## Abstract

We discuss how linear equilibrium pricing in certain competitive market structures may represent nonlinear equilibrium pricing of Aliprantis et al. (J Econ Theory 100:22–72, 2001, J Econ Theory 121:51–74, 2005). Their work extends the theory of value beyond the scope of the Walrasian single market linear price model. Our arguments include a new and general result on the existence of linear price equilibrium with multiple markets. Each market has its own price vector (linear functional), and agents’ involvement in various markets is heterogeneous. As a result, price differences across markets may prevail in equilibrium. We present an example in which single market linear price equilibrium does not exist, but certain corresponding equilibrium with two markets does. This example is a particular instance of a prevalent nonexistence problem in atomless economies with differential information. Bypassing the nonexistence problem is one of the achievements of the nonlinear equilibrium theory. Our equilibrium with multiple markets, on the other hand, offers a solution with a more standard economic interpretation. Besides, our general framework is a model of multiple markets in their own right, and our results are related to the role of economic intermediation and bilateral trade.

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## Additional information

The idea of this paper occurred to the author while he studied examples of nonlinear price decentralization of Pareto efficient allocations in Tourky and Yannelis (2003). The author thanks his Ph.D. supervisor at the ANU, Professor Rabee Tourky, for kindly sharing this working paper, helpful comments, and discussions. Two anonymous referees and the editor are gratefully acknowledged for questions that led to significant improvements. The author appreciates valuable feedback at various stages from Patrick Beissner, Simon Grant, Tai-Wei Hu, M. Ali Khan, Jeff Kline, Kieron Meagher, Idione Meneghel, Romans Pancs, Martin Richardson, Ronald Stauber, Jan Werner, Nicholas Yannelis, Valentin Zelenyuk, and an ANU audience.

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Klishchuk, B. Multiple markets: new perspective on nonlinear pricing.
*Econ Theory* **66, **525–545 (2018). https://doi.org/10.1007/s00199-017-1071-y

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### Keywords

- Multiple markets
- Nonlinear price
- Equilibrium price
- Equilibrium existence
- Equilibrium nonexistence

### JEL Classification

- D4
- D5
- D6
- D8