Introduction to the Bertrand Model The Bertrand model was developed by Joseph Bertrand to challenge Cournot’s work on non-cooperative oligopolies. Cournot’s model dealt with an N number of firms who will choose a specific quantity of output where price is a known decreasing function of total output. (About.com 2011) However‚ Bertrand’s argument was with regard to the setting of prices. He said the only factors influencing the price in an oligopolistic market were the firms themselves and therefore
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outcome for the players jointly; both players would prefer that neither of them confess. For this reason‚ the Prisoners dilemma is the paradigmatic example of self-interested‚ rational behaviour not leading to a socially optimal result. In a Nash equilibrium‚ each player’s
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response Ri (s−i ) is a set. • In the n-player normal-form game G = {S1 ‚ . . . ‚ Sn ; u1 ‚ . . . ‚ un }‚ the strategy profile (s∗ ‚ . . . ‚ s∗ ) is a pure-strategy Nash equilibrium if 1 n s∗ ∈ Ri (s∗ )‚ i −i equivalently‚ ui (s∗ ‚ s∗ ) = max ui (si ‚ s∗ )‚ −i i −i si ∈Si ∀i = 1‚ . . . ‚ n‚ ∀i = 1‚ . . . ‚ n. • {Nash equilibrium(a)} ⊂ {Outcomes of IESDS}. ∗ Email: xiangsun@nus.edu.sg; Mobile: 9169 7677; Office: S17-06-14. 1 MA4264 Game Theory 2/10 Solution to Tutorial 1 2
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a) If Alice chooses not buy‚ best response of Caterpillar is to choose bad. And if Caterpillar chooses bad‚ best response of Alice is to choose not buy. Therefore‚ pure strategy Nash equilibria is bottom right corner. Not buy from Alice and bad from Caterpillar. b) No‚ there isn’t a trigger strategy that induces buy/good for 10 periods. If this was infinitely repeated interaction‚ δ would equal to 1/3‚ computed from trigger condition Equation. Using the same tools‚ we derive following
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ECON 3311 – Fall 2012 Extra Credit Homework – Game Theory 1. What is the Nash equilibrium in the following game? 2. Does the following game have a Nash equilibrium? Does it have more than one Nash equilibrium? If so‚ what are they? 3. Coca-Cola and Pepsi are competing in the Brazilian soft-drink market. Each firm is deciding whether to follow an aggressive advertising strategy‚ in which the firm significantly increases its spending on media and billboard advertising over
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still 6 for each‚ but the benefit is doubled to 8 because they benefit from each other ’s policies. Using this structure‚ we can construct this normal form of the game: from Acre & Sandler Vol. 34 In this model it is clear that the Nash Equilibrium is where neither government has a proactive policy towards terrorists. Because neither government is willing to bear the entire cost‚ neither government will be proactive although the largest
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Important Things To Know * Markup = P-MCP= -1price elasticity of demand * Market demand = firm’s demand for a monopoly ONLY * TR=aQ-bQ2 and MR=a-2bQ * Monopoly output is ALWAYS LESS than competitive output * Colluding leads to the ideal situation (illegal) * MC=WMPL * X=aa+b×MPx or Y=ba+b×MPy * Y = M/Py – (Px/Py)X * Isocost Line: C(Q)=wL+rK | Variation: K=TCr-wrL | Slope: -(w/r) * Isoquant Slope: -(MPL/MPK) | MPLMPK=aKbL=∆K∆L * Optimal cost-minimization:
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to different sides‚ they will avoid collision. However‚ if they choose to swerve the same side‚ they will collide. Is there Nash equilibrium in this game? Explain While driving makes communication difficult (i.e.‚ one driver cannot ask the other which way they will serve); intuition suggests that each driver will swerve away from the other. There are two pure Nash equilibria: either both swerve right or both swerve left. Which side the drivers swerve to is irrelevant so long as they both swerve
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FedEx versus Djoker: Through the Lens of Game Theory Term Paper | IIMK | PGP 15 Submitted By: Group 13 Ranjith P (PGP/015/041) Ankur Pandit (PGP/015/206) Anurag Butoliya (PGP/015/207) Paran Gupta (PGP/015/240) FedEx versus Djoker: Through the Lens of game Theory Executive Summary: Being inspired by the recent clash between Federer and Djokovic in Wimbledon 2012‚ we as a group decided to explore the game theory dynamics of this celebrated matchup. Both these players
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GAMES THEORY In game theory‚ Nash equilibrium (named after John Forbes Nash‚ who proposed it) is a solution concept of a game involving two or more players‚ in which each player is assumed to know the equilibrium strategies of the other players‚ and no player has anything to gain by changing only his own strategy unilaterally. If each player has chosen a strategy and no player can benefit by changing his or her strategy while the other players keep theirs unchanged‚ then the current set of strategy
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