Do urban redevelopment incentives promote asset deterioration? A game-theoretic approach

Abstract

The elapsed time between a government’s announcement of its intention to redevelop and the launch of the new construction may often be quite lengthy. This study uses a game-theoretic framework to examine the effect of the option to redevelop on the quality of the existing housing stock during this extended pre-redevelopment period. We show that the benefits that accompany future redevelopment may lead to accelerated deterioration in the pre-redevelopment period. Moreover, we identify circumstances under which there exists a unique perfect Nash equilibrium where, in order to discourage objections by other homeowners, those who support redevelopment intentionally promote structural deterioration during the pre-redevelopment period. Our results highlight the need to shorten the period of time between the announcement of the option to redevelop and its implementation.

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Fig. 1
Fig. 2

Notes

  1. 1.

    It should be noted that while in some countries (including the U.S., Singapore, China, and Hong Kong) redevelopment programs commonly involve the collective sale of homeowner rights to the developer, in others (for example, Israel and Korea) the owners commonly maintain their ownership, and the additional allowable floor area/housing units are used as a financing tool for incentivizing the redevelopment. .

  2. 2.

    In cases of programs that require the developers’ acquisition of the majority of properties, multi-ownership further complicates the issue of land assembly and the multi-party bargaining problem. Strange (1995) and Eckart (1985) model the assembly of land from multiple landowners as a game among rational agents, and find that owners of smaller parcels of land demand a greater price per acre. Fu, McMillen, and Somerville (2002) offer empirical evidence of premiums extracted by owners of smaller properties. There is an expectation that the negotiation process that follows the announcement of a redevelopment program will delay the implementation of the redevelopment.

  3. 3.

    Note that legislative initiatives indicate that owners often impose barriers to redevelopment. Examples include Singapore’s Land Title Act of 4 May 1999, which abandoned the statutory requirement to obtain unanimous consent from owners, and replaced it with an 80–90% threshold (depending on the age of the structure) in order to minimize delay in the collective sales process (see Sing and Lim 2004); and recent legislation in Israel that allows owners, in some cases, to file a claim for damages against property owners opposing the implementation of redevelopment (see http://www.moch.gov.il/English/regeneration_and_renewal/urban_renewal/Pages/opposing_property_owners.aspx, last accessed Jan. 2019). Also, the share of supporting homeowners required in order to authorize redevelopment in Israel (either 67% or 80%) depends on the type of the project.

  4. 4.

    According to Carmon (1999), redevelopment phases may extend over more than a decade; Geva and Rosen (2018) discuss the risk of extended and/or failed negotiations among owners and developers in the context of “Raze and Rebuild” projects; further, Shin and Kim (2015) and Fassmann and Hatz (2006) report low levels of implementation of redevelopment programs; Adair et al. (2007) provide interview-based evidence indicating that investment fund managers expect a minimum of 20 years from the time of initiation of a regeneration project to its completion; finally, August (2016) provides various explanations for the limited tenant resistance to mixed-income social housing redevelopment, yet reports on a implementation phase that lasts 15–20 years.

  5. 5.

    The notion of “Nash Equilibrium” captures a steady state of play of a strategic game in which each player holds the correct expectation about the other players’ behavior and acts rationally. In other words, no player can profitably deviate, given the actions of the other players. For the equilibrium to qualify for a perfect Nash equilibrium (or a subgame perfect equilibrium), each player must therefore pursue her optimal actions and, as a result, “incredible threats”—in which a player’s strategy negatively affects not only another player’s payoff but her own as well—are eliminated [see, e.g., Osborne and Rubinstein (1994)].

  6. 6.

    In this context, see also Amirtahmasebi et al. (2016); Hui et al. (2008); Gordon (2003); Carmon (1999); and Alterman (1995). Amirtahmasebi et al. (2016), for example, argue that the prevalence of poor quality and underutilized urban areas weaken the city’s image, livability, and productivity.

  7. 7.

    Fu et al. (2002) offer further empirical evidence of premiums extracted by small landlords. The negotiation process that follows the announcement of a redevelopment program may be another source of delay in the implementation of the project.

