Environmental awards in a duopoly with green consumers

Heidelmeier, Lisa; Sahm, Marco Working Paper Environmental awards in a duopoly with green consumers BERG Working Paper Series, No. 207 Provided in Cooperation with: Bamberg Economic Research Group, Bamberg University Suggested Citation: Heidelmeier, Lisa; Sahm, Marco (2025) : Environmental awards in a duopoly with green consumers, BERG Working Paper Series, No. 207, Bamberg University, Bamberg Economic Research Group (BERG), Bamberg, https://doi.org/10.20378/irb-108373 This Version is available at: https://hdl.handle.net/10419/319885.2 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Environmental Awards in a Duopoly with Green Consumers Lisa Heidelmeier and Marco Sahm Working Paper No. 207 May 2025 k* b 0 k B A M AMBERG CONOMIC ESEARCH ROUP B E R G Working Paper SeriesBERG Bamberg Economic Research Group Bamberg University Feldkirchenstraße 21 D-96052 Bamberg Telephone: (0951) 863 2687 [email protected] http://www.uni-bamberg.de/vwl/forschung/berg/ https://doi.org/10.20378/irb-108373 Redaktion: Dr. Felix Stübben  [email protected] https://creativecommons.org/licenses/by/4.0/ Environmental Awards in a Duopoly with Green Consumers∗ Lisa Heidelmeier†Marco Sahm∗∗ This version: May 9, 2025 Abstract We investigate the impact of an environmental award in a Bertrand duopoly with green consumers considering a three-stage game. First, the regulator designs the environmental contest. Second, firms choose their green investments, and the winner of the contest is awarded. Third, firms compete in prices, and consumption takes place. We illustrate that the award not only incentivizes green investments and may thus reduce environmental externalities. As consumers perceive the product of the awarded firm to be of superior quality, it also gives rise to vertical product differentiation. This induces market power, and thus anti-competitive effects: Rents shift from consumers to producers, and consumer surplus may decrease, particularly if marginal investment costs in green technologies are high compared to the strength of environmental damage. Keywords: Bertrand Competition; Contests; Environmental Award; Green Consumer; Product Differentiation JEL classification: D43, H23, L13, L51, Q52, Q58 ∗We are grateful to Fabian Dietz, Stephan Eitel, Stefanie Schmitt, and participants at the 16th RGS Doctoral Conference in Economics, the 22nd Bavarian Micro Day, the 50th Annual Conference of the European Association for Research in Industrial Economics, the Annual Conference of the Verein f¨ur Socialpolitik 2023, the Innsbruck Winter School on Credence Goods, Incentives and Behavior, the 29th Annual Conference of the European Association of Environmental and Resource Economists, the ifo Public Economics Workshop 2024, and research seminars at the University of Bamberg for valuable comments and suggestions. Lisa Heidelmeier gratefully acknowledges financial support from the HansB¨ockler-Stiftung. A former version of this paper circulated under the title ’A Vertically Differentiated Duopoly Model with Environmental Awards’. †University of Bamberg, Department of Economics, Feldkirchenstraße 21, 96052 Bamberg, Germany. ∗∗Corresponding author: University of Bamberg, Department of Economics, Feldkirchenstraße 21, 96052 Bamberg, Germany; and CESifo, Poschingerstraße 5, 81679 Munich, Germany. E-mail: [email protected], Telephone: +49–951–863–2728. 1 Introduction Traditional responses to climate change, such as emission trading or taxation, are partly reaching their limits. The IPCC Sixth Assessment Report warns that global net carbon emissions need to decline by 45% of 2010 levels by 2030 to reach net zero by around 2050 (IPCC, 2022). The OECD (2017) underscores that promoting policy packages to mobilize investment in carbon neutral infrastructure and technologies is one of the key steps to combat global warming. This paper analyzes an alternative incentive and internalization measure that has hardly been studied so far: environmental awards. Here, individuals, firms, or organizations decide to participate in an environmental contest. Each participant applies with his environmental effort. Then the contest takes place, and one contest winner is assigned based on his environmental performance. Environmental awards are increasingly used, as the Champions of the Earth award, the UN Global Climate Action Award or the German Sustainability Award show. However, theoretical support is lacking. Further, we see that a growing fraction of consumers prefers to buy products from firms that use environmentally-friendly production technologies and accepts to pay a