Real options and game theoretical approaches to real estate development projects: multiple equilibria and the implications of different tie-breaking rules

This paper contributes to a fast growing literature which introduces game theory in the analysis of real option investments in a competitive setting. Specifically, in this paper we focus on the issue of multiple equilibria and on the implications that different equilibrium selections may have for the pricing of real options and for subsequent strategic decisions. We present some theoretical results of the necessary conditions to have multiple equilibria and we show under which conditions different tie-breaking rules result in different economic decisions. We then present a numerical exercise using the in formation set obtained on a real estate development in South London. We find that risk aversion reduces option value and this reduction decreases marginally as negative externalities decrease.

Strategy-proof tie-breaking

We study a general class of priority-based allocation problems with weak priority orders and identify conditions under which there exists a strategy-proof mechanism which always chooses an agent-optimal stable, or constrained efficient, matching. A priority structure for which these two requirements are compatible is called solvable. For the general class of priority-based allocation problems with weak priority orders,we introduce three simple necessary conditions on the priority structure. We show that these conditions completely characterize solvable environments within the class of indifferences at the bottom (IB) environments, where ties occur only at the bottom of the priority structure. This generalizes and unifies previously known results on solvable and unsolvable environments established in school choice, housing markets and house allocation with existing tenants. We show how the previously known solvable cases can be viewed as extreme cases of solvable environments. For sufficiency of our conditions we introduce a version of the agent-proposing deferred acceptance algorithm with exogenous and preference-based tie-breaking.

Top trading with fixed tie-breaking in markets with indivisible goods

We study markets with indivisible goods where monetary compensations are not possible. Each individual is endowed with an object and a preference relation over all objects. When preferences are strict, Gale's top trading cycle algorithm finds the unique core allocation. When preferences are not necessarily strict, we use an exogenous profile of tie-breakers to resolve any ties in individuals' preferences and apply Gale's top trading cycle algorithm for the resulting profile of strict preferences. We provide a foundation of these simple extensions of Gale's top trading cycle algorithm from strict preferences to weak preferences. We show that Gale's top trading cycle algorithm with fixed tie-breaking is characterized by individual rationality, strategy-proofness, weak efficiency, non-bossiness, and consistency. Our result supports the common practice in applications to break ties in weak preferences using some fixed exogenous criteria and then to use a 'good and simple' rule for the resulting strict preferences. This reinforces the market-based approach even in the presence of indifferences because always competitive allocations are chosen.

Strategy-proofness makes the difference: deferred-acceptance with responsive priorities

In college admissions and student placements at public schools, the admission decision can be thought of as assigning indivisible objects with capacity constraints to a set of students such that each student receives at most one object and monetary compensations are not allowed. In these important market design problems, the agent-proposing deferred-acceptance (DA-)mechanism with responsive strict priorities performs well and economists have successfully implemented DA-mechanisms or slight variants thereof. We show that almost all real-life mechanisms used in such environments - including the large classes of priority mechanisms and linear programming mechanisms - satisfy a set of simple and intuitive properties. Once we add strategy-proofness to these properties, DA-mechanisms are the only ones surviving. In market design problems that are based on weak priorities (like school choice), generally multiple tie-breaking (MTB)procedures are used and then a mechanism is implemented with the obtained strict priorities. By adding stability with respect to the weak priorities, we establish the first normative foundation for MTB-DA-mechanisms that are used in NYC.

The mitochondrial targeting function of randomly generated peptide sequences correlates with predicted helical amphiphilicity.

A pool of oligonucleotides encoding a start methionine and nine random amino acids was inserted at the 5'-end of the gene for the yeast cytochrome oxidase subunit IV lacking its own mitochondrial targeting sequence. Approximately one-quarter of the randomly generated sequences targeted subunit IV to its correct intramitochondrial location in vivo. Sequence analysis of 89 randomly generated sequences showed that their efficiencies as mitochondrial targeting signals correlated with the potential to fold into an amphiphilic alpha-helix. Functional targeting sequences were enriched in arginine and isoleucine residues but contained few aspartate, glutamate, and proline residues. Nonfunctional sequences predicted to have significant helical amphiphilicity often had at least one acidic or multiple helix-breaking residues that would be expected to interfere with targeting functioning. These results support the hypothesis that the signal for targeting a protein into the mitochondrial matrix is usually a positively charged amphiphilic helix.

