Efficient Exploitation Of Waste Heat: Coordination Management For A Waste Heat Utilization Project From Economic Perspectives

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1 Efficient Exploitation Of Waste Heat: Coordination Management For A Waste Heat Utilization Project From Economic Perspectives Nguyen Huu Phuc a,, Yoshiyuki Matsuura a, Motonobu Kubo a a Graduate School of Innovation and Technology Management, Yamaguchi University, Japan Abstract We apply the concept of risk dominance in an asymmetric normal form of coordination game of waste heat utilization. One firm while producing its own product emits waste heat. The other firm can use the heat as its energy input. We show that even excluding all possible risks, there exists a critical value that if the efficiency gain from the cooperation is smaller than it, the cooperation will fail. It is that two parties will prefer not to participate in the project even if they can earn positive net profits from the cooperative waste heat project. Furthermore, to the best of our knowledge, our paper is the only study that develops the concept of risk dominance to show that i) first, under some conditions, there exists payoff transfer between parties to enable Pareto dominant equilibrium to be the risk-dominant equilibrium even when the efficiency gain is smaller than the critical value. It implies that energy cooperation can be achieved without government subsidy. ii) second, our analysis presents computational mechanism to obtain the minimum required amount of subsidy for the coordination agreement. Key words: Waste Heat, Energy Efficiency, Stag-hunt Game, Risk Dominance Corresponding author. addresses: phuc@yamaguchi-u.ac.jp (Nguyen Huu Phuc), matu@yamaguchi-u.ac.jp (Yoshiyuki Matsuura), kubomo@yamaguchi-u.ac.jp (Motonobu Kubo).

2 1 Introduction In industrial sectors, it is believed that manufacturing firms have in the past endeavored for energy saving and there is little room for further increase in energy efficiency by individual activities. Japanese government (and the related IAA, specifically New Energy and Industrial Technology Development Organization (NEDO)) thus put political emphasis on coordinative energy reduction activities beyond organizational boundaries rather than on individual efforts to increase energy efficiency. The preceding investigations which employed advanced engineering technology such as PINCH analysis proved the significant opportunities to dramatically improve local energy efficiency of major regional industrial complexes. Meanwhile, enormous energy economics literatures have proven the existence of and found the reasons for (energy) efficiency gap from various perspectives (Jaffe and Stavins, 1994). Efficiency gap can be roughly defined as energy efficiency s untapped potential (International Energy Association, 2007) and thus the definition may involve a wide range of untapped potential. However, the extant knowledge has been constructed on the researches focusing on the delay of individual investment decision to replace existing equipment with technologically efficient (and cost effective) one 1. We call this kind of efficiency gap stemming from technological development as technological efficient gap. Contrary, we call another kind of gap or unexploited potential caused by the absence of cooperative efforts beyond organizational boundary as institutional efficiency gap which is not examined fully. Particularly, in Japan, in-house power generations in many manufacturing plants located in industrial complexes waste a staggering amount of energy. Nearly two-thirds of the energy they produce is waste heat, even though it is not difficult to find useful applications for large quantities of low temperature heat in the industrial complexes 2 where various firms of different industries are located in close proximity. However, unfortunately there are few waste heat utilization projects implemented between firms even though the estimated profits for the firms apparently surpasses the total cost of the heat ducting and all other related operating cost 3. For filling up this hole, this paper envisages the conditions institutional efficiency gap would be resolved with focusing on waste heat exploitation. 1 See (Ansar and Sparks, 2009) as a recent advanced analysis based on real option based integrated approach. 2 In Japan, an industrial complex often comprises many firms from various industries. It is, therefore, not difficult to find a useful application for low temperature heat in the complex. 3 See for the recent cases of coordinative effort among manufacturing units located closely, Nikkei Newspaper June 7, 2007

