equilibrium ◽  
Directed Graph ◽  
Subgame Perfect Equilibrium ◽  
Payoff Function ◽  
Synthesis Problem ◽  
Perfect Equilibrium ◽  
Computer Aided ◽  
Comprehensive Introduction

In this survey, we propose a comprehensive introduction to game theory applied to computer-aided synthesis. We study multi-player turn-based infinite-duration games played on a finite directed graph such that each player aims at maximizing a payoff function. We present the well-known notions of Nash equilibrium and subgame perfect equilibrium, as well as interesting strategy profiles of players as response to the strategy announced by a specific player. We provide classical and recent results about the related threshold synthesis problem.

Step-by-Step: The Subgame-Perfect Equilibrium

2020 ◽  
pp. 125-140
Author(s):  
Manfred J. Holler ◽  
Barbara Klose-Ullmann
Keyword(s):  
Subgame Perfect Equilibrium ◽  
Perfect Equilibrium

scholarly journals Dinamicke igre ulaska na trziste

2005 ◽  
Vol 50 (165) ◽  
pp. 121-144
Author(s):  
Bozo Stojanovic
Keyword(s):  
Nash Equilibrium ◽  
Dynamic Games ◽  
Nash Equilibria ◽  
Dynamic Game ◽  
Backward Induction ◽  
Perfect Equilibrium ◽  
Equilibrium Concept ◽  
Reasonable Solution ◽  
Multiple Nash Equilibria ◽  
Entry Games

Market processes can be analyzed by means of dynamic games. In a number of dynamic games multiple Nash equilibria appear. These equilibria often involve no credible threats the implementation of which is not in the interests of the players making them. The concept of sub game perfect equilibrium rules out these situations by stating that a reasonable solution to a game cannot involve players believing and acting upon noncredible threats or promises. A simple way of finding the sub game perfect Nash equilibrium of a dynamic game is by using the principle of backward induction. To explain how this equilibrium concept is applied, we analyze the dynamic entry games.

scholarly journals An Algorithmic Procedure for Finding Nash Equilibrium

2020 ◽  
Vol 40 (1) ◽  
pp. 71-85
Author(s):  
HK Das ◽  
T Saha
Keyword(s):  
Nash Equilibrium ◽  
Nash Equilibria ◽  
Payoff Matrix ◽  
Matrix Game ◽  
Perfect Equilibrium ◽  
Repeated Use ◽  
Definition Of ◽  
Zero Sum ◽  
Mathematical Construction ◽  
Algorithmic Procedure

This paper proposes a heuristic algorithm for the computation of Nash equilibrium of a bi-matrix game, which extends the idea of a single payoff matrix of two-person zero-sum game problems. As for auxiliary but making the comparison, we also introduce here the well-known definition of Nash equilibrium and a mathematical construction via a set-valued map for finding the Nash equilibrium and illustrates them. An important feature of our algorithm is that it finds a perfect equilibrium when at the start of all actions are played. Furthermore, we can find all Nash equilibria of repeated use of this algorithm. It is found from our illustrative examples and extensive experiment on the current phenomenon that some games have a single Nash equilibrium, some possess no Nash equilibrium, and others had many Nash equilibria. These suggest that our proposed algorithm is capable of solving all types of problems. Finally, we explore the economic behaviour of game theory and its social implications to draw a conclusion stating the privilege of our algorithm. GANIT J. Bangladesh Math. Soc.Vol. 40 (2020) 71-85

Field Centipedes

2009 ◽  
Vol 99 (4) ◽  
pp. 1619-1635 ◽  
Author(s):  
Ignacio Palacios-Huerta ◽  
Oscar Volij
Keyword(s):  
Field Experiment ◽  
Laboratory Experiment ◽  
Experimental Evidence ◽  
Subgame Perfect Equilibrium ◽  
Perfect Equilibrium ◽  
Previous Evidence ◽  
Chess Players

In the centipede game, all standard equilibrium concepts dictate that the player who decides first must stop the game immediately. There is vast experimental evidence, however, that this rarely occurs. We first conduct a field experiment in which highly ranked chess players play this game. Contrary to previous evidence, our results show that 69 percent of chess players stop immediately. When we restrict attention to Grandmasters, this percentage escalates to 100 percent. We then conduct a laboratory experiment in which chess players and students are matched in different treatments. When students play against chess players, the outcome approaches the subgame-perfect equilibrium. (JEL C72, C93)

Sign in / Sign up

Export Citation Format

Share Document