Arrow's Theorem in Spatial Environments

In spatial environments, we consider social welfare functions satisfying Arrow's requirements. i.e., weak Pareto and independence of irrelevant alternatives. When the policy space os a one-dimensional continuum, such a welfare function is determined by a collection of 2n strictly quasi-concave preferences and a tie-breaking rule. As a corrollary, we obtain that when the number of voters is odd, simple majority voting is transitive if and only if each voter's preference is strictly quasi-concave. When the policy space is multi-dimensional, we establish Arrow's impossibility theorem. Among others, we show that weak Pareto, independence of irrelevant alternatives, and non-dictatorship are inconsistent if the set of alternatives has a non-empty interior and it is compact and convex.

Respecting Priorities when Assigning Students to Schools

We consider the problem of assigning students to schools on the basis of priorities. Students are allowed to have equal priority at a school. We characterize the efficient rules which weakly/strongly respect students’ priorities. When priority orderings are not strict, it is not possible to simply break ties in a fixed manner. All possibilities of resolving the indifferences need to be considered. Neither the deferred acceptance algorithm nor the top trading cycle algorithm successfully solve the problem of efficiently assigning the students to schools whereas a modified version of the deferred acceptance algorithm might. In this version tie breaking depends on students’ preferences.

Pure strategy equilibria of multidimensional and non-monotonic auctions

We give necessary and sufficient conditions for the existence of symmetric equilibrium without ties in interdependent values auctions, with multidimensional independent types and no monotonic assumptions. In this case, non-monotonic equilibria might happen. When the necessary and sufficient conditions are not satisfied, there are ties with positive probability. In such case, we are still able to prove the existence of pure strategy equilibrium with an all-pay auction tie-breaking rule. As a direct implication of these results, we obtain a generalization of the Revenue Equivalence Theorem. From the robustness of equilibrium existence for all-pay auctions in multidimensional setting, an interpretation of our results can give a new justification to the use of tournaments in practice.

Non-manipulable domains for the Borda count

We characterize the preference domains on which the Borda count satises Arrow's "independence of irrelevant alternatives" condition. Under a weak richness condition, these domains are obtained by xing one preference ordering and including all its cyclic permutations ("Condorcet cycles"). We then ask on which domains the Borda count is non-manipulable. It turns out that it is non-manipulable on a broader class of domains when combined with appropriately chosen tie-breaking rules. On the other hand, we also prove that the rich domains on which the Borda count is non-manipulable for all possible tie-breaking rules are again the cyclic permutation domains.

Nash implementable domains for the Borda count

We characterize the preference domains on which the Borda count satisfies Maskin monotonicity. The basic concept is the notion of a "cyclic permutation domain" which arises by fixing one particular ordering of alternatives and including all its cyclic permutations. The cyclic permutation domains are exactly the maximal domains on which the Borda count is strategy-proof when combined with every possible tie breaking rule. It turns out that the Borda count is monotonic on a larger class of domains. We show that the maximal domains on which the Borda count satisfies Maskin monotonicity are the "cyclically nested permutation domains" which are obtained from the cyclic permutation domains in an appropriately specified recursive way. ------ *We thank József Mala for posing the question of Nash implementability on restricted domains that led to this research. We are very grateful to two anonymous referees and an associate editor for their helpful comments and suggestions. The second author gratefully acknowledges financial support from the Hungarian Academy of Sciences (MTA) through the Bolyai János research fellowship.

