Green Agreement in the Electricity Market

An ex-post evaluation of the 2013 Dutch Coal Power Plants Closure Agreement by Ilaria Noviello and Shaun Tey ’21

Smoke stacks
Photo by Andreas Felske on Unsplash

The full title of this project is “Green Agreement in the Electricity Market: An ex-post evaluation of the 2013 Dutch Coal Power Plants Closure Agreement.”

Editor’s note: This post is part of a series showcasing Barcelona School of Economics master projects. The project is a required component of all BSE Master’s programs.


There has been much theoretical discussion on whether Green Agreements can be a cost efficient means of improving the sustainability of products, but no empirical studies have been done on what the cost and benefits of past Green Agreements have been. 

In order to provide a substantive contribution to this discussion, we have undertaken an ex-post analysis of an agreement in the Netherlands to close five aging coal power plants in 2016 and 2017. First, we evaluated the ACM’s assumption that the plant closures would result in an increase of the Dutch wholesale electricity price in the Netherlands by undertaking a before-and-after analysis. Second, we examined how the ACM quantification of the benefits deriving from emissions reductions would have changed if it used its same methodology a year after the plants closed (in mid-2018). Third, we considered how the quantification of the benefits would have changed if the ACM used an alternative evaluation technique based on estimating consumers’ willingness to pay for Green Electricity.

Our findings indicate that the ACM was likely incorrect to oppose the agreement to close the coal power plants.


  • The before-and-after analysis indicates that the agreement to close the coal power plants did not result in any increase in the wholesale price of electricity in the Netherlands. This implies that this Green Agreement had no cost, while still producing a benefit of reduced emissions.
  • Our examination of the ACM’s method for quantifying the benefits derived from reduced emissions finds it to be volatile. In particular, due to subsequent changes to the methods used by the Dutch Government for valuing reduced emissions, the benefit of the Closure Agreement would be regarded as far higher if evaluated today. 
  • We find that it is unviable to use an alternative evaluation technique based on estimating consumers’ willingness to pay for Green Electricity.

Our conclusion suggests that those working on ex-ante assessments of Green Agreements should recognise that the volatility of their government’s approach to environmental policy can alter the accuracy of their assessments. As a result of this, regulators should coordinate better across government departments, in order to understand which methodologies are currently subject to scrutiny and could possibly change in the future.

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About the BSE Master’s Program in Competition and Market Regulation

Implications of Market Rating-based Segmentation on Intra-platform Competition

An application to Airbnb’s market in Barcelona. Competition and Market Regulation master project by Paul Arenas and Saúl Paredes ’21

Aerial view of Barcelona's Eixample neighborhood
Photo by Erwan Hesry on Unsplash

Editor’s note: This post is part of a series showcasing Barcelona School of Economics master projects. The project is a required component of all BSE Master’s programs.


In recent years, large platforms have raised concerns that they may engage in anti-competitive practices that affect market competition. Therefore, analyzing the competition structure inside platforms is a relevant issue that has not been treated in much empirical research.

This study analyzes how a platform’s owner could affect the degree of competition among members of one group in the platform through biasing search results using rating classifications. In this paper, we perform an application to Airbnb‘s market in Barcelona given the particularity of rating is an unavailable searching filter to guests.

We found evidence that listing’s rating classification represents an important market segmentation in the Airbnb’s market in Barcelona that could imply a possible practice of biasing search results. Moreover, we found that the intensity of competition is differentiated by the rating-related segments, which means that these segments are concentrating competition.


We found an inelastic demand for Airbnb’s listings in Barcelona in a market that is divided by rating classification. In particular, our empirical results show the following two points:

First, the majority of hosts face an inelastic demand. These results are consistent under the two main models we used. From the nested logit model under rating segmentation, we found that when there is a 10% increase in price of available nights, there is an expected decrease in booked nights of 4.5%. These results imply that there is room to increase the price without reducing the revenues of the hosts.