higher price for green goods.1This trend opens up the possibility for firms to use green investments as strategic variables to differentiate from their competitors and to relax price competition. In this article, we elaborate on the two observations named above: dealing with current challenges of environmental policy by means of a contest while observing consumers with an increasing willingness to pay for green products. In order to shape firms’ incentives, we use a model of vertical product differentiation. Vertical preferences imply that consumers prefer the good of higher perceived environmental quality and are willing to pay a higher price for this good. More specifically, to examine the effectiveness of an environmental contest, we consider a Bertrand duopoly where the firms’ products differ in the perceived level of environmental quality. We analyze competition between the two firms in the framework of a game with three stages: In the first stage, the regulator designs the environmental award, that is, the salience of the winner’s product. In the second stage, firms decide simultaneously how much to invest in environmentally-friendly technologies. After observing the investment efforts, the contest winner is awarded. The environmental award reveals to consumers which product is (perceived to be) the greener one. In the third stage, firms simultaneously set their market prices. Thereafter, consumers make their consumption decisions. Our baseline model concentrates on a covered market with unit demand: Each consumer buys exactly one unit of the product. Moreover, the contest is organized as an all-pay auction. This reflects the assumption that the contest designer can perfectly observe firms’ investment levels and thus awards the firm with the highest investment level. We distinguish between two different objectives of environmental policy: The regulator maximizes either welfare (total surplus) or consumer surplus. For both objectives, we find that the regulator implements the contest as long as the firms’ marginal green investment costs are not too high in relation to the marginal strength of environmental damage. The welfare maximizing award, however, will raise consumer surplus if and only if the marginal green investment costs are sufficiently low compared 1See, e.g., Ward et al. (2011), Berger (2019), Kuhn and Uler (2019), Hulshof and Mulder (2020), Gomes et al. (2023), European Commission—Directorate-General for Communication. (2024), Ruggeri et al. (2024). 2 to the marginal strength of environmental damage. Otherwise, the welfare maximizing contest will be detrimental to consumers. Intuitively, using an environmental contest induces the following trade-off: On the one hand, the award motivates firms to invest in green technologies and, thereby, to internalize part of the environmental externality. Consequently, consumers profit from reduced environmental damage. However, on the other hand, the award implies product differentiation that confers market power on firms. This leads to higher prices and shifts rents from consumers to producers. Compared to a welfare maximizing regulator, a regulator who maximizes consumer surplus thus chooses a lower environmental award and accepts higher environmental damage. The main results also hold for two variants of the baseline model. In the extension section, we first relax the assumption of a covered market. If some consumers stop buying if the environmental contest is installed, additional quantity effects will arise as consumption levels decrease. Secondly, we relax the assumption that the contest designer can perfectly observe investment levels. To allow for some noise, the environmental contest is modeled as a lottery: A firm can (ceteris paribus) increase its probability of winning the award by increasing its investment, but the firm with the higher investment does not win for sure. The remainder of the article is organized as follows: Section 2 reviews the related literature. Section 3 introduces the baseline model and Section 4 presents the main results. In Section 5, we discuss the two extensions of the baseline model. Section 6 concludes. 