American Institute of Mathematical Sciences

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October  2014, 1(4): 579-598. doi: 10.3934/jdg.2014.1.579

Investment under uncertainty, competition and regulation

Adrien Nguyen Huu 1,

1. 

IMPA, Estrada Dona Castorina, 110, Rio De Janeiro, 22460-320, Brazil

Received  September 2013 Revised  February 2014 Published  November 2014

We investigate a randomization procedure undertaken in real option games which can serve as a basic model of regulation in a duopoly model of preemptive investment. We recall the rigorous framework of M. Grasselli, V. Leclère and M. Ludkovsky (Priority Option: the value of being a leader, International Journal of Theoretical and Applied Finance, 16, 2013), and extend it to a random regulator. This model generalizes and unifies the different competitive frameworks proposed in the literature, and creates a new one similar to a Stackelberg leadership. We fully characterize strategic interactions in the several situations following from the parametrization of the regulator. Finally, we study the effect of the coordination game and uncertainty of outcome when agents are risk-averse, providing new intuitions for the standard case.
Keywords: investment, regulation, Cournot competition., Stackelberg competition, preemption game, Real option game.
Mathematics Subject Classification: Primary: 91B06, 91A55; Secondary: 91A8.
Citation: Adrien Nguyen Huu. Investment under uncertainty, competition and regulation. Journal of Dynamics & Games, 2014, 1 (4) : 579-598. doi: 10.3934/jdg.2014.1.579
References:
[1]

A. F. Azevedo and D. A. Paxson, Real options game models: A review, Real Options 2010, 2010. Google Scholar

[2]

F. Black and M. Scholes, The pricing of options and corporate liabilities, The journal of political economy, 81 (1973), 637-654. doi: 10.1086/260062.  Google Scholar

[3]

A. Bensoussan, J. D. Diltz and S. Hoe, Real options games in complete and incomplete markets with several decision makers, SIAM Journal on Financial Mathematics, 1 (2010), 666-728. doi: 10.1137/090768060.  Google Scholar

[4]

D. Becherer, Rational hedging and valuation of integrated risks under constant absolute risk aversion, Insurance: Mathematics and economics, 33 (2003), 1-28. doi: 10.1016/S0167-6687(03)00140-9.  Google Scholar

[5]

B. Chevalier-Roignant, C. M. Flath, A. Huchzermeier and L. Trigeorgis, Strategic investment under uncertainty: A synthesis, European Journal of Operational Research, 215 (2011), 639-650. doi: 10.1016/j.ejor.2011.05.038.  Google Scholar

[6]

D. Fudenberg and J. Tirole, Preemption and rent equalization in the adoption of new technology, The Review of Economic Studies, 52 (1985), 383-401. doi: 10.2307/2297660.  Google Scholar

[7]

M. Grasselli, V. Leclere and M. Ludkovski, Priority Option: The Value of Being a Leader, International Journal of Theoretical and Applied Finance, 16 (2013), 1350004, 37pp. doi: 10.1142/S0219024913500040.  Google Scholar

[8]

S. R. Grenadier, The strategic exercise of options: Development cascades and overbuilding in real estate markets, The Journal of Finance, 51 (1996), 1653-1679. doi: 10.2307/2329533.  Google Scholar

[9]

S. R. Grenadier, Option exercise games: The intersection of real options and game theory, Journal of Applied Corporate Finance, 13 (2000), 99-107. doi: 10.1111/j.1745-6622.2000.tb00057.x.  Google Scholar

[10]

C.-f. Huang and L. Lode, Entry and exit: Subgame perfect equilibria in continuous-time stopping games, working paper, 1991. Google Scholar

[11]

D. Paxson and H. Pinto, Rivalry under price and quantity uncertainty, Review of Financial Economics, 14 (2005), 209-224. doi: 10.1016/j.rfe.2005.04.002.  Google Scholar

[12]

F. Smets, Essays on Foreign Direct Investment, Ph.D. Thesis, Yale University, 1993. Google Scholar

[13]

A. Tsekrekos, The effect of first-mover's advantages on the strategic exercise of real option, in Real R&D Options (eds. D. Paxson), Butterworth-Heinemann, (2003), 185-207. doi: 10.1016/B978-075065332-9.50011-2.  Google Scholar

[14]