Second, even though the rating is not available as a filter in the Airbnb web page, it creates an important market segmentation. This means that the competition between two listings that belong to the same segment is different from the competition faced by two listings that belong to different rating classifications. Moreover, we found differences in intensity of competition faced by listings that belong to different segments.

Finally, these results show that the existence of segmentation suggests that Airbnb is performing a rating-based market division. Yet the rating segmentation does not show a clear pattern of competition intensity in each group.

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About the BSE Master’s Program in Competition and Market Regulation

Demand Estimation in a Two-Sided Market: Viewers and Advertisers in the Spanish Free-to-Air TV Market

Competition and Market Regulation master project by Sully Calderón and Aida Moreu ’20

Photo by Glenn Carstens-Peters on Unsplash

Editor’s note: This post is part of a series showcasing Barcelona School of Economics master projects. The project is a required component of all BSE Master’s programs.


Our research arises in a context where “free” services in one market cannot be understood without taking into consideration the other side of the market. The Spanish free-to-air TV industry is a two-sided market in which viewers demand TV programs (for free) and advertisers demand advertising spots for which they pay a price that depends mainly on audience.  Our main contribution to the two-sided market literature is estimating both viewers and advertisers demand to be able to understand the interactions of both sides of the free-to-air TV market.

This analysis is carried out by developing an econometric analysis of the free to air TV market in Spain that captures the reaction of viewers to a change in advertising quantity and the effect on price of ads that this would bring. We specified Viewers Demand in the Spanish free-to-air TV through a logit model to analyse the impact of advertising minutes on the audience share and, we specified Advertisers Demand by an adaptation of the model of Wilbur (2008) to understand the effect of audience share and advertising quantity on prices of ads.  


The results of the Viewers Demand model show an elastic demand and that viewers are averse to advertising regardless of the day but during prime time they are a bit more ad tolerant, especially from 10pm to 11 pm. 

Logit estimation of Viewers Demand. Download the paper to read text version.

On the other side of the market, the Advertising Demand model shows that advertisers are relatively inelastic to both an increase of adds and an increase in audience share. This may be due to the fact that the data available for this project is precisely coming from the most viewed channels, for which advertisers would have more inelastic demand.

Logit estimation of Advertising Demand. Download the paper to read text version.

As expected, the results show that advertisers are more elastic with regards to audience share than to quantity of advertising.

Connect with the authors

  • Sully Calderón, Economic Advisor at Comisión Federal de Competencia Económica (México)
  • Aida Moreu, Research Analyst at Compass Lexecon (Madrid)

About the BSE Master’s Program in Competition and Market Regulation

Competition and Price Asymmetries in the Retail Gasoline Market: an Application to a Spanish Cartel Case

Competition and Market Regulation master project by Silvia Brumana and Roger Medina ’20

Editor’s note: This post is part of a series showcasing Barcelona School of Economics master projects. The project is a required component of all BSE Master’s programs.


Asymmetric pricing in the retail fuel market describes the situation in which retail prices are adjusted quickly in case of positive shocks in the wholesale costs, whereas the adjustment is much slower in case of negative ones. This asymmetry in the reaction of retail operators is captured by the well-known expression rockets and feathers. By relying on a reduced version of a database used in Moral and Gonzalez (2019) containing the series of diesel prices in Spain and Brent prices for the period 08/2014-06/2015, we address the following research question: how did the fuel prices of the retail gas stations in a subset of Spanish provinces react in this period to changes in the price of Brent? In order to answer this question, we construct a pricing equation that takes into account all the possible factors that can affect pricing with the aim of isolating the effect of negative shocks and the effect of positive shocks in the price of Brent on the price of gasoline of the various Spanish operators. Then, we check whether the difference between these two effects is statistically significant to see whether there were asymmetric reactions. Furthermore, since the common rocket and feathers phenomenon could be considered as a collusive device, and since in the period covered by the database a cartel was active among the main fuel companies in Spain, we also investigate the relation between asymmetric pricing and competition.

