Abstract
In this chapter we describe our model of a market with strategically behaving agents on both sides. First, we characterize the stage game between the firms in the model. Then, we proceed to the formulation of the countable infinite repeated game with discounting of payoffs. In Sect. 2.3 we define the solution concepts that we apply to the repeated game: SRPE and SSPE.
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- 1.
Only the quantities of the inputs purchased from the producers in J are the arguments of f k . We assume that the other inputs are fixed unless buyer k decides to leave the analyzed market.
- 2.
Of course, from the modeling point of view, we need the upper bounds on the prices in the analyzed market in order to ensure that the stage game payoffs are bounded and the repeated game (described in Sect. 2.2) is continuous at infinity.
- 3.
The producers can sell their product to different buyers at different prices. This enables us to construct a punishment for a deviation by a proper coalition of buyers, which does not harm the buyers who did not deviate, in the repeated game.
- 4.
We assume here that a firm can leave the analyzed market in one period. In the repeated game (described in the following section), we assume that a firm can enter the analyzed market in one period and the entry requires only paying the fixed cost. Our qualitative results hold if the exit from and entry into the analyzed market took more than one period and entry required the incurring of a sunk cost (exceeding the single period fixed cost).
- 5.
We use the symbol s C for a profile of the behavioral strategies of the members of a coalition C determined by a previously mentioned profile of the behavioral strategies (of all firms) s ∈ S and the symbol s (C) for a profile of the behavioral strategies of the members of a coalition C that is not determined by any previously mentioned s ∈ S.
- 6.
Of course, the functional values of π k depend on δ. Nevertheless, in order to avoid unnecessary notational complication, we use the symbol π k instead of π k, δ.
- 7.
Let s ∗ ∈ S be an equilibrium strategy profile and let h ∈ H f . Then, the continuation equilibrium in subgame Γ(h)(δ) is s (h) ∗, and the continuation equilibrium payoff vector is π(h)(s (h) ∗).
References
Aumann, R.J.: “Subjectivity and Correlation in Randomized Strategies,” Journal of Mathematical Economics 1 (1974), 67-96.
Hildenbrand, W.: Core and Equilibria of a Large Economy. Princeton, N.J.: Princeton University Press, 1974.
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© 2011 Springer-Verlag Berlin Heidelberg
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Horniaček, M. (2011). Model. In: Cooperation and Efficiency in Markets. Lecture Notes in Economics and Mathematical Systems, vol 649. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19763-5_2
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DOI: https://doi.org/10.1007/978-3-642-19763-5_2
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