J. J. Thijssen, Preemption in a real option game with a first mover advantage and player-specific uncertainty, Journal of Economic Theory, 145 (2010), 2448-2462. doi: 10.1016/j.jet.2010.10.002.  Google Scholar

[15]

J. J. Thijssen, K. J. Huisman and P. M. Kort, Symmetric equilibrium strategies in game theoretic real option models, Journal of Mathematical Economics, 48 (2012), 219-225. doi: 10.1016/j.jmateco.2012.05.004.  Google Scholar

[16]

H. Weeds, Strategic delay in a real options model of R&D competition, The Review of Economic Studies, 69 (2002), 729-747. doi: 10.1111/1467-937X.t01-1-00029.  Google Scholar

show all references

References:
[1]

A. F. Azevedo and D. A. Paxson, Real options game models: A review, Real Options 2010, 2010. Google Scholar

[2]

F. Black and M. Scholes, The pricing of options and corporate liabilities, The journal of political economy, 81 (1973), 637-654. doi: 10.1086/260062.  Google Scholar

[3]

A. Bensoussan, J. D. Diltz and S. Hoe, Real options games in complete and incomplete markets with several decision makers, SIAM Journal on Financial Mathematics, 1 (2010), 666-728. doi: 10.1137/090768060.  Google Scholar

[4]

D. Becherer, Rational hedging and valuation of integrated risks under constant absolute risk aversion, Insurance: Mathematics and economics, 33 (2003), 1-28. doi: 10.1016/S0167-6687(03)00140-9.  Google Scholar

[5]

B. Chevalier-Roignant, C. M. Flath, A. Huchzermeier and L. Trigeorgis, Strategic investment under uncertainty: A synthesis, European Journal of Operational Research, 215 (2011), 639-650. doi: 10.1016/j.ejor.2011.05.038.  Google Scholar

[6]

D. Fudenberg and J. Tirole, Preemption and rent equalization in the adoption of new technology, The Review of Economic Studies, 52 (1985), 383-401. doi: 10.2307/2297660.  Google Scholar

[7]

M. Grasselli, V. Leclere and M. Ludkovski, Priority Option: The Value of Being a Leader, International Journal of Theoretical and Applied Finance, 16 (2013), 1350004, 37pp. doi: 10.1142/S0219024913500040.  Google Scholar

[8]

S. R. Grenadier, The strategic exercise of options: Development cascades and overbuilding in real estate markets, The Journal of Finance, 51 (1996), 1653-1679. doi: 10.2307/2329533.  Google Scholar

[9]

S. R. Grenadier, Option exercise games: The intersection of real options and game theory, Journal of Applied Corporate Finance, 13 (2000), 99-107. doi: 10.1111/j.1745-6622.2000.tb00057.x.  Google Scholar

[10]

C.-f. Huang and L. Lode, Entry and exit: Subgame perfect equilibria in continuous-time stopping games, working paper, 1991. Google Scholar

[11]

D. Paxson and H. Pinto, Rivalry under price and quantity uncertainty, Review of Financial Economics, 14 (2005), 209-224. doi: 10.1016/j.rfe.2005.04.002.  Google Scholar

[12]

F. Smets, Essays on Foreign Direct Investment, Ph.D. Thesis, Yale University, 1993. Google Scholar

[13]

A. Tsekrekos, The effect of first-mover's advantages on the strategic exercise of real option, in Real R&D Options (eds. D. Paxson), Butterworth-Heinemann, (2003), 185-207. doi: 10.1016/B978-075065332-9.50011-2.  Google Scholar

[14]

J. J. Thijssen, Preemption in a real option game with a first mover advantage and player-specific uncertainty, Journal of Economic Theory, 145 (2010), 2448-2462. doi: 10.1016/j.jet.2010.10.002.  Google Scholar

[15]

J. J. Thijssen, K. J. Huisman and P. M. Kort, Symmetric equilibrium strategies in game theoretic real option models, Journal of Mathematical Economics, 48 (2012), 219-225. doi: 10.1016/j.jmateco.2012.05.004.  Google Scholar

[16]

H. Weeds, Strategic delay in a real options model of R&D competition, The Review of Economic Studies, 69 (2002), 729-747. doi: 10.1111/1467-937X.t01-1-00029.  Google Scholar

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