Figure 1. Spatial distribution of gas stations in Barcelona


The aim of our project was to capture the presence of asymmetric pricing in nine Spanish provinces between 2014 and 2015 by taking into account the fact that during the period considered the CNMC fined five of the largest oil companies in Spain for collusion. To do this, we estimated an Error Correction Model for each province by accounting for both panel heterogeneity and cross-sectional dependence to capture both the short-run and the long-run relation between the retail diesel prices and the Brent price. 

Our results show that there exists a correction mechanism that pushes the retail prices back to the long-run equilibrium relation with the Brent in case of shocks, even if the magnitude of the correction may be overestimated potentially because of the pattern of the retail fuel price in the period before the fine of the CNMC became public.

Figure 2. Evolution of the Brent price and the average retail fuel price in Alicante in the period considered. Note that the CNMC fined the major oil companies in Spain in February 2015.

As far as the short-term adjustments are concerned, the results are less clear because of the lack of significance of most of the coefficients; this is potentially due both to the presence of imperfect collinearity arising from issues with the lag selection in each province as well as to the already mentioned patterns of the diesel prices. Furthermore, as to what concerns the effect of the fine of the CNMC, the results show that in many provinces there is some variability in the pricing of the gas stations after February 2015 that is not accounted for in the rest of the model. We may not confidently state that this is entirely due to the fine of the CNMC: in fact, the related coefficient may capture some variability due to the attempts of firms of recovering the losses incurred before the fine was issued. Consequently, we suggested that we may need to first solve the issue of the lag selection and then, if the effect of the fine is still significant, we may eventually add some control for the profitability of the firms, even if this would imply expanding the database because of the absence of variables capturing the evolution of profits of the firms observed.

To conclude, although our analysis may still need some refinement especially in the lag selection procedure, we suggest that the relation between asymmetric pricing and competition is worth exploring. In addition, it would be also interesting to understand whether aggregating the data in the database we used at a weekly level, for instance, would lead to different estimates and insights or would simply lead to biased findings as suggested in the literature.

Connect with the authors

  • Silvia Brumana, Economics Intern at the UK Competition & Markets Authority (CMA)
  • Roger Medina, Senior Research Fellow at the Ostrom Institute

About the BSE Master’s Program in Competition and Market Regulation

Evaluating the performance of merger simulation using different demand systems

Competition and Market Regulation master project by Leandro Benítez and Ádám Torda ’19

Evaluating the performance of merger simulation using different demand systems: Evidence from the Argentinian beer market

Editor’s note: This post is part of a series showcasing Barcelona School of Economics master projects. The project is a required component of all BSE Master’s programs.


This research arises in a context of strong debate on the effectiveness of merger control and how competition authorities assess the potential anticompetitive effects of mergers. In order to contribute to the discussion, we apply merger simulation –the most sophisticated and often used tool to assess unilateral effects– to predict the post-merger prices of the AB InBev / SAB-Miller merger in Argentina.

The basic idea of merger simulation is to simulate post-merger equilibrium from estimated structural parameters of the demand and supply equations. Assuming that firms compete a la Bertrand, we use different discrete choice demand systems –Logit, Nested Logit and Random Coefficients Logit models– in order to test how sensible the predictions are to changes in demand specification. Then, to get a measure of the precision of the method we compare these predictions with actual post-merger prices.

Finally, to conclude, we point out the importance of post-merger evaluation of merger simulation methods applied in complex cases, as well as the advantages and limitations of using these type of demand models.


Merger simulations yield mixed conclusions on the use of different demand models. The Logit model is ex-ante considered inappropriate because of its restrictive pattern of substitution, however it performed better than expected. Its predictions on average were close to the predictions of the Random Coefficients Logit model, which should yield the most realistic and precise estimates. Conversely, the Nested Logit model largely overestimated the post-merger prices. However, the poor performance is mainly motivated by the nests configuration: the swap of brands generates almost two close to monopoly positions in the standard and low-end segment for AB InBev and CCU, respectively. This issue, added to the high correlation of preferences for products in the same nest, generates enhanced price effects.


