What is the theorem related to Pareto-efficiency in game theory?

In a game involving multiple NE that can be pareto-ranked, the adoption of sequential play leads to the selection of the Pareto-efficient equilibrium as the Subgame Perfect Equilibrium.

What is the theorem related to Stackelberg-solvable games?

It holds only for discrete games: Under perfect information, choices driven by individual rationality may go hand in hand with social efficiency.

What can the centipede game teach us?

It is useful to understand that backward induction, as other instruments, has its limits.

What is a mixed strategy?

The player chooses probabilities optimally: every player must choose a vector of probabilities in order to make each of the rival indifferent between his pure strategies.

Elements in the Bertrand Game

- imperfect, complete and symmetric info - homogeneous good - same technology - price competition - demand function: p=a-q1-q2

What is the outcome of the Bertrand Game?

The firms will reach the NE: where the price will equalize the marginal cost

Why does Bertrand seems to replicate Perfect Competition? Why it isn't true?

It seems so because p = Mc. It isn't true because: - Demand is negatively sloped - Therefore, demand isn't perfectly elastic to price

What happens in the Bertrand Game is firms have different technologies?

The most efficient firm will become the monopolist, this is an incentive for firms in investing in R&D

Cournot Model and its elements

- quantity competition - profit function: πi = (a-qi-qj-c)qi - At NE, each firms will maximize π iw.r.t. qi, for any given qj - Reaction function: qi* = (a-qj-c)/2 - Cournot NE Output: qCN = (a-c)/3 - Partial derivative of qi* w.r.t. qj is equal to -1/2, as qj increases, qi will decrease, quantities are strategic substitutes

What are the implications in oligopoly of the cournot model if firms are symmetric and their number goes to infinity?

- In this case they become atomistic and earn zero profits. - In the fully symmetric Cournot model, sonsumer surpls and welfare are monotonically increasing in n. - And in the limit n--> ∞ welfare and consumer surplus coincide

Waht happens if you add Fixed cost F in the Cournot Oligopoly?

- The entry process will stop when the Profits in equilibrum = 0 - In the long run, there will be excess entry - The authority has to accomodate the number of firms in order to maximize social welfare - There are two visions fighting: the authority and the firm

Tell me something about the Bertrand monopoly and Cournot duopoly, related to Fixed costs

We can see from computation that if F is between ((a-c)^2)/16 and (5(a-c)^2)/72, the welfare produced in the cournot duopoly is higher

What Salant says about horizontal mergers?

Horizontal mergers, in a market with no fixed cost and constant marginal costs, are profitable iff 80% of firms partecipate. Horiz. merg. are always welfare decreasing. So horizontal mergers, especially small ones, are not profitable, and they decrease a bit the social welfare. Should we accept the starting assumptions? The answer is No, they are unrealistic

What Perry, Porter, Farrel and Shapiro demonstrated?

By assuming a market with positive fixed costs (which may decrease after the merger) and convex cost function: - Small mergers may be profitable - If the efficiency gained by saving upon the cost of entry is sufficient, the social welfare may increase, even if consumer surplus will decrease, so the merger can be socially efficient

Adressing approach in product differentiation

Related to Hotelling, the firms are focused on the characteristics of the product, that are part of the strategies of the firms

What happens if we have no fixed costs but product differentiation in Bertrand?

The merger is always profitable but socially inefficient

What is the Bertrand critique to Cournot when it comes to consumers' demand

Cournot assumes firms implicitly know what comes into consumers' minds

Important formulas in Cournot model with product differentiation

1) pi = a - qi - sqj 2) qi = (a - c)/(s + 2) 3) πCN = (a - c)^2/(s + 2)^2

Important formulas in Bertrand model with product differentiation

1) qi = (a/(1+s)) - (pi/(1-s^2)) + (spj/(1-s^2)) 2) πBN = ((a - c)^2 (1 - s))/((1 + s) (2-s)^2)

Non-addressing approach in product differentiation

Related to Bawley, it assumes that the consumer has love for variety and firms may choose price and quantity but the degree of differentiation is related to the consumer

What about the type of complements of price and quantity in Bertrand and Cournot

If s is greater than 0 and less or equal to one, we can see that: - In the Bertrand model prices are strategic complements - In the Cournot model quantities are strategic substitutes

What happens in the mixed case assuming product differentiation (one firm quantity setter and the other price setter)?

