Nash equilibrium

(A) Explain, using examples, the following concepts from game theory: (i) a strategy, (ii) a strategy profile, (iii) dominant strategy equilibrium, (iv) pure strategy Nash equilibrium, (v) mixed strategy Nash equilibrium, (vi) a reaction function. (i) A strategy: A strategy refers to a move or action a player can make in any given game, where the outcome will depend on the players actions and the actions of others. A strategy determines what move/action a player will make at any given stage during a game. For example, a dominant strategy is a strategy which dominates all others i.e. a player will always be better off choosing A over B, regardless of the choices of the other players. In the Prisoner’s Dilemma, the best thing Clyde can do in…

A Beautiful Mind is a movie that follows a young man named John Nash throughout his life from the time he enrolls in Princeton University until he receives the Noble Prize. Nash is determined to come up with his own original idea for his thesis which he does after a harsh rejection from a woman at a bar and inspires an idea. This allows Nash to write his paper then later leads to him teaching at MIT. Slowly and slowly throughout the movie, you can see Nash’s paranoia and mental instability…

time, and the followers (drivers) move sequentially by reducing their travel time. The authority can control the travel time for the whole network by responding advance in an optimal way to the drivers’ selfishness. In this study, the game theory concepts are incorporated into the system optimal (for authority) and user equilibrium (drivers). Bjørnskau and Elvik (1992) admits that game theory provide better insights than traditional choice theory, in their study of traffic law enforcement and…

interactive situations. (Ross, 1997) A significant contribution to understanding the above-mentioned changes has been done by John Nash and his followers who developed the concept of Game Theory and Nash Equilibrium in particular. For the purpose of this essay, the Game Theory would be defined as “study of decision-making where several players must make choices that potentially affect the interests of the other players” (Turocy and Stengel, 2001). The Nash’s equilibrium would be referred as ‘the…

police (Nash Equilibrium, n.d.). Each criminal is offered a lighter sentence if he testifies against the other. Their other choice is to remain silent. If the first criminal gives up the second one, the he is free to go and the second one will have a ten-year sentence, and vice versa. However, if both remain silent, they both will receive a one-year sentence. Finally, if both testify against each other, both will receive a five-year sentence. Now, each criminal must decide whether to solely look…

with John Forbes Nash Jr., a genius among the time, who comes to Princeton University as a graduate student after receiving the Carnegie Scholarship for his work in mathematics. While Nash is at a bar with some of his fellow students, they try to come up with a strategy to talk to some woman there. As they discuss some possible approaches, Nash creates an idea, which becomes known as the Nash Equilibrium and publishes a piece on it. This game theory basically states that if there are two…

model, marginal cost equals zero in order to focus on how firms interact around the demand curve, therefore the market demand curve is known by each firm as well as their cost structures. The nature of this model is that each firm takes the other firms output as fixed and then sets its own output quantity. However, the main assumption associated to the Cournot model suggest that firms ignore their interdependence. This means that each firm’s conjectural variation is equaled to zero. The belief…

I. Introduction to Game Theory Originally the theory of games was developed to look at games, applying to games such as chess, checkers, and tic-tac-toe (Owen, 2013). Game theory has not become a standard language in economics and other social sciences but this branch of study was original developed in 1944 by John von Neumann and Oskar Morgenstern. It wasn’t until a few years later that a solution was proposed as to how rationale players would interact. John Nash proposed that players would…

of the students were majoring in economics but no one had any prior experience with this type of experiment. The results of the experiment revealed irrational bids in both cases. In the case of R = 1 (proportional probabilities), the level of dissipation is at the predicted level, and become more concentrated around the prediction during the last ten rounds. However, the theoretical model fails in predicting the ‘excessive dissipation’ where the level of dissipation is persistently higher but…

Mutual cooperation, though it would be the rational choice for both players, is not easily achieved or maintained. In the standard two-person, one-shot game, it appears that the safest option would be to defect, as this would result in either a five-year sentence or no prison at all, while cooperation yields either a one-year sentence or a fifteen-year sentence. Even when playing the game repeatedly, cooperation is improbable in the Prisoner’s Dilemma due to backwards inductive reasoning. The…