Regarding the substitution patterns, the Logit, Nested Logit and Random Coefficients Logit models yielded different results. The own-price elasticities are similar for the Logit and Nested Logit model, however for the Random Coefficients Logit model they are more almost tripled. This is likely driven by the estimated larger price coefficient as well as the standard deviations of the product characteristics. As expected, by construction the Random Coefficients Logit model yielded the most realistic cross-price elasticities.


Our question on how does the different discrete choice demand models affects merger simulation –and, by extension, their policy implications– is hard to be answered. For the AB InBev / SAB-Miller merger the Logit and Random Coefficients Logit model predict almost zero changes in prices. Conversely, according to the Nested Logit, both scenarios were equally harmful to consumers in terms of their unilateral effects. However, as mentioned above, given the particular post-merger nests configuration, evaluating this model solely by the precision of its predictions might be misleading. We cannot discard to have better predictions under different conditions.


As a concluding remark, we must acknowledge the virtues and limitations of merger simulation. Merger simulation is a useful tool for competition policy as it gives us the possibility to analyze different types of hypothetical scenarios –like approving the merger, or imposing conditions or directly blocking the operation–. However, we must take into account that it is still a static analysis framework. By focusing only on the current pre-merger market information, merger simulation does not consider dynamic factors such as product repositioning, entry and exit, or other external shocks.

Authors: Leandro Benítez and Ádám Torda

About the BSE Master’s Program in Competition and Market Regulation

Effective competition in non-workplace pensions

FCA publication with contributions by Lorenzo Migliaccio ’14 (Competition and Market Regulation)

FS19/5 in the context of FCA work across the pension saving value chain . Source: FS19/5

The Financial Conduct Authority has published three pensions papers covering advising on pension transfers, the retirement outcome review, and effective competition in non-workplace pensions. The last one – which I’ve contributed to – outlines a number of proposals to improve competition in the non-workplace pensions market in the UK.

To share my Head of Department’s words, ‘this has been one of the most challenging data gathering exercises I have been involved in’, with more than 100 firms providing input for our analysis.

We found similar weaknesses to those the OFT identified in the DC workplace pension market in 2013, ie demand-side weaknesses and reduced competition on charges.

We now invite stakeholders’ views and welcome alternative suggestions for the way we and the industry can address the issues identified. Here you can find more information and download the feedback statement (pdf).


Lorenzo Migliaccio ’14 is Senior Associate Economist at the Financial Conduct Authority. He is an alum of the Barcelona GSE Master’s in Competition and Market Regulation.

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Price Parity Clauses: Setting a new legal standard


Editor’s note: This post is part of a series showcasing Barcelona GSE master projects by students in the Class of 2018. The project is a required component of every master program.


Samantha Catalina Guerrero Putz and Josep Peya

Master’s Program:

Competition and Market Regulation

Paper Abstract:

Under the context of digital platforms who act as an intermediary between consumers and sellers, Price Parity Clauses (PPCs) is a contractual restriction for the seller not to sell at a lower price through any other channel (the so-called wide PPCs), or only in its own channel (narrow PPCs). These clauses present a trade-off between efficiencies and anticompetitive effects. On one side, PPCs act as a committing device of the seller to solve the show-rooming effect suffered by platforms (a particular form of free- riding), at the same time that it ensures platforms viability and enhances its incentives to invest and innovate. On the other side, PPCs allow platforms to charge higher fees, and lead to foreclosure of the market. Currently, neither the EC nor NCAs have set a clear guidance on how to assess these clauses. The main contribution of this paper is to set a legal standard for both wide and narrow PPCs using the cost-error analysis. The conclusions we arrived to are that wide PPCs should be per se illegal; and narrow PPCs should be presumed legal unless proven otherwise, except if narrow PPCs are eliminating the competitive restraints of the platform, in which case the standard should be that of rebuttable presumption of illegality.