- The qi-setter firm sees pj as strategic complement - The pi-setter firm sees qj as strategic complement

So, how will the 2 firms would play, setting price or quantity?

If s is greater than 0 and lower than 1, both firms will play a la Cournot since the strategy q weakly dominates strategy p, since πCN>πBN, equilibrum is (q, q)

What is the intuition of Kreps and Scheinkman, describe it

Reling on Sigh and Vives, firms have to choose k before playing in the market stage. They points out that adding endogeneous capacity in the Bertrand game it will lead to Cournot outcomes. By imposing ki = qi for both, neither of the firm will steal rival's demand when undercutting, this action will only damage the firm.

Meaning of horizontal and vertical differentiation

- Two products are horizontally differentiated if there are at least two consumers, ranking them differently, all else being equal - Two products are vertically differentiated if all the consumers express the same ranking, all else being equal

The three main points related to product differentiation

1) How intensive is the incentive of differentiation for firms? 2) May be an excess differentiation in the Equilibrum point, because of profits, that could decrease SW 3) How manny firms would enter the market in the long - run? Shall we expect excess entry?

Describe the Hotelling model, the outcomes and problems related

- 2 firms, homogeneous good - Same technology, zero costs - Consumers uniformally distributed on a linear space, full coverage assumption - Noncooperative game under complete, symmetric, and imperfect, perfect between stages, information - The first stage in the location space, the second one in the price space - SPE via backward induction - Firms will locate in 0.5, where the average consumer lies - Principle of minimum differentiation: the demand effect prevails on the strategic effect 1) In price competition p=Mc, so p=0 2) If one of the firm lower price, the probability of splitting the market 50/50 is 0

What about dAGT formulation of the Hotelling's lemma

If one firm set piU, so undercutting, it will start a price race, it will be so strong the competition that the price would instantly collapse to the marginal cost before the arising of product homogeneity. The Hotelling equilibrum is not a Nash equilibrum, and not a SPE, because the structure of the consumers' preferencies are non-convex, to overcome this problem we assume quadratic transportation costs. Undercutting is never profitable and the principle of minimum differentiation is undermined, instead, there is the principle of maximum differentiation

Social efficiency related to Hotelling and dAGT

In this case authorities are only concerned about minimising the integral of transportation costs, if there are two firms the result is 0.25 and 0.75. There are 2 points of view that are different: firms and authorities. At the equilibrum the degree of differentiation is higher than the optimal one. This is even more clear if the firms will locate themselves outside the "city" at -0.25 and 1.25 Also, until profits reach Mc, there could enter infinitely many firms, and the market will be similar to a perfect competitive one, likened to the monopolistic one. But there are some problems: 1) The adjacent firms would have a fierce Bertrand competition 2) The firms will earn zero profits

Economides and his consideration on the transportation cost function

By starting from the Hotelling model, Where n∈[1,2]n \in [1, 2]n∈[1,2] controls how fast transport costs rise with distance. 1) for n between [1, 1.25] the pure strategy Nash equilibrum in prices does not exists 2) for n between (1.25, 1.66) the game has a unique SPE 3) for n between [1.66,2] the game has a unique SPE in which firms locate in 0 and 1

Industrial Economics Flashcards

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39 questions

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1.

FLASHCARD QUESTION

Front

What is a game? And its elements?

Back

A Game is a mathematical object that formalises strategic interactions between players:

- list of players
- list of strategies
- list of each players' payoff

2.

FLASHCARD QUESTION

Front

What is Nash Equilibrium 1?

Back

Every player has no unilateral ex-post regret.

3.

FLASHCARD QUESTION

Front

What is Nash Equilibrium 2?

Back

The strategy of each player is qualified as the best reply to the rivals' strategies.

4.

FLASHCARD QUESTION

Front

What is a Dominant Strategy?

Back

It is the best reply of a player invariant in the rivals' strategies.

5.

FLASHCARD QUESTION

Front

What is Subgame Perfect Equilibrium (SPE)?

Back

An outcome that induces a Nash Equilibrium by backward induction in every proper subgame of G, more demanding than the NE.

6.

FLASHCARD QUESTION

Front

What are the characteristics of SPE?

Back

The SPE is sensitive to the sequential play and there exists a first-mover advantage.

7.

FLASHCARD QUESTION

Front

What happens if information is imperfect in game theory?

Back

Nash Equilibrium (NE) and Subgame Perfect Equilibrium (SPE) are the same.

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