  8. 8.

    For example, according to Kiefer (1980), deterioration can lead to more frequent moves, which may come with both economic costs to households and social costs to communities.

  9. 9.

    Pavlov and Blazenko (2005) use a similar representation of neighborhood effect.

  10. 10.

    That the cost of maintenance may vary from individual to individual follows from, for example, different skills or the ability to undertake construction activities themselves (see Reschovsky 1992). It may also follow from heterogeneity in budget constraints and subjective non-monetary costs associated with upkeep activity (such as noise, dust, and risk aversion). Finally, the cost of redevelopment may vary by tenure mode and homeowner age (for detailed discussion see, respectively, Geva and Rosen 2018; and Chui 2001).

  11. 11.

    For ease of presentation, the choices made at each period by Owner 1 and Owner 2 are represented as sequential rather than simultaneous. However, it should be noted, in that regard, that an analysis of a similar model, though one in which each period’s choices are made simultaneously, or the order is reversed between the players, yields similar results. Also, in a parallel setting, Varian (1994) shows that in the case of contribution to a public good (rather than the externality case under our setting), a sequential game allows the agent who plays first to exploit his position in the game and shift the burden to the players that follow. Importantly, while we do not suggest that our setting does not allow for an owner to exploit his/her position in the game, our focus is on the externality effect of maintenance rather than free ridership within a public-good context.

  12. 12.

    It is clear that even if investment in maintenance were allowed in the second period, it would have been dominated by the prior choice to do so in the first period; thus the option to invest in maintenance in the second period becomes redundant.

  13. 13.

    Note, however, that this is not to be confused with a “free rider” phenomenon. The rent effect of an investment in maintenance by the homeowner of unit i splits between units i and j such that their total value remains fixed for any level of α. Therefore, when α is relatively low, the homeowner of unit i is less affected by the maintenance and, consequently, less motivated to invest in maintenance.

  14. 14.

    Low positive values of \(Q^{m} - C_{i}^{m}\) are more likely, for example, in lower socio-economic and deteriorated neighborhoods (see, for example, the assumptions underlying theoretical model by Kiefer [1980]).

  15. 15.

    As shown in the proof of Result 6, this strategy of Owner 2 is effective only if the externality effect of an unmaintained unit 2 on the rent of unit 1 is sufficient to change the optimal second period action of Owner 1 from no-redevelopment to redevelopment. Note also that during the first period, the outcome for Owner 2 is negatively affected as well if he chooses to act “strategically,” since he avoids investment in profitable maintenance. Therefore, Owner 2 must be better off giving up rent at the first period in return for redevelopment in the second period.

  16. 16.

    For simplicity, the analysis below assumes risk-neutral homeowners. Nevertheless, as the analysis is parametric, adjustments in the probability values can be made in order to account for risk aversion as long as there are no differences in the attitudes toward risk across owners. In addition, it should be noted that \(p^{l}\), \(p^{ml}\), and \(p^{m}\) are the probabilities as perceived by the owners (rather than actual probabilities).

  17. 17.

    In this case, the excessive private investment in maintenance should be weighed against the social benefits from the externalities that are associated with the expected increased quality in the first period. It can be a mechanism that overcomes a possible “prisoners’ dilemma” situation (say, across different buildings in the neighborhood), where each owner faces an incentive to avoid investment in maintenance, while owners are collectively better off if they all make such investment.

  18. 18.

    Wong et al. (2005), for example, find that while age negatively correlates with building performance, there are older (newer) buildings that perform well (poorly). Consequently, they suggest that policies should replace the building age cutoff criterion with a case-specific examination. In contrast, however, as shown in our analysis, case-specific examination in the framework of redevelopment policies may change the level of maintenance. The advantage of a general criterion (such as age cutoff) is that it is exogenous and cannot be changed by the owners’ actions.

  19. 19.

