Skip to main content
Log in

Endogenous formation of security exchanges

Economic Theory Aims and scope Submit manuscript

Cite this article


We use club theory for the first time to provide a model of securities exchange (SX) formation. We think of a SX as a local public good that allows its traders to diversify risk by trading their securities with other SX members. In our two-stage equilibrium setting, traders evaluate SXs depending on their risk-sharing possibilities and, given these evaluations, choose the SX they want to join. Security prices can differ among SXs and traders may value SX memberships differently. We establish continuity properties in both stages and show that equilibrium exists for a generic set of economies.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others


  1. For notational convenience, we use boldface letters to denote a set, except when we refer to a subset of traders, or exchange, here denoted by S.

  2. As stated in the Hong Kong Exchange (HKEx) rules, any trader intending to operate a brokerage business for products available on HKEx, using the trading facilities of the stock exchange and/or futures exchange, must be admitted and registered as an exchange participant of that exchange, and pay the corresponding membership fee. The acquisition of an exchange membership usually involves a commitment for trading in the exchange for a long period of time—usually, the exchange participant stays in the exchange since it enters. See, for example, the MICEX list of participants:

  3. Alternatively, we could assign to each exchange S a subset of assets (in the broad sense) \(\mathbf {J}(S)\subseteq \mathbf {J}\) that traders in exchange S agree to issue for later trading. We leave this possibility for future research.

  4. For simplicity, we do not model trading fees, which have become substantially less important since implementation of the Mifid regulation (see Colliard and Foucault 2012 for a survey of this literature and for an analysis of the effect of trading fees on the efficiency of the markets); nor do we consider transaction fees (e.g., stamp duty). We focus instead on the pure trading aspects of security markets.

  5. See the HKEx security trading infrastructure at

  6. Allouch and Wooders (2008) demonstrate that, given communication costs, for all sufficiently large economies, the core is non-empty and the set of price-taking equilibrium outcomes is equivalent to the core.

  7. In a more sophisticated model with additional benefits of exchange membership (other than risk diversification, e.g., information acquisition or increasing gains from a larger exchange), we should modify the domain of the trader’s utility function as follows: \(u^{i}(x_{0},F[i;\mathbf {I} ],x_{1},x(1),\ldots , x(\Xi )).\) This extension is left for future research.

  8. An example is a set of parameterized Cobb–Douglas utility functions, where the set of parameters is defined in a finite dimensional space.

  9. Observe that AW (2008, pp. 271–272) only requires assumption (f) to be satisfied for a consumption \(x_{0}^{i}\) bounded above by the aggregate endowments plus some \(\varepsilon >0\).

  10. Anecdotal evidence shows that this was a common belief until 2006. See The Economist, March 25, 2006 ( “Liquidity and technology will inevitably make trading a natural monopoly”.

  11. Cole and Prescott (1997), Ellickson et al. (2001), Luque (2013), and Wooders (1980,1997) require bounded club sizes. In contrast, Wooders (1989) and Allouch and Wooders (2008) permit both unbounded club sizes and ever-increasing gains from larger clubs. The main difference between the two cases is the extent to which approximation or coalition formation costs are required to obtain existence of equilibrium. Konishi et al. (1998) allow for an arbitrary number of jurisdictions, but take as given the size of the population, rather than looking at “large” economies. See Luque (2014) for a review of the different approaches to the presence of equilibrium in local public good economies.

  12. AW (2008, Theorem 2) says that: “Given communication costs, for all sufficiently large economies the core is non-empty and the set of \(c(\varepsilon _{0})\)-equilibrium outcomes (similar notion to our Definition 2) is equivalent to the core”.

  13. In Faias and Luque (2015a), we provide an equilibrium existence proof for a general equilibrium economy with exogenous exchange structures, cross-listings, and multiple memberships. It remains an open question as to how to modify club models to allow for an agent’s utility function to depend on the whole structure of clubs.

  14. Notice that the equilibrium correspondence is defined in the finite set of exchange structures; therefore, a continuous measurable selector is not needed. Continuous selectors are in general used to construct continuous objective functions. Thus, they fit only if the correspondence is defined in a continuum set.