2 Related Literature Our paper contributes to two strands of the literature: specifically, models that adopt a contest to internalize externalities, and, more generally, articles that highlight measures to make firms’ environmental performance visible. To create an incentive scheme for green investment, we develop a theoretical model based on contest theory.2Related studies are found in the public goods literature, as protecting the quality of the environment can be interpreted as a public good. Previous work on contests in the public goods literature focuses mainly on the effects of monetary prizes and player heterogeneity, as well as on correcting distortions in consumption due to taxation (see, e.g., Morgan, 2000; Giebe and Schweinzer, 2014; Kolmar and Sisak, 2014).3 Another, as yet small, field of research combines market-based environmental policy with contest theory. MacKenzie et al. (2009) develop a mechanism that distributes emission permits to firms based on a rank-order contest. Bos et al. (2016) implement a contest to incentivize the formation of international environmental agreements, ensuring that harmful emissions are reduced to the socially efficient level without sacrificing productive efficiency. Similarly to our approach, two recent papers by Osorio and Zhang incentivize green investment by applying a contest mechanism. In Osorio and Zhang (2022a), firms compete for an environmental subsidy. The authors compare two subsidy mechanisms: Firms compete by investing in green product features or by investing in emission abatement. The 2For an overview, see Konrad (2009). 3Another branch of the contest literature uses political contests to model the process of environmental regulation under lobbying, see, e.g., Heyes (1997), Liston-Heyes (2001), Dijkstra (2007), Ansink and Weikard (2025). 3 article suggests the green product feature design in industries with relatively high emission levels and the abatement design in industries with relatively low emission levels. In their second paper, Osorio and Zhang (2022b) examine different contest designs to determine emission taxes endogenously. They find that the optimal tax mechanism depends on the level of environmental damage in the respective industry. The studies surveyed above emphasize the welfare-enhancing effects of contests. In contrast, our approach reveals that using a contest may also have anti-competitive effects which, to our knowledge, have not been taken into account in previous research. Our main contribution is to provide a theoretical framework for an environmental award based on contest theory and a comprehensive analysis of how environmental awards affect consumer behavior. Firms need to promote their environmentally-friendly image to attract consumers for their green products. One way for firms to reveal their environmental efforts is by participating in an environmental contest. Another, more prevalent way, is to adopt an eco-label. There is extensive literature on eco-labeling.4Current eco-labeling literature stresses that the labeling design, firms’ cost structures, abatement technologies, and costs for eco-labeling determine the effectiveness of eco-labels (see, e.g., Amacher et al., 2004; Ibanez and Grolleau, 2008; Li and van’t Veld, 2015; Fischer and Lyon, 2019). On the consumer side, environmental consciousness, information structures, consumer informedness, and altruism play a crucial role (see, e.g., Br´ecard, 2017; Heyes et al., 2020; Ghazzai and Lahmandi-Ayed, 2021). Ben Youssef and Lahmandi-Ayed (2008) endogenously determine the labeling criteria that maximize total welfare. Similarly to our paper, but for labels, Ben Youssef and Lahmandi-Ayed (2008) show that introducing an eco-label may induce anti-competitive effects resulting in price increases that harm consumers. Bringing together the literature on environmental awards and eco-labels, Heidelmeier and Schmitt (2025) compare awards and labels as two instruments that allow firms to draw consumers’ attention to the environmental quality of their products. In particular, the paper discusses the impact of awards and labels on firms’ investments in environmental quality and on social welfare. Heidelmeier and Schmitt (2025) show that a social welfare maximizing regulator implements an environmental award if and only if marginal damage and salience of the environmental quality are sufficiently high such that consumers overestimate the environmental quality of the awarded and labeled goods. Our contest approach stands out against traditional environmental regulatory instruments (such as emission taxation or trading systems) in terms of its positive investment incentives: The environmental contest allows firms to differentiate their products from those of their competitors with respect to environmental quality. As products get differentiated, firms can generate higher profits. Thus, the environmental award incentivizes firms to participate voluntarily in the contest. Firms invest in green technologies and, thereby, contribute to internalizing the environmental externality. While traditional instruments mainly concentrate on emission regulation and sanctions based on negative incentives, the contest mechanism sets positive investment incentives - similar to the use of eco-labels. Many studies examine eco-labeling as an incentive mechanism for green technology investment, whereas the literature on environmental awards is scarce. Yet, Lai et al. (2022) and Li et al. (2024) provide empirical evidence that environmental awards can indeed be a significant driver of green technology innovation. Besides these posi4For an overview, see Yokessa and Marette (2019) or van’t Veld (2020). 