  1. Digital Economy will rise the use of Digital Platforms. Network externalities inherent to two-sided markets lead to high market power that make platforms an indispensable ally.
  2. Digital Platforms use PPCs and this is capturing the interest of Competition Authorities. But there is no consensus with respect to the legal standard.
  3. PPCs present a trade-off: On the one hand efficiencies results in reduction of search costs, prevents showrooming, incentives on investment and innovation. On the other hand, anti-competitive effects arise, creating high fees, foreclosure, collusion.
  4. The results of our cost-error analysis are that Wide PPCs Min Type II error, therefore should be Per se illegal. Narrow PPCs Min Type I error: Rebuttable Presumption of Legality, except if (i) One-Stop Shop/Network; (ii) Brand Positioning; (iii) Switching costs: Min. Type II: Rebuttable Presumption of illegality

Download the full paper [pdf]

More about the Competition and Market Regulation Program at the Barcelona Graduate School of Economics

2017 Competition Curtain Raiser, Part 1: Excessive Pricing

This is the first in a series of posts highlighting competition issues and cases that are set to drive the debate in Europe this year.

Pfizer and Flynn Pharma: a major decision from the CMA

On 7 December 2016, the United Kingdom’s (UK’s) Competition and Markets Authority (CMA) issued a potentially precedent-setting decision against pharmaceutical producer Pfizer and distributor Flynn Pharma, imposing a fine of nearly £90 million for excessive pricing.

In September 2012, Pfizer sold the distribution rights to its anti-epilepsy drug Epanutin (phenytoin sodium) to Flynn Pharma, which debranded (or “genericised”) the drug, with the effect that it was no longer subject to price regulation. Following the sale, Pfizer increased its price for phenytoin sodium to Flynn Pharma by between 780% and 1,600% relative to the price at which it had previously sold the drug in the UK, and in turn Flynn Pharma increased the wholesale price of the drug to between 2,300% and 2,600% of the former price.

A key feature of phenytoin sodium appears to be that patients taking the drug cannot readily switch to the same drug manufactured by another producer, since even minor differences in production processes could affect the efficacy of the drug in treating epilepsy in individual patients. Therefore, despite the fact that the drug was genericised, the CMA appears to have found that Pfizer and Flynn Pharma retained a de facto monopoly over the sale of the drug to existing patients taking Epanutin. Such a finding would also imply that alternative epilepsy treatments were not viable substitutes for phenytoin sodium in respect of the relevant patients, and were therefore not included in the definition of the relevant market.

The excessive pricing debate

The prohibition of excessive or unfair pricing by dominant firms is a controversial part of UK and European competition law (it has no meaningful counterpart in US legislation or case law). On the one hand, there are strong economic arguments, at least from a static point of view, for preventing a dominant firm from exploiting its monopoly position by charging prices higher than the theoretical competitive price. One of the key results of microeconomic theory (and indeed the foundation of competition policy) is that monopoly pricing lowers overall welfare compared to a competitive market outcome, since the monopoly maximises profits by producing a less-than-efficient quantity of the relevant good and selling it at a higher-than-efficient price.

However, enforcing a prohibition against excessive pricing presents various difficulties. One of these is to establish a benchmark price against which the actual price charged by the dominant firm is to be evaluated, and deciding whether the margin above this benchmark is excessive. According to the CMA press release, it appears to have had regard both to the initial regulated price of phenytoin sodium, and the price charged by Pfizer in other European countries, in reaching a finding of excessive pricing.

It is important to note, however, that there is no inherent reason why such prices should represent useful comparators. In other words, although a price increase of 2,600% naturally appears alarming at first glance, a range of factors could have resulted in the initial price being very low, especially if it was regulated. In this case, Pfizer and Flynn Pharma argue that the regulated price of Epanutin in the UK prior to September 2012 had been loss-making. It remains to be seen how the CMA established a relevant benchmark when its non-confidential decision is made public.