  15. Here, q stands for the security price vector in trader i’s exchange.

  16. A set is a continuously differentiable function if all of its elements are continuously differentiable functions.


  • Aliprantis, C.D., Border, K.C.: Infinite Dimensional Analysis, 3rd edn. Springer, Berlin (2006)

    Google Scholar 

  • Allen, B.: Randomization and the limit points of monopolistic competition. J. Math. Econ. 23, 205–218 (1994)

    Article  Google Scholar 

  • Allouch, N., Wooders, M.H.: Price taking equilibrium in economies with multiple memberships in clubs and unbounded club sizes. J. Econ. Theory 140, 246–278 (2008)

    Article  Google Scholar 

  • Balasko, Y., Cass, D., Siconolfi, P.: The structure of financial equilibrium with exogenous yields: the case of restricted participation. J. Math. Econ. 19, 195–216 (1990)

    Article  Google Scholar 

  • Berliant, M., Page, F.: Income taxes and the provision of public goods: existence of an optimum. Econometrica 69, 771–784 (2001)

    Article  Google Scholar 

  • Biais, B.: Price formation and equilibrium liquidity in fragmented and centralized markets. J. Finance 48, 157–185 (1993)

    Article  Google Scholar 

  • Biais, B., Glosten, L., Spatt, C.: Market microstructure: a survey of microfoundations, empirical results, and policy implications. J. Financ. Mark. 8, 217–264 (2005)

    Article  Google Scholar 

  • Bottazzi, J.-M., Luque, J., Pascoa, M.: Securities market theory: possession, repo and rehypothecation. J. Econ. Theory 147, 477–1500 (2012)

    Article  Google Scholar 

  • Cole, H.L., Prescott, E.: Valuation equilibrium with clubs. J. Econ. Theory 74, 19–39 (1997)

    Article  Google Scholar 

  • Colliard, J.-E., Foucault, T.: Trading fees and efficiency in limit order markets. Rev. Financ. Stud. 25, 3389–3421 (2012)

    Article  Google Scholar 

  • Ellickson, B., Grodal, B., Scotchmer, S., Zame, W.: Clubs and the market: large finite economies. J. Econ. Theory 101, 40–77 (2001)

    Article  Google Scholar 

  • Faias, M.: Approximate equilibrium in pure strategies for a two-stage game of asset creation. Decis. Econ. Finance 31, 117–136 (2008)

    Article  Google Scholar 

  • Faias, M., Luque, J.: Risk Sharing Across Exchanges with Cross-Listings. Mimeo (2015a)

  • Faias, M., Luque, J.: Market Transparency and Endogenous Securities Market Fragmentation. Mimeo (2015b)

  • Faias, M., Moreno, E., Páscoa, M.: Real indeterminacy of equilibria and manipulability. J. Math. Econ. 37, 325–340 (2002)

    Article  Google Scholar 

  • Gabszewicz, J., Thisse, J.-F.: Price competition, quality and income disparities. J. Econ. Theory 20, 340–359 (1979)

    Article  Google Scholar 

  • Geanakoplos, J., Polemarchakis, H.: Existence, regularity, and constrained suboptimality of competitive allocations when the asset market is incomplete. Cowles Foundation Working Paper 652 (1986)

  • Grant, J.: Derivatives trading platform bypasses intermediary banks. The Financial Times, January 17 (2011)

  • Hens, T., Pilgrim, B.: General Equilibrium Foundations of Finance: Structure of Incomplete Markets Model. Springer, Berlin (2002)

    Book  Google Scholar 

  • Hojman, D.A., Szeidl, A.: Core and periphery in networks. J. Econ. Theory 139, 295–309 (2008)

    Article  Google Scholar 

  • Konishi, H., Le Breton, M., Weber, S.: Equilibrium in a finite local public goods economy. J. Econ. Theory 79, 224–244 (1998)