4 tive consequences, however, our model also highlights that an environmental award may induce anti-competitive effects and harm consumers. 3 Model We examine a duopoly model of price competition on a market with an environmental externality and green consumers. In principle, differences in the intensities of the consumers’ preferences for environmental quality give rise to vertical product differentiation (Shaked and Sutton, 1982; Motta, 1993). We assume, however, that a firm can (credibly) signal the (superior) environmental quality of its product only by winning an environmental award. Designing the respective environmental contest is the only (remaining) policy tool of a benevolent regulator who aims to internalize the environmental externality in order to maximize social welfare or, alternatively, consumer surplus. 3.1 Firms We consider a market with price competition between two firms. Each Firm i∈ {1,2} produces one version of a product with (perceived) environmental quality µiand sells it at price piper unit. For simplicity, we assume the (constant) marginal costs of production to be zero (Motta, 1993). The production of each unit of the good causes an environmental externality equal to 1 −xi, where xidenotes Firm i’s investment into environmental quality. The marginal costs of green investments are constant and equal to c > 0. We assume, however, that neither the firms’ investments nor the resulting environmental qualities are directly observable by consumers.5Without any (further) information on Firm i’s investment, consumers perceive the firm’s environmental quality as µℓ, which we interpret as the minimum standard quality. 3.2 Consumers We consider a continuum of consumers indexed by θ. The parameter θrepresents the consumer’s marginal valuation of environmental quality. For the sake of concreteness, we assume that θis uniformly distributed on the interval [0,1]. We assume discrete choice and unit demand: Each consumer has the same reservation price rfor a good with environmental quality 0 and buys either none or exactly one unit of the good, either from Firm 1 or from Firm 2. For sufficiently large income y, the preferences of consumer θ can be described by the following (indirect) utility function (Mussa and Rosen, 1978):6 U(y, p, µ) = max{0,maxi∈{1,2}ui(y, p, µ)}, where ui(y, p, µ) = r+θµi−pi.(1) In our baseline model, we assume that the reservation price ris high enough to ensure that the market is covered, i.e., each consumer buys exactly one unit of the good, either from Firm 1 or from Firm 2.7 5Firms’ environmental quality and the underlying green investments satisfy the criteria characterizing a credence good: While goods are often differentiated by their environmental quality, e.g., low-emission electricity, consumers may be unable to observe these differences, even after consumption. Therefore, consumers have to rely on instruments, as an award, to make firms’ environmental performance visible. 6Peitz (1995) provides a thorough foundation for this kind of modeling. 7In Section 5, we relax this assumption allowing for an uncovered market, where some consumers do not buy any of the two versions of the good. 5 3.3 Regulator We consider a benevolent regulator who is able to observe the firms’ environmental investments. As the only (remaining) instrument for providing investment incentives and, thereby, reducing the environmental externality, the regulator designs an environmental contest. In the baseline model, the contest is organized as an all-pay auction:8The firm with the higher environmental investment wins the contest and receives the award. While consumers perceive the loser’s environmental quality as the minimum standard quality µℓ, they perceive the winner’s environmental quality as µw. We assume that the regulator can freely choose the winner’s perceived environmental quality µw≥µℓ, and refer to it as the environmental award. The award µwcan be interpreted as the attention-generating effect of the contest that may, e.g., depend on the regulator’s publicity campaign regarding the contest.9We ignore