A further risk in enforcing a prohibition of excessive pricing, partly related to the issue discussed above, is that it could have a negative impact on firms’ dynamic incentives to invest across the economy. For example, over-enforcement could prevent a firm from earning economic profits where it has innovated in order to gain a temporary competitive advantage. More generally, over-enforcement runs the risk of creating uncertainty, and thereby lowering incentives to invest, if businesses fear that their future profits will be capped by a competition authority at a level which they cannot predict in advance.

For such reasons, economists such as Massimo Motta and Jorge Padilla (both teaching in the Competition masters at BGSE)  have proposed that excessive pricing provisions should be enforced only in cases where there is little or no prospect of the relevant market eventually correcting itself, and where a sector regulator would not be better placed than the competition authority to intervene (among further restrictive conditions). In this case the CMA may have concluded that the inability of other phenytoin sodium producers to compete for existing Epanutin patients created such a situation where entry is infeasible. Even so, the question remains whether this issue could not better be addressed through amending existing drug price regulation. The release of the CMA’s final decision is likely shed more light on this issue.

What to look out for in 2017

In the meantime, Flynn Pharma has appealed the CMA’s decision to the Competition Appeals Tribunal (CAT). 2017 could therefore reveal how the CAT views the different considerations surrounding excessive pricing, and to what extent the CMA decision will be applicable to other drugs and industries. The finding of excessive pricing also raises the prospect that Flynn Pharma’s customers, and specifically the UK Department of Health, could sue it for damages resulting from the high price, which would raise further interesting issues in so-called “private”  excessive pricing enforcement.


Evans, D.S. & Padilla, A.J. 2005. “Excessive Prices: Using Economics to Define Administrable Legal Rules”. Journal of Competition Law and Economics 1(1), pp. 97–122.

Motta, M & de Streel, A. 2007. “Excessive Pricing in Competition Law: Never say Never?” The Pros and Cons of High Prices, pp. 14-46. Swedish Competition Authority.

Price parity in two-sided markets: a new perspective

Editor’s note: This post is part of a series showcasing Barcelona GSE master projects by students in the Class of 2016. The project is a required component of every master program.

Sara Del Vecchio, César Ulate

Master’s Program:

Competition and Market Regulation

Paper Abstract:

Online platforms are believed to be beneficial to consumers in a number of ways. They facilitate consumers’ search and comparison, which in turn fosters competition between sellers. They drive the so called long tail effect that increases the variety of products offered, improving the consumer’s ability to find the right match for their needs. Platforms might adopt some particular measures aimed at protecting their profits, and potentially the viability of their business model. In the past few years, many online platforms have been under the scrutiny of various competition authorities regarding a particular clause they include in their contracts with sellers commonly called ’price parity clause’ or more specifically Across Platform Parity Agreement (APPA), this limits the seller’s ability to set lower prices (or better conditions) on other sale channels. At face value, price parity seems like a restriction on sellers’ pricing abilities which benefits consumers, as they can enjoy increased value service at apparently no additional cost.

We build a stylized model and we show that platforms can increase welfare and have pro-competitive effects, while price parity clauses are generally harmful for consumers surplus and welfare, nevertheless they can be good if they are indispensable for the platform viability.


The price parity clause included in platforms’ contracts with sellers, can be categorized as narrow or wide according to the scope of the price limitation. As illustrated in the figure below a ‘narrow APPA’ (the purple rectangular in the figure) refers to a clause where the seller is restricted from charging a lower price on their direct channel. By contrast, a ’wide APPA’ (the orange rectangular in the figure) is when the seller is limited from setting a lower price not only on their own website but also on any other competing platform. This will allow the platform to make claims, such as the ’best price guarantee’ as shown in the figure.