    In this context, it should be noted that redevelopment-related issues have contributed considerably to the normative debate that pertains to regulators’ intervention in the market. It has been argued that redevelopment projects facilitated through public–private partnerships (PPP), for example, have blurred the line between the regulator as a guardian of the public interest and the private entrepreneur, who serves his own interest (see, e.g., Margalit 2014; Sager 2011). For a related critical view of intervention in the context of urban planning, see, e.g., Webster and Lai (2003) and Pennington (2000).

  20. 20.

    It is important to note that while our model focuses on an externality effect of maintenance investment as a possible tool used by homeowners to achieve redevelopment, for ease of presentation and comprehensiveness, it ignores many related aspects, such as extended and continuous time periods, continuous maintenance choices, homeowner discretion in expediting or delaying the implementation of redevelopment, and potential investment in maintenance by renters rather than owners (see Olsen 1988).

  21. 21.

    \(P_{i}^{k}\) represents the payoff for owner i at terminal node k.

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Acknowledgements

I thank Danny Ben-Shahar, Elad Kravi, Yuval Arbel, Ji Won Lee, the anonymous referees and participants of the 2019 Israel Regional Science meeting and the 59th ERSA Congress for helpful comments. I thank the Alrov Institute for Real Estate Research for the financial support.

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Appendices

Appendix 1: Proofs

Proof of Results 1 and 2

If redevelopment is exogenously imposed on the owners, then regardless of the action of Owner 1 (see nodes <2> and <3> in Fig. 1), if Owner 2 chooses I, his payoff increases by \(\alpha Q^{m} - C_{2}^{m}\). Similarly, if no-redevelopment is exogenously imposed on the owners, then regardless of the action of Owner 1, if Owner 2 chooses I, his payoff increases by \(2\alpha Q^{m} - C_{2}^{m}\). Hence, when redevelopment (no-redevelopment) is exogenously imposed, choosing I is Owner 2’s dominant action if and only if \(C_{2}^{m} < \alpha Q^{m}\) (if and only if \(C_{2}^{m} < 2\alpha Q^{m}\)); otherwise, NI is Owner 2’s dominant strategy. Further, when redevelopment (no-redevelopment) is exogenously imposed, and given that Owner 2 follows his dominant strategy, Owner 1’s payoff increases by \(\alpha Q^{m} - C_{1}^{m}\) (by \(2\alpha Q^{m} - C_{1}^{m}\)) if she chooses I in the first period. Hence, choosing I is Owner 1’s dominant action if and only if \(C_{1}^{m} < \alpha Q^{m}\) (if and only if \(C_{1}^{m} < 2\alpha Q^{m}\)); otherwise, NI is Owner 1’s dominant strategy.□

Proof of Result 3

The condition for investment in maintenance under an exogenously imposed redevelopment (\(C_{i}^{m} < \alpha Q^{m}\); see Result 1) is more restrictive than the condition for investment in maintenance in the absence of a redevelopment option (\(C_{i}^{m} < 2\alpha Q^{m}\); see Result 2).□

Proof of Result 4

The backward induction process, presented in “Appendix 2”, details the optimal choice at each node for any given set of model parameters. Specifically, Tables 1 and 2 detail the conditions under which Owner 1 and Owner 2, respectively, opt for investing in maintenance in the first period. Recall that following Result 1, the condition for owner i’s investment in maintenance when no-redevelopment is exogenously imposed is \(C_{i}^{m} < 2\alpha Q^{m}\). As can be seen, the conditions listed in Tables 1 and 2 are never less, but are sometimes more, restrictive than the condition \(C_{i}^{m} < 2\alpha Q^{m} .\) In other words, any owner who opts for no-investment in maintenance under an imposed no-redevelopment order, opts for no-investment in maintenance if redevelopment is endogenously determined. However, some owners who opt for investment in maintenance under an imposed no-redevelopment order opt for no-investment in maintenance if redevelopment is endogenously determined.□

Proof of Result 5

Let \(Rent_{i}^{1}\) be the first-period rent collected by owner i. Owner i therefore opts for redevelopment (R) if and only if \(Rent_{i}^{1} < Q^{h} - C_{i}^{h}\). Thus, the lower \(Rent_{i}^{1}\), the more likely that owner i opts for R.□