3 We apply the concept of risk dominance (Harsanyi and Selten, 1988) in an asymmetric normal form of coordination game. A simple version of it is the stag-hunt game (Skyrms, 2004) that is symmetric. The stag hunt game is derived from Rousean s example in A Discourse on Inequality. Our model is a coordination game on waste heat utilization. One firm while producing its own product emits waste heat. The other firm can use the heat as its energy input. We show that even excluding all possible risks, there exists a critical value that if the efficiency gain from the cooperation is smaller than it, the cooperation will fail. It is that two parties will prefer not to participate in the project even if they can earn positive net profits from the cooperative waste heat project. Like in a stag hunt game, it is best for both parties, if they cooperate. But each fears that the other may not play their part and is then motivated to defect. Not being sure of the cooperative dispositions of the others, they may themselves rationally defect, and the Pareto dominant equilibrium is missed. There are a few papers dealing with similar coordination problems using the same analysis framework, such as Olcina and Penarrubia (2002). However, their analysis was based on the symmetric form that has very limited practical implications. Our paper suggests the solutions using a generic asymmetric game. Furthermore, to the best of our knowledge, our paper is the only study that develops the concept of risk dominance to show that i) first, under some conditions, there exists payoff transfer between parties to enable Pareto dominant equilibrium to be the risk-dominant equilibrium even when the efficiency gain is smaller than the critical value. It implies that energy cooperation can be achieved without government subsidy. ii) second, our analysis presents computational mechanism to obtain the minimum required amount of subsidy for the coordination agreement. 2 Coordination problems Coordination problems arise when coordination yields a greater surplus to be divided between the partners. On the other hand, it reduces a partner s payoff, provided his rival does not coordinate. When the parties face this strategic situation, there are two Nash equilibria in pure strategies: one allocation is efficient (both partners coordinate) and the other allocation is inefficient (both do not coordinate). Under plausible conditions, it is so risky that the parties will choose the inefficient but the less risky equilibrium. The simple version of this type of game is the stag-hunt game. There are two equilibrium concepts to select the focal equilibrium in the coordination game. One concept for determining coordination equilibria in a coordination problem is called payoff dominance related to the payoff level

4 of each equilibrium. Hence, a coordination equilibrium payoff dominates (or is more efficient than) another coordination equilibrium, if and only if each player s payoff is greater in the former equilibrium than in the latter one. A different concept for determining coordination equilibria is related to the risk associated with each equilibrium. It is called risk dominance(harsanyi and Selten, 1988). The calculation procedure follows that of Young (1998). Consider, for example, the following generic coordination game. D C D a 11, b 11 a 12, b 12 Table 1 A generic game C a 21, b 21 a 22, b 22 This game is a coordination game with pure strategy Nash equilibrium (a 11, b 11 ) and (a 22, b 22 ), iff the following inequalities are satisfied: a 11 > a 21, b 11 > b 12, a 22 > a 12, b 22 > b 21. (1) We define the risk factor of equilibrium (a 22, b 22 ) as the smallest probability, say p, such that if one believes that his rival is going to play action C with probability greater than p, then C is the unique optimal action to take. For player A, the smallest such p satisfies a 11 (1 p) + a 12 (p) a 21 (1 p) + a 22 (p) (2) Or equivalently, a 11 a 21 def p = = α (3) a 11 a 12 a 21 + a 22 Similarly, for player B, the smallest such p satisfies p = b 11 b 12 b 11 b 12 b 21 + b 22 def = β (4) Then, the risk factor of the equilibrium (C, C) will be r C def = min{α, β}. Similarly, the risk factor of the coordination equilibrium (D, D) will be r D = min{(1 α), (1 β)}. A risk-dominant equlibrium in a 2 x 2 game is an equlibrium whose risk factor is lowest. Hence, equilibrium (C, C) is risk dominant iff r C r D (5) Equlibrium (D, D) is risk dominant iff r D r C (6)