Narrow & Wide Across-Platform Parity Agreements

Online platforms often argue that they need to include this constraint on seller’s price, otherwise consumers would just free ride on the platform services, and then complete the transaction on the seller’s own website which offers a lower price. At the same time, such clause in the seller-platform contract might generate anticompetitive effects, In particular, they may raise costs for sellers, which in turn are reflected into higher prices for consumers. Sellers pay a fee to intermediaries, which are insulated from competitive pressure due to the price parity clause itself.

Indeed, in the past few years many online intermediaries have been under the scrutiny of various competition authorities regarding APPAs that they were including in their contracts with sellers. There have been several cases across the world related to this clause, starting from the Apple eBook case in 2013, until the recent series of investigations in Europe regarding the online travel agent

In particular, the case shows some inconsistencies in the decisions across Europe, in most of the countries (including UK, France, Italy and Sweden), settled by agreeing to allow online travel agents, to offer lower room rates via’s competitors, by dropping its wide APPA, restoring competition between online travel agencies. The commitments do allow to retain its narrow APPA for prices and booking conditions, ensuring hotels offer the same rates and conditions that are provided on their own direct website. In Germany, instead, the Bundeskartellamt decided also to prohibit the narrow APPA. Nevertheless, in France they recently passed a Law (la Loi Macron) whereby they made APPAs illegal per se, with the aim of liberalising the economy and boosting growth. Furthermore, would be desirable more guidance on how to set out the most appropriate theory of harm in order to have convergence at European level in relation to these clauses.

Modeling Approach:

In this paper we build a stylised model with three different types of rational agents: (i) sellers, (ii) platforms and (iii) consumers. They all take sequential decisions in an infinitely repeated game. We include different search costs for consumers depending on the channel used to search and purchase a product. We focus only on pure strategies that lead to a particular Sub-Game Perfect Nash Equilibrium (SPNE) where all agents participate. We compare this SPNE across different scenarios: from the setting where there is a monopoly platforms, to the setting where we have competing platforms. We look at the equilibrium prices and welfare that arise in each of these scenarios with and without narrow and wide APPAs. Finally, we compare it to the counter-factual where no platform operates in the market.

Findings and Conclusion:

In terms of policy approach towards these clauses, our findings are in line with great part of the literature with respect to wide APPAs. Our model suggests that under no condition this clause can have pro-competitive effects, therefore the current European move towards a prohibition seems economically sound and sensible. With regards to narrow APPAs, instead, we believe the current call in many European countries for an outright ban could be detrimental for welfare, as it overlooks the benefits that platforms bring to the market. Indeed, we find that under some conditions these clauses despite limiting competition, do lead to efficiencies that the authorities should take into account.

We conclude that the existence of a platform is in general good, because as a first order effect it increases the number of transactions and reduces search costs for consumers. However, we find that prices will only be lower if there is effective competition between platforms. Furthermore, if the platform is not able to recover its costs though sales, then the viability of the platform may depend on the existence of the APPA. Hence, as shown the narrow APPA decreases welfare unless it is indispensable for the platform to operate.

Three-legged Centipede Game

An essay by Chaoran Sun ’15, Barcelona GSE Master Program in Competition and Market Regulation

Robert Aumann once complained in the foreword of Roth and Sotomayor (1992):

It is sometimes asserted that game theory is not “descriptive” of the “real world”, that people don’t behave according to game-theoretic prescriptions. To back up such assertions, some workers have conducted experiments using poorly motivated subjects, subjects who do not understand what they are about and are paid off by pittance, as if such experiments represents the real world.

Indeed, it is all too familiar for us hearing people cite Rosenthal’s centipede Game as an evidence that game theory is not “descriptive” of the “real world”. When faced with the follow-up question as to why game theory doesn’t work, they usually pointed out that it lies in game theorists’ obsession of some obviously mistaken assumptions associating with common knowledge, unbounded rationality, et cetera.

In this essay, we argue that, at least for Rosenthal’s centipede game, it’s not the case game theory is inconsistent with the findings of experiments that subjects don’t wind up on the backward induction path. To be precise, even though we accept the strong assumption of common belief of rationality, which is everyone believe everyone plays rationally, everyone believe everyone believe everyone plays rationally, ad infinitum, we shouldn’t expect backward induction path as an unavoidable outcome. The example presented here is well-known, and this essay only serves for expository purpose.