Proof of Result 6

Consider the following conditions: (1) \(Q^{h} - \alpha Q^{m} > C_{1}^{h} > Q^{h} - Q^{m}\); (2) \(C_{2}^{h} < Q^{h} - Q^{m}\); (3) \(C_{1}^{m} < \left( {2\alpha - 1} \right)Q^{m}\); (4) \(C_{2}^{m} < \alpha Q^{m}\); and (5) \(C_{2}^{m} < \left( {\alpha + 1} \right)Q^{m} - Q^{h} + C_{2}^{h}\). Under these conditions, according to the backward induction (see “Appendix 2”), Owner 2 at node <3> (node <2>) chooses between terminal nodes <17> and <18> (<15> and <13>), where \(P_{2}^{17} > P_{2}^{18}\)(\(P_{2}^{15} > P_{2}^{13}\)).Footnote 21 He therefore opts for NI at node <3> (opts for I at node <2>). Accordingly, Owner 1 at node <1> chooses between terminal nodes <17> and <15>, where \(P_{2}^{17} > P_{2}^{15}\). She therefore opts for I at node <1>. Note that in this case \(C_{2}^{m}\) is low enough for maintenance to be profitable for Owner 2, given exogenous implementation (or no implementation) of redevelopment. Yet by opting for NI, he reduces the rent of both units, and redevelopment thus becomes profitable for Owner 1.□

Proof of Result 7

Consider the following conditions: (1) \(Q^{h} - \left( {1 - \alpha } \right)Q^{m} > C_{1}^{h} > Q^{h} - Q^{m}\); (2) \(C_{2}^{h} < Q^{h} - Q^{m}\); (3) \(C_{1}^{m} > \left( {2\alpha - 1} \right)Q^{m}\); (4) \(C_{2}^{m} < \alpha Q^{m}\); and (5) \(C_{2}^{m} > \left( {\alpha + 1} \right)Q^{m} - Q^{h} + C_{2}^{h}\). Under these conditions, according to the backward induction (see “Appendix 2”), Owner 2 at node <3> (node <2>) chooses between terminal nodes <17> and <18> (<15> and <13>), where \(P_{2}^{17} > P_{2}^{18}\)(\(P_{2}^{15} > P_{2}^{13}\)). He therefore opts for NI at node <3> (I at node <2>). Owner 1 at node <1> accordingly chooses between terminal nodes <17> and <15>, where \(P_{2}^{15} > P_{2}^{17}\). She therefore opts for NI at node <1>. Note that in this case \(C_{1}^{m}\) is low enough for maintenance to be profitable for Owner 1, given the implementation of redevelopment. Yet by opting for NI, she assures Owner 2 that she will choose R, which in turn allows him to invest in maintenance.□

Proof of Result 8

Consider the following conditions: (1) both owners have identical parameters such that \(C_{1}^{h} = C_{2}^{h} = C^{h}\) and \(C_{1}^{m} = C_{2}^{m} = C^{m}\); (2) \(C^{m} < \alpha Q^{m}\); (3) \(p^{ml} = p^{m}\); (4) \(\left( {p^{l} - p^{m} } \right) \left( {Q^{h} - C^{h} } \right) > \left( {1 + p^{m} } \right)Q^{m} - C^{m}\). Under these conditions, given the opportunity, both owners opt for redevelopment in the second period. Nevertheless, their likelihood to receive the opportunity decreases if any of them opt for investing in maintenance. According to the backward induction (see “Appendix 2”), Owner 2 at node <2> (node <3>) chooses between nodes <2A> and <2B> (<3A> and <3B>), where the payoff expectancy that follows investment is smaller (is larger) than the payoff expectancy that follows no-investment. He therefore opts for NI at node <2> (I at node <3>). Owner 1 at node <1> accordingly chooses between nodes <3B> and <2A>, where his payoff expectancy that follows investment is smaller than the payoff expectancy that follows no-investment. She therefore opts for NI at node <1>. Note that in this case \(C_{1}^{m}\) and \(C_{2}^{m}\) are low enough for maintenance to be profitable for both owners, given the implementation of redevelopment. Yet they both opt in equilibrium for NI, due to the associated increased likelihood for redevelopment.□