5 Risk dominance captures the following intuition. When there are two Nash equilibria in a game, they are not sure if the other still continues to play their role in the equilibrium which requires coorperation. Not being sure of the cooperation, he may be then motivated to move to a safer but less efficient equilibrium. In the present setting, risk dominance suggests that there is a trade-off between the energy efficieny gain in case of successful cooperation and the risk that one firm will withdraw its cooperation. 3 The model Consider two firms (A and B) located near to each other in an industrial complex. Firm A while producing its own product emits waste heat. Suppose the waste heat has the following characteristics: (1) Non-storable good. (2) Disposal good to firm A. It is technologically useless (non-reusable) for firm A. (3) Reusable good to firm B. Firm B can use the heat as its energy input. (4) Therefore, there exists demand from firm B for the waste heat. (5) It requires a capital (heat ducting, say I) to transfer the waste heat from firm A to firm B. Although the transaction of waste heat has some similarities with other kinds of non-storable energy (say, electricity), there are two key differences between them: (1) disposability: the traditional energy like electricity is the main product that needs to be produced and supplied. The waste heat, however, in our model is a disposal by-product. This difference results in that unlike the electricity market, firm A loses nothing if it chooses not to participate in the project. Consequently, its payoff will be 0 then. (2) monopsony market: due to technological restrictions, the heat ducting is efficient within a limited area. Therefore, the buyers of waste heat, if any, are very few. It is absolutely different in the traditional peak-load problem where there is only one seller but many buyers (monopoly market). This characteristics will make the coordination model of waste heat utilization become 2 x 2 game. It enables us to use the concept of resistance (Guth and Kalkofen, 1989) or risk factor (Young, 1998) to characterize the risk dominant equilibrium. In addition to the stochastic nature of a waste heat transaction, the buyer is confronted with no less troubling risk. This is the damage loss occurred in its production line when the supplier fails to provide the contracted amount of

6 waste heat. As a result, we assumes that the buyer preserves existing energy generation facilities ready to operate for the case of unexpected supply stop until the end of coordination. If both sides agree to participate in the project, the investment cost that the waste heat supplier A and the buyer B have to bear are I A and I B respectively, with (I A +I B = I). The surplus V is obtained. It will be divided proportionally according to each player s investment cost. That is, V A = µ I A I for player A and V B = µ I B I for B. The project value is defined as µ, that is, the saving amount of waste heat for firm B. Even when firm B does not participate in the project, it still has to pay an amount of µ for its own demand of waste heat. We also define Π A and Π B as firm A and B s net project profit. The relation between the variables in the model is summarized as follows: µ def = V A + V B = (Π A + I A ) + (Π B + I B ) (7) I def = I A + I B (8) Efficiency gainπ def = µ I = Π A + Π B (9) Π A = I A I µ I A (10) Π B = I B I µ I B (11) There are three types of project risk assumed in our paper: (1) risk due to the supplier s responsibility that does not supply enough of the contracted volume of waste heat. Waste heat is the by-product obtained while firm A is producing its main products. As a consequence, the volume of waste heat is easily influenced by firm A s main product changes. There are times when firm A has to scale down its main product, then the cost for maintaining the contracted volume of waste heat may be higher than the contract compensation to firm B. (2) risk due to the buyer s responsibility buying waste heat less than the contracted volume. (3) (a) risk due to both parties responsibility, (b) external risk beyond the control of the parties. Risk involved in the project and its management is a very complicated issue and is beyong our paper. We will deal with it in our other papers. Hence, we

7 make a simple assumption that the amount of losses caused by these types of risk for firm A and firm B are R A and R B respectively. As a result, the payoff structure for firm A and B can be described as the follow table: D D 0, µ 0, ( I B µ) C I A, µ (Π A R A ), (Π B R B ) Table 2 Generic game of a waste heat coordination project C D and C mean defect and coordinate respectively. 4 Results First, we consider the case there is no losses caused by any kind of unexpected risk. The payoff of two firms can be described as follows: 4.1 Case 1: Critical value to avoid coordination failure D D 0, µ 0, ( I B µ) C I A, µ ( ) ( ) IAI µ I A, IBI µ I B Proposition 1 Coordination fails even when efficiency gain Π is positive. Proof 1 Calculate the risk factor R C and R D for the equilibrium (C, C) and (D, D) respectively. It is obvious that R C = min R D = min ( C ( ) I µ, I B µ + I B + Π B 1 I µ, 1 I B µ + I B + Π B ) (12) (13) I µ > I B µ + I B + Π B. (14)

