# Tag Info

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Yes, there is no equilibrium in pure strategies. For any price charged by firm 2 above $c_1$, firm one could only best respond by charging the largest price that is strictly smaller. which is impossible. If both firms charge at most $c_1$, one of these firms must make a loss, which cannot be a best response. So there is no Nash equilibrium in pure strategies....

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When there are few big firms and many smaller firms with a small market share, economists speak about a market with a competitive fringe. The smaller firms are price takers, have higher marginal and average costs and a lower markup than bigger firms. They have often a lower rate of profit than big firms. Although markets with heterogeneous firms are often ...

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It is my impression that this has been formalized under the $\varepsilon$-equilibrium concept ("epsilon-equilibrium"). It is even called "approximate-Nash" equilibrium. Shamelessly copying from the relevant wikipedia article (which includes some literature references) === The standard definition === Given a game and a real non-negative parameter $\... 4 An aspect of the matter could be described as follows: We want prompt replacement of (existing) fixed capital because, I guess, it creates currently "unacceptable" levels of negative externalities, and we know better than to think that through the pricing of the externalities we will be able to reverse the damages, and all swell. From this point of ... 4 The quote in the question isn't really rigorous about what a free market is, but it talks about monopolies and artificial scarcities, so I am interpreting the efficient outcome with price equal to marginal cost as being one necessary feature of what they understand as a free market. Let's look at the cournot model of competition. There are$n$firms, each ... 3 Interesting! A possible way to resolve this contradiction is by taking cost reducing technologies into consideration. Perhaps (example with made up numbers follows) in 1960 a gallon of milk cost \$1 to produce, package and market. Due to strong competition, the consumer could get this for \$1.02, meaning a markup of only 2%. Today, due to technological ... 3 What do we mean by "makes the best decision based on what the other player has decided to do" Your question touches a little bit on the philosophical foundations for Nash Equilibrium. As you know, a Nash Equilibrium occurs when each player chooses the best response to the strategies chosen by others. In other, words, they act as if they know what the ... 3 The basics are of course Cournot, Stackelberg and Bertrand competition, which you can find in any textbook. If you are referring to needing references for research, then the paper you absolutely must know is Dixit and Stiglitz (1977) "Monopolistic Competition and Optimum Product Diversity". American Economic Review. With over 10k citations, the importance ... 3 As the graph notes, the red segment of the demand curve is relatively inelastic, meaning that compared to the blue segment, the red segment of demand is relatively insensitive to price changes. This does not mean that price elasticity anywhere on the red segment is less than 1 (which implies inelasticity in the absolute sense). 3 The market for lemons. Paper is here. The example most commonly given is used cars. The result is market failure. 3 The Bertrand case you mention is a little special because it induces a discontinuity in the demand function. Suppose that market demand is$D(P)=1-P$, zero marginal cost, and that all consumers buy from the low priced firm (and split equally in the event of a tie). If the two firms try to collude around a price$p=0.5$(with quantity$0.25$each) then each ... 3 This market is an oligopoly that is subject to government regulation. It cannot be a monopoly because there is more than one firm. The presence of the regulating government body is a "red herring", it distracts from the main point- there are multiple firms. It does not appear to be competitive because: Four is subjectively few firms Implicitly, ... 3 The trick is to draw the whole reaction function—including the part that coincides with the axis. Hopefully these figures make it clear: 3 In your example, you would still use backward induction to solve for the Perfect Bayesian Equilibrium (assuming the distribution of private costs has full support). In fact, the second stage of your example is similar to a Bertrand competition with asymmetric information. You can refer to the following paper for a general solution of the second stage game: ... 3 The gist/shortened and generalized version of the above answer: In the context where$Q = \sum_i q_i$the equation $$\frac{\partial \pi_i}{\partial q_i} + \frac{\partial \pi_i}{\partial Q} = \frac{\partial \pi_i}{\partial q_i} + \frac{\partial Q}{\partial q_i}\frac{\partial \pi_i}{\partial Q}$$ holds as $$\frac{\partial Q}{\partial q_i} = 1.$$ 2 There is a sense of differentiation thus this is not competitive market clearly. Government regulations in an industry cannot be regarded as a monopoly as government mostly will decide on a price ceiling or floor and not the quantity of transport supplied. Since there are only 4 firms this is an oligopoly clearly. They can collude to restrict output and ... 2 I would recommend taking a look at Jean Tirole's "The Theory of Industrial Organization". This textbook provides a clean exposition of the models of Bertrand, Cournot, Stackelberg, Hotelling, and Salop (read chapters 5 and 7). This will provide a reasonably complete foundation for modern, game theoretic oligopoly theory. 2 It seems you interpret the game as a sequential game. If Windward would know that its move was observed by Airtouch it would act as you say. But this is not the case, they move simultaneously, and it is a one-shot game (as defined it is only played once). Given your reasoning, Windward understands the situation and hence it would choose the evening. ... 2 I think standard in Bertrand competition with different constant marginal cost is another assumption in case of equal prices. Instead of sharing demand equally, you could assume that in case of equal prices the more efficient firms supplies the entire demand. As a result, all price pairs$p_1=p_2=p$with$p \in [c_1,c_2]$constitute an equilibrium. All ... 2 I assume that you found Firm 3's best response to be $$q_3^*(q_1,q_2)=\frac12(16-q_1-q_2).$$ The next step would be to solve for Firm 2's best response. Since Firm 2 observes Firm 1's output and correctly anticipates Firm 3's best response, its profit maximization problem is \max_{q_2}\;(16-q_1-q_2-q_3^*(q_1,... 2 I don't have a question to "correctly interpret" , but I think the way you are calculating the demand function is correct. The demand curve in an oligopoly can be kinked (bowed out), as this one is. I think it is mathematically accurate to write the function split across the domains, as such:$Q = \begin{cases} 700 - P, & 0 \leq P\leq 500 \\ 2200 - 4P,...