Spatial and temporal changes in multiple hormone groups during lateral bud release shortly following apex decapitation of chickpea (Cicer arietinum) seedlings

Although the co-ordination of promotive root-sourced cytokinin (CK) and inhibitory shoot apex-sourced auxin (IAA) is central to all current models on lateral bud dormancy release, control by those hormones alone has appeared inadequate in many studies. Thus it was hypothesized that the IAA : CK model is the central control but that it must be considered within the relevant timeframe leading to lateral bud release and against a backdrop of interactions with other hormone groups. Therefore, IAA and a wide survey of cytokinins (CKs), were examined along with abscisic acid (ABA) and polyamines (PAs) in released buds, tissue surrounding buds and xylem sap at 1 and 4 h after apex removal, when lateral buds of chickpea are known to break dormancy. Three potential lateral bud growth inhibitors, IAA, ABA and cis-zeatin 9-riboside (ZR), declined sharply in the released buds and xylem following decapitation. This is in contrast to potential dormancy breaking CKs like trans-ZR and trans-zeantin 9-riboside 5'phosphate (ZRMP), which represented the strongest correlative changes by increasing 3.5-fold in xylem sap and 22-fold in buds. PAs had not changed significantly in buds or other tissues after 4 h, so they were not directly involved in the breaking of bud dormancy. Results from the xylem and surrounding tissues indicated that bud CK increases resulted from a combination synthesis in the bud and selective loading of CK nucleotides into the xylem from the root.

Monitoring multiple angiogenesis-related molecules in the blood of cancer patients shows a correlation between VEGF-A and MMP-9 levels before treatment and divergent changes after surgical vs. conservative therapy.

Anti-angiogenic therapies are currently in cancer clinical trials, but to date there are no established tests for evaluating the angiogenic status of a patient. We measured 11 circulating angiogenesis-associated molecules in cancer patients before and after local treatment. The purpose of our study was to screen for possible relationships among the different molecules and between individual molecules and tumor burden. We measured VEGF-A, PlGF, SCF, MMP-9, EDB+ -fibronectin, sVEGFR-2, sVEGFR-1, salphaVbeta3, sTie-2, IL-8 and CRP in the blood of 22 healthy volunteers, 17 early breast, 17 early colorectal, and 8 advanced sarcoma/melanoma cancer patients. Breast cancer patients had elevated levels of VEGF-A and sTie-2, colorectal cancer patients of VEGF-A, MMP-9, sTie-2, IL-8 and CRP, and melanoma/sarcoma patients of sVEGFR-1. salphaVbeta3 was decreased in colorectal cancer patients. A correlation between VEGF-A and MMP-9 was found. After tumor removal, MMP-9 and salphaVbeta3 significantly decreased in breast and CRP in colorectal cancer, whereas sVEGFR-1 increased in colorectal cancer patients. In sarcoma/melanoma patients treated regionally with TNF and chemotherapy we observed a rise in VEGF-A, SCF, VEGFR-2, MMP-9, Tie-2 and CRP, a correlation between CRP and IL-8, and a decreased in sVEGFR-1 levels. In conclusion, among all factors measured, only VEGF-A and MMP-9 consistently correlated to each other, elevated CRP levels were associated with tumor burden, whereas sVEGF-R1 increased after tumor removal in colorectal cancer. Treatment with chemotherapy and TNF induced changes consistent with an angiogenic switch. These results warrant a prospective study to compare the effect of surgical tumor removal vs. chemotherapy on some of these markers and to evaluate their prognostic/predictive value.

Breaking the panels: an application to the GDP per capita

This paper proposes a test statistic for the null hypothesis of panel stationarity that allows for the presence of multiple structural breaks. Two different speci¿cations are considered depending on the structural breaks affecting the individual effects and/or the time trend. The model is ¿exible enough to allow the number of breaks and their position to differ across individuals. The test is shown to have an exact limit distribution with a good ¿nite sample performance. Its application to a typical panel data set of real per capita GDP gives support to the trend stationarity of these series

Breaking the panels: an application to the GDP per capita

This paper proposes a test statistic for the null hypothesis of panel stationarity that allows for the presence of multiple structural breaks. Two different speci¿cations are considered depending on the structural breaks affecting the individual effects and/or the time trend. The model is ¿exible enough to allow the number of breaks and their position to differ across individuals. The test is shown to have an exact limit distribution with a good ¿nite sample performance. Its application to a typical panel data set of real per capita GDP gives support to the trend stationarity of these series