8 Consequently, (D, D) is strictly risk dominant iff Or equivalently, 1 I µ < I B µ + I B + Π B (15) f(µ) def = µ 2 + µ(π B I) I(Π B + I B ) < 0 (16) Let µ 1 < µ 2 be the roots of f(µ) = 0. It is trivial that µ 1 < 0 < µ 2. Therefore, to satisfy the relation (16), the value of µ has to vary within: µ 1 < µ < µ 2. Furthermore, due to f(i) < 0, f (I) > 0, for I < µ < µ 2, the cooperation will fail even when the efficiency gain Π > 0, since (D, D) equilibrium is risk dominant. 4.2 Existence of a transfer ϵ enabling equilibrium (C, C) to be risk-dominant, even when µ < µ 2 Next, even when when µ < x 2, we study a possibility to enable the risk dominanted equilibrium (C, C) to become a risk dominant equilibrium by transfering the payoff between two players. We will examine the following payoff table with ϵ being the payoff transfer. If ϵ > 0, we move the payoff of ϵ from firm A to firm B. If ϵ < 0, the reverse holds. D D 0, µ 0, ( I B µ) C I A, µ ( ) ( ) IAI µ I A + ϵ, IBI µ I B ϵ Proposition 2 (Transfer) Even µ < x 2, if δ 0 and a payoff transfer is allowed between firm A and B, then there exists a transfer enabling the equilibrium (C,C) to become a risk dominant equilibrium satisfies the following condition: ϵ 1 ϵ ϵ 2 < 0 (17) with ϵ 1, ϵ 2, such that ϵ 1 < ϵ 2, as the roots of the following equation g(ϵ) when it equals to 0: and g(ϵ) def = ϵ 2 ϵ(2π B + I) + (I B V A Π A (V A + µ)) (18) δ def = (2Π B + I) 2 4(I B V A Π A (V A + µ)) (19) It implies the importance of transfering some payoff value from the supplier A to the buyer B to initiate the coordination in case 2. C

9 Proof 2 Calculate the risk factor R C and R D in case 2 for the equilibrium (C, C) and (D, D) respectively. R C = min ( ) IA V A + ϵ, I B µ + V B ϵ (20) R D = min ( 1 I ) A V A + ϵ, 1 I B µ + V B ϵ Due to the nature of coordination game, ϵ < min{π A, Π B }. If Π A > Π B (equivalently, I A > I B ), then I A V A + ϵ = 1 µ + ϵ > I I A 1 µ + Π > B I IA 1 µ + µ ϵ = I I B I B µ + V B ϵ (21) (22) We obtain the same result if Π A < Π B. As a result, in case 2, for equilibrium (C, C) risk dominates equilibrium (D, D) iff the following inequalities is satisfied: I B µ + V B ϵ 1 I A (23) V A + ϵ I B µ + V B > 1 I A V A (equivalent to (15)) (24) Consequently, the inequalities (23) and (24) are equivalent to the following inequalities: g(ϵ) 0 (25) I B V A Π A (V B + µ) > 0 (26) Due to (2Π B +I) > 0 and the inequality (26), from (24), we can conclude that ϵ 1 < ϵ 2 < 0. Hence, it is easy to prove the remaining part of the proposition. 4.3 Case 3: Government Subsidy What is the solution for a possible cooperation if δ < 0, or the transfer cannot be properly implemented because of the existence of information asymmetry between the players? There are three following situations: (1) Payoff transfer between the parties cannot be applicable in any form. (2) The transfer is applicable and δ < 0. (3) The transfer is applicable and δ > 0. This is the problem solved in the Proposition 2. Proposition 3 (Subsidy) If µ < µ 2, then

10 (1) If no transfer is allowed between A and B, the following subsidy ψ granted for both sides to enable equilibrium (C, C) to become risk-dominant: δ µ 2 µ (27) (2) If a transfer is allowed between the players, and δ < 0, the following subsidy ψ is needed granted for player B to enable equilibrium (C, C) to become risk-dominant: ψ 4(I B V A Π A (V A + µ)) (2Π B + I) 2 (28) Proof 3 From Proposition 1 and 2, the proof of Proposition is obvious. 4.4 Case 4: Existence of R A and R B D D 0, µ 0, ( I B µ) C I A, µ (Π A R A ), (Π B R B ) Corollary 1 For all value of R A < Π A and R B < Π B, the following inequality is always satisfied: I A I B > (29) V A R A µ + V B R B C Proof 4 Or equivalently, I A V A R A > I B µ + V B R B (30) V A R A < µ + V B R B (31) I A I B 1 ( µ I ) A I A I R A < 1 ( µ + µ I ) B I B I R B (32) R B < µ + I B I A R A (33) The inequality (33) is always correct for any R A < Π A, R B < Π B. The corollary 1 is equivalent to the inequality (14). Therefore, it completes the following proposition: Proposition 4 Under the condition R A < Π A and R B < Π B, repeating the calculation procedure applied in cases 1-3, we will obtain the same results even when there exists the damage loss from unexpected risk R A, R B.