the cost of the contest program, which is a reasonable assumption as long as it is small compared to the environmental externality and investments. Below, we consider two alternative objectives the regulator may have: the maximization of either total welfare (as the sum of producer surplus and net consumer surplus) or net consumer surplus only. We define net consumer surplus as the difference between consumer surplus net of consumers’ environmental concerns10 and the social loss caused by the environmental externality. For the sake of concreteness, we assume a quadratic loss function, L=δε2, where the parameter δ≥0 scales the damage associated with the aggregate externality ε. 3.4 Timing of events We model the interdependent decisions as a game with three stages. In the first stage, the regulator decides upon the award for the winner of the environmental contest, µw. In the second stage, firms choose simultaneously their investments in environmental quality xi, i∈ {1,2}, the contest takes place, and the winner’s product is awarded. In the last stage, firms choose simultaneously the prices pi,i∈ {1,2}, for their so differentiated products, and consumers make their consumption decisions. 4 Analysis and Results Before we describe the decisions on the three stages in more detail and solve the game by backward induction for its subgame-perfect equilibrium, we briefly discuss the unregulated market (laissez-faire economy) as a benchmark. 8In Section 5, we consider a lottery contest as an alternative choice of modeling. 9The assumption that the regulator has full control over the perceived environmental qualities is a simplification. Implicitly, it rests upon a behavioral assumption on consumers, e.g., limited attention or awareness: Consumers recognize only the winner’s environmental effort, all the more the more salient the award is. See, e.g., Eliaz and Spiegler (2011), Bordalo et al. (2016), Hefti and Liu (2020), Carroni et al. (2023). 10I.e., aggregating individual utilities, the regulator includes only the net utility from consumption, r−pi, but not the extra surplus from environmental quality, θµi. The reason for this assumption is that an unbiased regulator should take into account only the real consequences of environmental quality (i.e., the environmental externality) but not the perceived ones (i.e., the consumers’ different green consciousness). Moreover, this keeps our model free from additional incentives for the regulator to raise µwin order to increase consumer surplus directly (besides stimulating green investments). 6 following analysis to a welfare maximizing regulator. An uncovered market thus arises if r < p∗ ℓ= (9c(10δ−9c))/(50δ). 5.1.1 Stage 3: Price game In the third stage of the game, the awarded firm, w, and the non-awarded firm, ℓ, simultaneously choose their prices pwand pℓ. Now, under the assumption of an uncovered market, we have two margins: Consumers decide whether to buy the good produced by the firm having won the contest with perceived environmental quality µwor to buy the good produced by the firm having lost the contest with perceived environmental quality µℓor not to buy the good at all. As before, the marginal consumer being indifferent between the two quality levels is thus defined by θ≡(pw−pℓ)/(µw−µℓ). Similarly, the marginal consumer being indifferent between not buying and buying the good of perceived environmental quality µℓis described by θ≡(pℓ−r)/µℓ. Accordingly, firms’ demand functions are Dw= 1 −θand Dℓ=θ−θ, where θis the share of consumers not buying. Firm i∈ {ℓ, w}thus chooses the price piin order to maximize its profit πi=pi·Di. We derive the firms’ best response functions from the first-order conditions for solutions of these maximization problems and use them to compute the equilibrium. Lemma 3 summarizes the results. Lemma 3. Assume that the market is uncovered. Denote by w(ℓ) the firm that wins (loses) the contest and offers the perceived environmental quality µw(µℓ). Then, thirdstage equilibrium prices, market shares, and profits are p∗ w= ((µw−µℓ)(r+ 2µw))/(4µw− µℓ),p∗ ℓ= ((µw−µℓ)(2r+µℓ))/(4µw−µℓ)),D∗ w= (r+ 2µw)/(4µw−µℓ),D∗ ℓ= (µw(2r+ µℓ))/(4µw−µℓ),π∗ w= ((µw−µℓ)(r+ 2µw)2)/(4µw−µℓ)2, and π∗ ℓ= (µw(µw−µℓ)(2r+ µℓ)2)/(µℓ(4µw−µℓ)2). Lemma 3 shows that the difference in prices and profits is even higher in the uncovered market than in the covered market. 