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You have solved the Cournot part correctly, but then you've gone completely off the road, by mistaking economics for mathematics. This usually happens. First of all, you shouldn't assume just any value for $q^*_2$ unless you want to show some contradiction by a counterexample. Moreover, even if it was somehow correct, you have used the most unreasonable ...

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I believe "Auctions of Homogeneous Goods: A Case for Pay-as-Bid" by Pycia and Woodward answers your questions theoretically. This is quite recent and their results are striking. They also briefly discuss some empirical insights. The pay-as-bid (or discriminatory) auction is a prominent format for selling homogenous goods such as treasury ...

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You are right that you first have to find F3's best-response function. F1 and F2 take as given this reaction of F3 to whatever they produce. Hence, you plug this best-response function into the incumbents' profit maximization problem. In that way, you take care of the fact that the incumbents anticipate F3's reaction, indirectly determining $q_3$. You ...

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Start with the second stage, this is just Cournot competition between firm 2 and firm 3. You can solve this for the Nash equilibrium by setting the first order condition for firm 2 and firm 3 and solving these two equations, taking $q_1$ as given. This will give you quantities $q_2$ and $q_3$ in terms of $q_1$ which you can then plug into the profit function ...

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The temporal constraints (i.e. what happens in a period) are not very clear in this question. It is likely that the good sold is not a durable good and hence there is no "leftover demand" between periods, demand is simply 'reset'. In period 2 leftover demand appears because firm B assumes firm A will not change its production from period 1. Then in period ...

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Producing more will decrease the price and therefore the profit per unit sold. For a monopolist, all units are their own units. For a duopolist, many units will be the competitor's units. Viewed differently, producing more produces an externality between producers via prices in a duopoly. A monopolist internalizes these externalities completely.

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Your answer is correct. Given that you have a net profit function once you substract the costs of the events, the way to proceed is differentiating that profit function, taking the behaviour of the other firm as fixed and setting that to 0. Profit maximization involves producing upto the point where marginal benefits equal marginal costs and that is exactly ...

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Hendricks and McAfee (2007) offer a theory of bilateral oligopoly. They consider the example of the wholesale gasoline market on the west coast of the United States, which is composed of a small number of large sellers and large buyers who compete against each other in the downstream retail market. They are specifically interested in the effect of a merger ...

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