Appendix 2: A backward induction process

Owner 2’s optimal action at nodes <8> through <11>:

  • Node <11>

    Owner 2 opts for R if \(Q^{h} - C_{2}^{h} > Q^{m}\); otherwise he opts for NR

  • Node <10>

    Owner 2 opts for R if \(Q^{h} - C_{2}^{h} > \left( {1 - \alpha } \right)Q^{m}\); otherwise he opts for NR

  • Node <9>

    Owner 2 opts for R if \(Q^{h} - C_{2}^{h} > \alpha Q^{m}\); otherwise he opts for NR

  • Node <8>

    Owner 2 opts for R if \(Q^{h} - C_{2}^{h} > 0\); otherwise he opts for NR

Owner 1’s optimal action at nodes <4> through <7>:

  • Node <7>

    Owner 1 opts for R if \(Q^{h} - C_{1}^{h} > Q^{m}\); otherwise she opts for NR

  • Node <6>

    Owner 1 opts for R if \(Q^{h} - C_{1}^{h} > \alpha Q^{m}\); otherwise she opts for NR

  • Node <5>

    Owner 1 opts for R if \(Q^{h} - C_{1}^{h} > \left( {1 - \alpha } \right)Q^{m}\); otherwise she opts for NR

  • Node <4>

    Owner 1 opts for R if \(Q^{h} - C_{1}^{h} > 0\); otherwise she opts for NR

Owner 2’s optimal action at nodes <2> and <3>:

  • Nodes <2> and <3>

    The backward induction process conducted above for the second period sub-game leads Owner 2 to essentially choose between 2 payoffs as he chooses I and NI at node <3> (node <2>). Table 1 below lists all possible outcome combinations and the conditions under which Owner 2 optimally opts for I. The shaded cells in the table indicate that no set of model parameters can lead Owner 2 to choose between these two alternative payoffs (given the analysis above); the values in gray correspond to the quality-dependent redevelopment incentives policy described in Sect. 4 and in Fig. 2. The table suggests that, given that the strategy of both owners in all the following nodes is R, Owner 2 opts for I at node <3> (<2>) only if \(C_{2}^{m} < \alpha Q^{m}\); if the strategy of at least one owner is NR, regardless of his current choice, Owner 2 opts for I only if \(C^{m} < 2\alpha Q^{m}\). Finally, otherwise (i.e., when implementation of redevelopment depends on his choice), Owner 2 opts for I only if \(C_{2}^{m} < \left( {1 + \alpha } \right)Q^{m} - Q^{h} + C_{2}^{h}\) (only if \(C_{2}^{m} < 2\alpha Q^{m} - Q^{h} + C_{2}^{h}\)).

Table 1 Conditions for Owner 2 to Opt for I given the relevant terminal node couplet

Owner 1’s optimal action at node <1>:

  • Node <1>

    The backward induction process above leads Owner 1 to essentially choose between two payoffs as she chooses I and NI at node <1>. Table 2 below lists all possible outcome combinations, and the conditions under which Owner 1 optimally opts for I. Shaded cells in the table indicate that no set of model parameters can lead Owner 1 to choose between these two alternative payoffs (given the analysis above). Note that all the conditions listed in Table 2 for Owner 1 to opt for I are at least as restrictive as \(2Q^{m} > C_{1}^{m}\). In other words, when \(2Q^{m} < C_{1}^{m}\), Owner 1’s optimal action at node <1> is NI. Results further suggest that there is no (non-negative) value of \(C_{1}^{m}\) under which Owner 1 optimally opts for I without further conditions.

Table 2 Conditions for Owner 1 to Opt for I given the relevant terminal node couplet

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Golan, R. Do urban redevelopment incentives promote asset deterioration? A game-theoretic approach. J Hous and the Built Environ 35, 879–896 (2020). https://doi.org/10.1007/s10901-019-09718-3

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Keywords

  • Redevelopment
  • Housing maintenance
  • Neighborhood effect
  • Incentives
  • Game theory