X.Liang et aL Journal of Cleaner Production 137 (2016)1300-1312 1305 that many owners and occupiers intend to implement green 1)Players:Two players are involved in the game,namely,the retrofit,but only a few can reach a consensus and continue its owner and the occupier,as elaborated in Section 2.1. implementation.Although other methods can be used to identify 2)Strategies:In general,the owner is the entity who establishes the reasons behind the actions,game theory focuses on players the initiative to retrofit and provides the initial retrofit plans. different actions influenced by the actions of other players.In the However,the occupiers have become increasingly active in beginning of green retrofit,owners and occupiers,as key decision green retrofit projects in recent years.Given that numerous makers,are interdependent and have different interests on the buildings have been retrofitted over the past few years,the issue.For example,when the owners intend to administer green successful experiences have attracted the occupiers because of retrofit to improve their social reputation or to reduce maintenance the learning effect.In 2015,81 occupiers actively raised 16 cost,they have to consider the rent contracts with occupiers.On the million CNY to finish the green retrofit project in the Interna- contrary,when the occupiers want to implement green retrofit to tional Trade Center of Shenzhen,China(Xiao,2015).Therefore, save energy cost,they have to consider the attitudes of the owners. both the owner and occupier in this game have two strategies, Thus,the final green retrofit decision depends on the actions of namely,"initiative to retrofit"and "reluctant to retrofit"The both the owners and occupiers.In this case,game theory can be former strategy is initiative to conduct green retrofit,whereas adopted to analyze the strategies of both parties.The results of the the latter is the resistance to the implementation of green game theory analysis presented in this paper can provide causal retrofit but keeps regular operation. and solid proof for green retrofit decisions. 3)Payoffs:The payoffs of owners and occupiers depend on their Game theory was established to identify the optimal solutions respective strategies,which are shown in the payoff matrix in for economic behaviors (Von Neumann and Morgenstern.1945). Fig.3.Bow11.Bow12.Bow21 and Bow22 represent the benefits of an Nash (1950)developed a definition of an "optimum"strategy for owner under different strategies, whereas multiplayer games.This strategy,which is well-known as the "Nash Boc11.Boc12.Boc21.and Boc22 represent the benefits of an occupier. Equilibrium",indicates that every player cannot obtain a benefit by changing his or her own action:thus,the equilibrium is stable (Healy.2006).Nash equilibrium,which is a type of game theory,is 4.Retrofit decision for owner-occupied building generally used to analyze the competition or collaboration prob- lems between two decision makers,such as the prisoner's dilemma The owner-occupied building is first discussed,because it is the (Fudenberg and Tirole,1991).Three basic elements exist in game simplest occupancy type and can be used as a baseline.In this type theory (ie.,player,strategy,and payoff).A player,who assumes of building,the occupiers also own the building,and they can make absolutely rational self-interest,is an individual participant in the retrofit decisions by themselves without negotiation.The income of decision-making of strategic choices.Strategy is the choice or ac- the owners comes from the energy cost saving.maintenance cost tion of a player,that can either be a pure or mixed strategy in saving.building value increase,and public impact.The costs are the certain probabilities.Payoff is the interest that a player accrues by retrofit investment and operation disturbance.The rent,occupancy adopting a strategy (Peng et al.,2014).Payoffs,which are quanti- rate,and turnover rate are not considered in this owner-occupied tative,are normally described by a payoff matrix to illustrate the situation.These variables are described in Table 3.The column of interest of a player based on all decisions. "Driver/Barrier"shows the corresponding relation between the Game theory is widely used in research related to sustainable variables and the drivers or barriers illustrated in Tables 1 and 2 development and green building,particularly with regard to the This study assumes that the decision to retrofit depends on the relationship among the stakeholders and their decision making.Gu benefits that the decision makers can reap from retrofit.Therefore, et al.