5.1.2 Stage 2: Investment game In the second stage, the firms anticipate these profits and decide simultaneously on their green investments xi,i∈ {1,2}, which determine their success in the environmental contest. As above, the unique Nash-equilibrium is in mixed strategies and can be derived form the property that the mixed strategy of Firm jmust leave Firm iindifferent between all its pure strategies (played with positive density), where i, j ∈ {1,2}and i=j. This implies, again, that Firm i’s expected profit from choosing any investment level xi>0 (with positive density) equals the expected profit from choosing an investment level of xi= 0 and losing the contest almost surely: E[πi] = πw·Fj(xi) + πℓ·(1 −Fj(xi)) −cxi=πℓ for i, j ∈ {1,2}and i=j. In combination with Lemma 3, this yields F∗ i(xi) = cxi πw−πℓ =cxi µℓ(4µw−µℓ) (µw−µℓ)(µℓµw−r2) as the mixed equilibrium strategy of Firm i∈ {1,2}. Lemma 4 summarizes the results. 13 Lemma 4. Assume that the market is uncovered and the environmental contest is organized as an all-pay auction with award µw> µℓ. In the second-stage equilibrium, firm i∈ {1,2}makes an expected green investment of E[xi] = (πw−πℓ)/(2c) = 1 2c (µw−µℓ)(µℓµw−r2) µℓ(4µw−µℓ) and has a winning probability of αi= 1/2. Moreover, conditional on the outcome of the contest, the expected green investment of the winner and loser, respectively, are E[xw|xw> xℓ] = 2 ·(µw−µℓ)(µℓµw−r2) 3cµℓ(4µw−µℓ),(6) E[xℓ|xℓ< xw] = (µw−µℓ)(µℓµw−r2) 3cµℓ(4µw−µℓ).(7) 5.1.3 Stage 1: Setting the environmental award In the first stage, the regulator sets the level of the environmental award µwin order to maximize total welfare, which we compute based on Lemmata 3 and 4: W=pℓ·Dℓ+pw·Dw−c·(E[xℓ|xℓ< xw] + E[xw|xw> xℓ]) +Zθ θ (r−pℓ)dθ +Z1 θ (r−pw)dθ −δ·(Dℓ·(1 −E[xℓ|xℓ< xw]) + Dw·(1 −E[xw|xw> xℓ]))2 =µw(µ2 ℓ−µwµℓ+ 3rµℓ+ 3r2) µℓ(4µw−µℓ) −δ(µℓ−µw)[5µℓµw+ 2r(µℓ+µw)](µℓµw−r2) + 3cµℓ(4µw−µℓ)[2rµw+µℓ(3µw+r)]2·1 9c2µ4 ℓ(4µw−µℓ)4. (8) If the market is not covered, increasing prices will not only shift surplus from consumers to producers, but also reduce aggregate demand. Thus, when choosing the award µwto promote environmental investments, the welfare maximizing regulator not only faces a trade-off between investment costs on the one hand and greener production on the other. The regulator also accounts for two opposing effects that stem from the reduced market volume: While a lower production level leads to a lower aggregate level of the environmental externality, lower market coverage reduces the aggregate utility of consumers. Based on the first-order condition dW/dµw= 0, we use numerical methods of the software Mathematica to exemplarily compute the equilibrium value µ∗ wfor the (corner) case of r= 0,12 fixed investment costs c= 1, fixed standard quality µℓ= 1, and different values of the strength of the externality δ. As Figure 2 illustrates, the main results of the covered market model also hold for the uncovered market: If the ratio c/δ is less 12Notice that for r= 0 the lower market coverage does not reduce the aggregate utility of consumers because, then, consumer surplus net of environmental concerns is zero even in the laissez-faire benchmark. Here, we show that even in this case where the environmental contest does not cause additional harm to consumers due to lower consumption, a welfare maximizing environmental contest may still reduce consumer surplus. 14 c=1 μl= -0.2 0.0 0.2 0.4 0.6 0.8 1.0 δ 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 μw * (a) c=1 μl=1 0.4 0.5 0.6 0.7 0.8 0.9 1.0 δ -0.02 0.02 0.04 0.06 0.08 0.10 0.12 ΔCS =CS*-CSLF (b) Figure 2: Uncovered market: (a) The optimal level of the environmental award as a function of marginal environmental damage δ.(b) Difference in consumer surplus between a contestdesigned (all-pay auction) equilibrium and a laissez-faire equilibrium. than a first threshold (that is, here, δ > 9/28), the regulator implements the contest, cf. Proposition 1 and Figure 2(a); but as long as that ratio is not less than a second threshold (that is, here, δis not greater than about 0.648), the implementation of the contest is detrimental to consumers, cf. Proposition 2 and Figure 2(b). 5.2 A welfare maximizing lottery contest In the baseline model of Section 4, the environmental contest is organized as an all-pay auction. The deterministic all-pay auction is fully discriminatory in the sense that the contestant with the highest investment wins for sure. It is well known that, in symmetric settings like ours, the all-pay auction is the contest success function that provokes the highest possible investments, which is desirable in our context for an effective reduction of the environmental externality. The assumption that the regulator can perfectly observe firms’ investments and fully discriminate when assigning the environmental award may, however, not always be fulfilled in practice. In this section, we consider an environmental contest organized as a lottery contest. Being based on a random success function, the lottery contest incorporates some noise: A contestant’s winning probability is given by the ratio between her own investment and the aggregate investments of all contestants. Thus, the player with the higher investment is more likely to succeed but does not win for sure. Assuming a covered market and a welfare maximizing regulator, we replicate the analysis of Section 4 for this alternative contest success function and compare the results. 