11 5 Conclusion This paper theoretically investigates the conditions in which the negotiation for coordinative waste heat utilization between two parties would be agreed based on an asymmetric normal form framework of stag-hunt game. On the course, we focus on two complementary measures. These are, the payoff transfer between the parties and the involved government subsidy. The analysis yields the following two implications for political actions designed to initiate coordinative energy exploitation. First, our results suggest that, even when inherit risk exists, coordination can be achieved without subsidy. Therefore, closer scrutiny of, and management for negotiation process on the payoff transfer can increase the possibility of reaching agreement so that government may reduce the amount of subsidy. Second, we obtain the minimum required amount of subsidy for the agreement. Japanese government currently grant arbitrary proportion, (say 30% or 50%), of the initial investment for coordination parties based on the cost-benefit analysis in terms of expected increase in energy efficiency per investment. Our analysis presents computational mechanism of lower threshold for granting and consequently contributes to decide more efficient subsidy strategy. Since waste heat exploitation is one powerful and implementable approach for increased energy efficiency in any country other than Japan, we believe our analysis can help individuals and bodies who plan energy policy with generality. For instance, carbon tax effect on waste heat of which many developed countries examine can be easily incorporated into our analytical framework. Additionally, we do not exclude the possibility of household sector being on demand side so that our conclusion is applicable beyond industrial sector. Finally, we should mention the major limitations of the paper. First, we put a strong assumption on the demand side payoff. In our model, the energy buyer is assumed to be able to freely access alternative heat supply at the same unit price before the coordination. This means an unlikely situation that the demand side preserves existing energy generation facilities ready to operate for the case of unexpected supply stop until the end of coordination. However, it is more plausible to imagine that the buyer wants to retire the existing facilities at least partially. In that case, any unscheduled stop may cause loss beyond energy generation cost because of manufacturing facilities shutdown. These sequential consequences are not fully reflected in our game. Second, we also assume that both parties perfectly share the loss probabilities accrued to each party. However, it seems exceptional that each party voluntarily communicates the quality of maintenance activity and fundamental manufacturing schedule to the other, especially when the two parties may have some competition in their own product markets. Third, we do not consider the technological

12 efficiency gap problem. Thus, as we do not integrate so far the technological efficiency gap and institutional gap, we cannot propose a comprehensive efficient regional energy management scheme. Hopefully, these issues are to be solved in future research. References Skyrms, Brian: The Stag Hunt and Evolution of Social Structure, Cambridge University Press (2004). John C. Harsanyi and Reinhard Selten: A General Theory of Equilibrium Selection in Games, MIT Press (1988). H. Peyton Young: Individual Strategy and Social Structure: An Evolutionary Theory of Institutions, Princeton University Press (1998). R. Selten: An axiomatic theory of a risk dominance measure for bipolar garnes with linear incentives, Games and Economic Behavior 8: (1995). J. Ansar and R. Sparks: The experience curve, option value, and the energy paradox, Energy Policy, forthcoming (2009). A.B. Jaffe and R.N. Stavins: The energy efficiency gap, Energy Policy 22(10): (1994). International Energy Association (IEA): Mind the Gap; Quantifying principalagent problems in energy efficiency, IEA Publications (2007). G. Olcina and Penarrubia C.: Specific investments and coordination failures, Economics Bulletin: Vol. 3, No. 2 pp. 1-7 (2002). W. Guth and Kalkofen, B.: Unique Solutions for Strategic Games: Equilibrium Selection Based on Resistance Avoidance, Springer-Verlag Berlin (1989).