(2009)analyzed the strategies for energy-efficient housing non-economic factors,such as the lack of building information developments with game theory by integrating four players. (Bow6)and lack of retrofit experience(Bow7).are not considered in namely,the administration,the developers,the architects,and the this analysis.The subsidies and tax reduction (Dow3)are not inhabitants.The study identified several crucial issues in energy- included in the variables,because the model focuses on the retrofit efficient building development and indicated that achieving the decisions without market interventions.In fact,the Chinese gov- energy efficiency objective is difficult if the actions of all the players ernment only provides incentive funds for the energy-efficiency are based on their respective rational self-interest(Gu et al.,2009). retrofit of the residential buildings in the northern heating area However,this conclusion is relatively general and is not based on a of China(Zhou et al.,2010)and of the public buildings in a few pilot concrete analysis of relationships and interests.Some studies have cities.Most areas are not funded by government,a condition that is specified and quantified the interest of the players in games (Li consistent with this model.The risks of retrofits(Dow5/Bow6)are et al 2011:Mohsenian-Rad et al..2010).Li et al.(2011)proposed likewise not considered in this analysis,which are discussed in a game theory model to analyze the energy-saving building market Section 7.3. in China through a game of customers and developers,whose in- Bocan then be calculated with the following formula,where terests were calculated quantitatively.Game theory has also been the superscript "oo"represents the owner-occupied condition: used to evaluate and simulate energy consumption (Mohsenian- B80=S8°+S8°+AVo0+Ap0-10-D0 (1) Rad et al.,2010:Soliman and Leon-Garcia,2014).However,the existing studies based on game theory are primarily for new energy All variables represent the life cycle value,which is an efficient efficiency building rather than for green retrofit.To elaborate the method in conducting an economic analysis of the building retrofit use of game theory in this study,the research problem definition issues (Ouyang et al,2011).Various factors may influence the de- are presented in the following sub-section. cision making of retrofit in different levels.The factors related to the direct economical profit.such as Doo and seo,may be 3.3.Problem definition considered as the high priority;otherwise,they are regarded as the relatively low priority (e.g..AP0).The difference among these The problem of developing a strategy on green retrofit is defined factors depends on specific projects and on the evaluation of the as a non-cooperative game between the owners and occupiers of owners.When Bo>0 in this owner-occupied scenario,the owners the existing buildings.The critical elements for the game analysis can benefit from the green retrofit and will choose it as the strategy. are specified below. Otherwise,the green retrofit will not be implemented.The buildingthat many owners and occupiers intend to implement green retrofit, but only a few can reach a consensus and continue its implementation. Although other methods can be used to identify the reasons behind the actions, game theory focuses on players' different actions influenced by the actions of other players. In the beginning of green retrofit, owners and occupiers, as key decision makers, are interdependent and have different interests on the issue. For example, when the owners intend to administer green retrofit to improve their social reputation or to reduce maintenance cost, they have to consider the rent contracts with occupiers. On the contrary, when the occupiers want to implement green retrofit to save energy cost, they have to consider the attitudes of the owners. Thus, the final green retrofit decision depends on the actions of both the owners and occupiers. In this case, game theory can be adopted to analyze the strategies of both parties. The results of the game theory analysis presented in this paper can provide causal and solid proof for green retrofit decisions. Game theory was established to identify the optimal solutions for economic behaviors (Von Neumann and Morgenstern, 1945). Nash (1950) developed a definition of an “optimum” strategy for multiplayer games. This strategy, which is well-known as the “Nash Equilibrium”, indicates that every player cannot obtain a benefit by changing his or her own action; thus, the equilibrium is stable (Healy, 2006). Nash equilibrium, which is a type of game theory, is generally used to analyze the competition or collaboration prob￾lems between two decision makers, such as the prisoner's dilemma (Fudenberg and Tirole, 1991). Three basic elements exist in game theory (i.e., player, strategy, and payoff). A player, who assumes absolutely rational self-interest, is an individual participant in the decision-making of strategic choices. Strategy is the choice or ac￾tion of a player, that can either be a pure or mixed strategy in certain probabilities. Payoff is the interest that a player accrues by adopting a strategy (Peng et al., 2014). Payoffs, which are quanti￾tative, are normally described by a payoff matrix to illustrate the interest of a player based on all decisions. Game theory is widely used in research related to sustainable development and green building, particularly with regard to the relationship among the stakeholders and their decision making. Gu et al. (2009) analyzed the strategies for energy-efficient housing developments with game theory by integrating four players, namely, the administration, the developers, the architects, and the inhabitants. The study identified several crucial issues in