5.2.1 Stage 3: Price game In the third stage, firms face the same pricing game as described in section 4.2. Lemma 1 describes market prices, profits, and the respective demand levels. 5.2.2 Stage 2: Investment game In the second stage, firms choose the amount of green investments xi. For i, j ∈ {1,2}, i=j, firm i’s probability of winning the environmental award is given by the lottery 15 contest success function13 αi(xi, xj) = 1 2if xi=xj, xi xi+xjotherwise. Hence, firm i∈ {1,2},i=j, chooses xiin order to maximize the expected profit E[πi] = pw·Dw·xi xi+xj +pℓ·Dℓ·1−xi xi+xj−cxi. We use the first order conditions dE[πi]/dxito compute the equilibrium investment levels, when applying a lottery contest, indexed L: xL 1=xL 2=µw−µℓ 12c.(9) 5.2.3 Stage 1: Setting the environmental award In the first stage, the regulator sets the award µwin order to maximize total welfare WL=pℓ·Dℓ+pw·Dw−c·xL ℓ+xL w +Z˜ θ 0 (r−pℓ)dθ +Z1 ˜ θ (r−pw)dθ −δ·Dℓ(1 −xL ℓ) + Dw(1 −xL w)2 =r−1 6(µw−µℓ)−δ12c+µℓ−µw 12c2 . (10) We use the first order condition dWL/dµwto compute the optimal level of the environmental award µL w=µℓ+12c(δ−c) δ.(11) It satisfies the constraint µL w> µℓif and only if 0 < c/δ < 1. As for the all-pay auction, it is optimal for the regulator to implement the lottery contest if and only if the marginal investment costs are sufficiently low compared to the strength of the environmental externality. The condition is, however, somewhat stricter. Comparative statics results are analog to the case of the all-pay auction as well. Therefore, qualitatively, the results of Proposition 1 apply. Based on Lemma 1 and Equations (9) and (11), Table 2 summarizes the equilibrium values of the respective variables if 0 < c/δ < 1; otherwise, the regulator does not implement the lottery contest (µL w=µℓ) and the laissez-faire results apply (see first column of Table 1). 5.2.4 Lottery contest vs. all-pay auction As a reference for comparison we use the equilibrium outcomes of the welfare maximizing all-pay auction design (see second column of Table 2). We find that, throughout, the all-pay auction is a more effective instrument than the lottery contest in the sense that it 13Skaperdas (1996) provides an axiomatic foundation. 16 Table 2: Equilibrium outcomes of a welfare maximizing lottery contest (L) for 0 < c/δ < 1 and a welfare maximizing all-pay auction contest (∗) for 0 < c/δ < 10/9. Welfare maximizing lottery contest Welfare maximizing APA µL w=µℓ+12c(δ−c) δµ∗ w=µℓ+27c(10δ−9c) 50δ pL w=8c(δ−c) δp∗ w=9c(10δ−9c) 25δ pL ℓ=4c(δ−c) δp∗ ℓ=9c(10δ−9c) 50δ xL 1=xL 2= 1 −c δE[x1]∗=E[x2]∗=9 100 (10 −9c δ) E[xw|xw> xℓ]∗=6 5−27c 25δ E[xℓ|xℓ< xw]∗=3 5−27c 50δ ϵL=c δ2ϵ∗=9c 10δ2 CSL=r−20c 3+17c2 3δCS∗=r−3c+189c2 100δ PSL=14c(δ−c) 3δPS∗=3c(10δ−9c) 25δ WL=r−2c+c2 δW∗=r−9c 5+81c2 100δ leads to both, higher welfare and lower environmental damage. Proposition 5 summarizes the results. Proposition 5. Comparing the welfare maximizing all-pay auction and the welfare maximizing lottery contest for 0< c/δ < 1in a covered market, the all-pay auction induces (i) higher social welfare (W∗> WL), (ii) lower environmental damage (ϵ∗< ϵL). Moreover, if the marginal investment costs are sufficiently low compared to the strength of the environmental externality, i.e., if 0< c/δ < 110 119 , the all-pay auction involves (iii) a lower environmental award (µ∗ w< µL w), (iv) lower prices (p∗ i< pL i), (v) higher consumer surplus (CS∗> CSL), but lower producer surplus (PS∗< PSL). Intuitively, as the all-pay auction is more competitive than the lottery contest, the regulator can induce the same level of aggregate green investments as in the optimal lottery contest using a lower award. This, in turn, results in a lower degree of vertical product differentiation and, hence, in lower market prices, in higher consumer surplus, but lower producer surplus when applying the all-pay auction design. While both firms choose the same (pure strategy) level of green investments in the lottery contest, the expected (mixed strategy) investment of the winning firm is larger than the expected (mixed strategy) investment of the losing firm in the all-pay auction. Since the winner of the contest has a higher market share, the same aggregate green investments reduce the expected environmental damage more effectively and, thus, increase the expected welfare more effectively if the regulator uses an all-pay auction instead of a lottery contest. A fortiori, the superiority of the all-pay auction will hold if the respective award is chosen optimally rather than for inducing the same level of aggregate green investments as in the optimal lottery contest.14 Figure 3 illustrates the results regarding consumer surplus. 