    Article  Google Scholar 

  • Lo, A.W., Mamaysky, H., Wang, J.: Asset prices and trading volume under fixed transactions costs. J. Polit. Econ. 112, 1054–1090 (2004)

    Article  Google Scholar 

  • Luque, J.: Heterogeneous Tiebout communities with private production and anonymous crowding. Reg. Sci. Urban Econ. 43, 117–123 (2013)

    Article  Google Scholar 

  • Luque, J.: Wages, local amenities and the rise of the multi-skilled city. Ann. Reg. Sci. 52, 457–467 (2014)

    Article  Google Scholar 

  • Madhavan, A.: Market microstructure. J. Financ. Mark. 3, 205–258 (2000)

    Article  Google Scholar 

  • Mas-Colell, A., Nachbar, J.H.: On the finiteness of the number of critical equilibria, with an application to random selections. J. Math. Econ. 4, 397–409 (1991)

    Article  Google Scholar 

  • Miao, J.: Competitive equilibria of economies with a continuum of consumers and aggregate shocks. J. Econ. Theory 128, 274–298 (2006)

    Article  Google Scholar 

  • Pagano, M.: Trading volume and asset liquidity. Q. J. Econ. 104, 255–274 (1989)

    Article  Google Scholar 

  • Pagnotta, E., Philippon, T.: Competition on Speed. Mimeo, New York (2012)

    Google Scholar 

  • Pancs, R.: Efficient dark markets. Econ. Theory 59, 605–624 (2015)

    Article  Google Scholar 

  • Santos, T., Scheinkman, J.: Competition among exchanges. Q. J. Econ. 116, 1027–1061 (2001)

    Article  Google Scholar 

  • Securities and Exchange Comission.: Concept release on equity market structure 34 (2010)

  • Shapley, L.S., Shubik, M.: Quasi-cores in a monetary economy with nonconvex preferences. Econometrica 34, 805–827 (1966)

    Article  Google Scholar 

  • Simon, L., Zame, W.R.: Discontinuous games and endogenous sharing rules. Econometrica 58, 861–872 (1990)

    Article  Google Scholar 

  • Stahn, H.: Monopolistic behaviors and general equilibrium: a generalization of Nikaido’s work. J. Math. Econ. 32, 87–112 (1999)

    Article  Google Scholar 

  • Wooders, M.H.: Equivalence of Lindahl equilibria with participation prices and the core. Econ. Theory 9, 115–128 (1997)

    Article  Google Scholar 

  • Wooders, M.H.: A Tiebout theorem. Math. Soc. Sci. 18(1989), 33–55 (1989)

    Article  Google Scholar 

  • Wooders, M.H.: The epsilon core of a large replica game. J. Math. Econ. 11, 277–300 (1983)

    Article  Google Scholar 

  • Wooders, M.H.: The Tiebout hypothesis; near optimality in local public good economies. Econometrica 48, 1467–1485 (1980)

    Article  Google Scholar 

  • Wooders, M.H.: Equilibria, the core, and jurisdiction structures in economies with a local public good. J. Econ. Theory 18, 328–348 (1978)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Jaime Luque.

Additional information

We thank comments and suggestions from Nizar Allouch, Antonio Cabrales, Jean-Eduard Colliard, Gionvani Nicolo, Mario Pascoa, Erwan Quintin, Mark Ready, Tim Riddiough, Marzena Rostek, Myrna Wooders, Randy Wright, and participants at the annual meetings of the APET 2010, EWGE 2011, SAET 2011, SEA 2011, and PEA 2012, and seminars at Indiana University, University of Miami, Purdue University, and University of Wisconsin–Madison. Luque gratefully acknowledges the Spanish Ministry of Education and Science for financial support in 2010 under Grant SEJ2008-03516. Faias gratefully acknowledges that this work was partially supported by the Fundação para a Ciência e a Tecnologia (Portuguese Foundation for Science and Technology) through UID/MAT/00297/2013 (CMA).

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Faias, M., Luque, J. Endogenous formation of security exchanges. Econ Theory 64, 331–355 (2017).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


JEL Classification