energy￾efficient building development and indicated that achieving the energy efficiency objective is difficult if the actions of all the players are based on their respective rational self-interest (Gu et al., 2009). However, this conclusion is relatively general and is not based on a concrete analysis of relationships and interests. Some studies have specified and quantified the interest of the players in games (Li et al., 2011; Mohsenian-Rad et al., 2010). Li et al. (2011) proposed a game theory model to analyze the energy-saving building market in China through a game of customers and developers, whose in￾terests were calculated quantitatively. Game theory has also been used to evaluate and simulate energy consumption (Mohsenian￾Rad et al., 2010; Soliman and Leon-Garcia, 2014). However, the existing studies based on game theory are primarily for new energy efficiency building rather than for green retrofit. To elaborate the use of game theory in this study, the research problem definition are presented in the following sub-section. 3.3. Problem definition The problem of developing a strategy on green retrofit is defined as a non-cooperative game between the owners and occupiers of the existing buildings. The critical elements for the game analysis are specified below. 1) Players: Two players are involved in the game, namely, the owner and the occupier, as elaborated in Section 2.1. 2) Strategies: In general, the owner is the entity who establishes the initiative to retrofit and provides the initial retrofit plans. However, the occupiers have become increasingly active in green retrofit projects in recent years. Given that numerous buildings have been retrofitted over the past few years, the successful experiences have attracted the occupiers because of the learning effect. In 2015, 81 occupiers actively raised 16 million CNY to finish the green retrofit project in the Interna￾tional Trade Center of Shenzhen, China (Xiao, 2015). Therefore, both the owner and occupier in this game have two strategies, namely, “initiative to retrofit” and “reluctant to retrofit.” The former strategy is initiative to conduct green retrofit, whereas the latter is the resistance to the implementation of green retrofit but keeps regular operation. 3) Payoffs: The payoffs of owners and occupiers depend on their respective strategies, which are shown in the payoff matrix in Fig. 3. Bow11, Bow12, Bow21 and Bow22 represent the benefits of an owner under different strategies, whereas Boc11, Boc12, Boc21, and Boc22 represent the benefits of an occupier. 4. Retrofit decision for owner-occupied building The owner-occupied building is first discussed, because it is the simplest occupancy type and can be used as a baseline. In this type of building, the occupiers also own the building, and they can make retrofit decisions by themselves without negotiation. The income of the owners comes from the energy cost saving, maintenance cost saving, building value increase, and public impact. The costs are the retrofit investment and operation disturbance. The rent, occupancy rate, and turnover rate are not considered in this owner-occupied situation. These variables are described in Table 3. The column of “Driver/Barrier” shows the corresponding relation between the variables and the drivers or barriers illustrated in Tables 1 and 2 This study assumes that the decision to retrofit depends on the benefits that the decision makers can reap from retrofit. Therefore, non-economic factors, such as the lack of building information (BOW6) and lack of retrofit experience (BOW7), are not considered in this analysis. The subsidies and tax reduction (DOW3) are not included in the variables, because the model focuses on the retrofit decisions without market interventions. In fact, the Chinese gov￾ernment only provides incentive funds for the energy-efficiency retrofit of the residential buildings in the northern heating area of China (Zhou et al., 2010) and of the public buildings in a few pilot cities. Most areas are not funded by government, a condition that is consistent with this model. The risks of retrofits (DOW5/BOW6) are likewise not considered in this analysis, which are discussed in Section 7.3. Boo ow can then be calculated with the following formula, where the superscript “oo” represents the owner-occupied condition: Boo ow ¼ Soo e þ Soo o þ DVoo þ DPoo I oo Doo (1) All variables represent the life cycle value, which is an efficient method in conducting an economic analysis of the building retrofit issues (Ouyang et al., 2011). Various factors may influence the de￾cision making of retrofit in different levels. The factors related to the direct economical profit, such as I oo, Doo and Soo e , may be considered as the high priority; otherwise, they are regarded as the relatively low priority (e.g., DPoo). The difference among these factors depends on specific projects and on the evaluation of the owners. When Boo ow >0 in this owner-occupied scenario, the owners can benefit from the green retrofit and will choose it as the strategy. Otherwise, the green retrofit will not be implemented. The building X. Liang et al. / Journal of Cleaner Production 137 (2016) 1300e1312 1305