14More generally, in the class of Tullock contests (Tullock, 1980), the all-pay auction constitutes an upper bound for environmental effectiveness. Notice that the standard Tullock contest with the contest success function αi(x1, ..., xn) = xr i Pn j=1 xr jconverges to an all-pay auction as r→ ∞ (Ewerhart, 2017). 17 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 c δCS*>CSL CS*<CSL Figure 3: Consumer surplus dependent on marginal green investment cost cand marginal damages δin a covered market. In the dark gray area, implementing the welfare maximizing all-pay auction contest yields higher consumer surplus, compared to the lottery contest. In the light gray area, implementing the welfare maximizing lottery contest yields higher consumer surplus, compared to the all-pay auction. The white area represents the constraint 0 < c/δ < 1. 6 Conclusion Beyond well-known policy instruments such as green subsidies, emission trading, or taxation, this paper has studied an environmental contest, issuing an environmental award, as an alternative measure to control greenhouse gas emissions. An advantage of an environmental contest is that firms have an incentive to participate voluntarily. The presence of an award allows firms to differentiate their products and increase their profits. This holds irrespective of whether or not a firm ends up winning the environmental award. Furthermore, firms do not have to disclose confidential data to implement the mechanism. Only the documentation of firms’ green investments is required. In particular, we have investigated the impact of an environmental award in a Bertrand duopoly with green consumers considering a three-stage game. First, the regulator designs the environmental contest. Second, firms choose their green investments, and the winner of the contest is awarded. Third, firms compete in prices, and consumption takes place. We have illustrated that the award not only incentivizes green investments and thus reduces environmental externalities. As consumers perceive the product of the awarded firm to be of superior quality, it also gives rise to vertical product differentiation. This induces market power, and thus anti-competitive effects: Rents shift from consumers to producers, and consumer surplus may decrease, particularly if marginal investment costs in green technologies are high. In search of a suitable instrument, a policy maker has to confront these potential drawbacks of an environmental contest with its aforementioned advantages. Our paper provides first insights into the mechanics of an environmental contest. We have shown that our main results are robust to variations of market demand (covered vs. uncovered market) and contest technologies (all-pay auction vs. lottery contest). 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International Review of Environmental and Resource Economics, 13(1-2):119–163. 21 Free access to all publications at: www.uni-bamberg.de/en/economics/research/wp/ BERG Working Paper Series (most recent publications) 190 Roberto Rozzi and Stefanie Y. Schmitt, Vertical product differentiation, prominence, and costly search 191 Florian Herold and Christoph Kuzmics, Farkas' Lemma and Complete Indifference 192 Sarah Mignot, Paolo Pellizzari, and Frank Westerhoff, Fake News and Asset Price Dynamics 193 Fabian Dietz and Marco Sahm, Fairness in Round-Robin Tournaments with Four Players and Endogenous Sequences 194 Jan Schulz, Caleb Agoha, Anna Gebhard, Bettina Gregg and Daniel M. 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Schmitt, Investments in environmental quality under limited attention 203 Jan Schulz and Jan David Weber, Power Laws in Socio-Economics 204 Rafael Kothe, Connecting the Dots: How Social Networks Shape Expectations Through Economic Narratives 205 Jan Schulz and Leonhard Ipsen, Poor Households and the Weight of Inflation 206 Lisa Heidelmeier and Stefanie Y. Schmitt, Awards vs. Labels: Incentivizing Investments in Environmental Quality 207 Lisa Heidelmeier and Marco Sahm, Environmental Awards in a Duopoly with Green Consumers