To begin, let’s have a look at technical difficulties. Since there’s no way for a player to mind-read another player, it’s absurd to assume away the possibility that one player’s subjective belief on her opponent’s strategy doesn’t coincide with the objective one1. Furthermore, we can’t stop there. What about players’ belief on their opponent’s belief, belief on beliefs on beliefs…If you wonder high-order beliefs might only have a negligible effect on the outcome of games, think about the dirty face and sage game and Rubinstein’s electronic mail game. This ever-increasing hierarchy of beliefs makes a fine line for common knowledge of game structure, the starting point of every game theory analysis, impossible. In a series of conceptual breakthroughs, Harsanyi (1967-68) postulated that this belief hierarchy can be summarized as a type so that “relaxing” the stringent requirement of common knowledge is tantamount to adding types in a game of incomplete information. It is also noteworthy that, a belief of a higher rank contains strictly more information than those of lower ranks, so it’s reasonable to require that beliefs of different ranks shan’t contradict with each other. The technical breakthrough came when Mertens and Zamir (1985) cast belief hierarchy with this coherency property into a category theory object, inverse limit and went on proving that Harsanyi universal type space attains a self-referential property, each player’s type is equivalent to a joint distribution of her opponent’s strategy and type. Now we have set the stage for the analysis of the centipede game.

centipede game

Consider a three-legged centipede game of incomplete information with Harsanyi’s universal type space. Ann of type a believes that Bob plays “In”, while Ann of type b believes that Bob plays “Out” . Bob, on the other hand believes Ann is type b and plays “Out”. Then we have:

Claim. At state (a, (In, Out), Out) whose outcome is different from backward induction path, Ann and Bob share a common belief of rationality.

What we need to verify for common belief of rationality are, at the given state:

  1. What Ann believes implies Ann is rational.
  2. What Ann believes Bob believes implies that Ann believes Bob is rational.
  3. What Ann believes Bob believes Ann believes implies Ann believes Bob believes Ann is rational.

. . . . . .

Notice that we only need to check the first three steps, what Ann believes Bob believes Ann believes is the same as what Ann believes Bob believes Ann believes…Bob believes Ann believes. They’re indeed the case. Next, apply the same procedure to a case with Ann and Bob interchanged.

Remark. When conducting experiments, we should be careful about how well subjects understand games they’re playing, how well they know about the opponents they’re play- ing against. Experimental findings in disfavor of backward induction might indicate that epistemic conditions for backward induction are not satisfied. Common knowledge of game structure and common belief of rationality, saving us from arbitrariness of off- equilibrium paths, could be relevant to resolving real world economic problems, if put into perspective.


  1. Aumann, Robert J. Backward induction and common knowledge of rationality. Games and Economic Behavior (1995), 6-19.
  2. Aumann, Robert J. On the Centipede Game. Games and Economic Behavior (1998), 97-105.
  3. Binmore, Ken. A Note on Backward Induction. Games and Economic Behavior (1996), 135-137.
  4. Harsanyi, John. Games on incomplete information played by Bayesian players. Parts I, II, III. Management Science (1967-1968), 159-182, 320-334, 486-502.
  5. Mertens, Jean. F. and Shmuel Zamir. Formulation of Bayesian analysis for games with incomplete information. International Journal of Game Theory (1985), 1-29.
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One of central question in game theory was under what setting, common belief of rationality implies backward induction. When Aumann(1995), (1998) derive backward induction path as a consequence of common knowledge of rationality rather than common belief of rationality, it attracted a lot of criticism related to the aforementioned reasoning that knowledge, for being necessarily true, is too strong (see Binmore(1996) and Stalnaker(1996)). In this essay, when we say a player believes an event, it means that player believes that this event is obtained with probability 1.