Outside options

With a certain probability, (1 — -0), the negotiation breaks down and the agents take their outside options, Wg and W y. 

To derive the SPE condition we evaluate the event tree backward from the leaf nodes. Since the event tree in the figure represents the case where the buyer gets the largest possible perfect equilibrium share, when the supplier makes the offer, she settles for the minimum perfect equilibrium share m. When the buyer makes the offer, she receives the maximum gain possible and leaves tt - M5 to the supplier. In case the bargaining breaks down, the supplier receives her outside option W5. The offers at the next tier follows the same logic. When the buyer makes the offer, she leaves tt — to supplier as before. If the supplier makes the offer, she settles for the least amount she expects to gain in the future, which is equal to... 

Since the maximum and the minimum SPE shares are equal for a given player, the SPE strategy is unique. We may interpret from expressions (3.9) and (3.10) that when a buyer (supplier) makes an offer, she ask for the difference between the system surplus tt and the supplier s (buyer s) outside option Wg (Wb) minus a risk premium equals to -Wb- Ws). Note that the... 

Proposition 4 The player who initiates, and the player who accepts the SPE offer both gain no less than their respective outside options. 

Proof For the player who initiates the offer, the difference between her SPE share and her outside option is as follows ... 

The expression above is always positive. Hence the player who initiates the SPE offer will gain no less than her outside option. For the player who accepts the SPE offer, the difference between her SPE share and her outside option is as follows ... 

This expression is always positive as well. Therefore, in SPE both players gain no less than their outside options, regardless of who initiate the offer, o... 

Proposition 5 The SPE share of the initiating player is linearly increasing (for > 0) in her outside option, and linearly decreasing in her opponent s outside option. 

Proof Taking the first and second derivatives of the buyer s SPE offer with respect to the outside options and Wg, we see that... 

Proposition 6 The SPE share of the initiating player is maximized when the breakdown probability approaches 7 ("(1 — -0) 1), where the share equals to the system surplus tt less the opponents outside option. 

From the above theorem, and more specifically from (3.15), note that the intermediary needs to be concerned about the supplier and the buyer s bargaining power. As the players outside options increase, it will become increasing difficult for the intermediary to stay viable, and disintermediation will eventually... 

When both the supplier and the buyer are in weak bargaining positions (limited outside options), or when direct trade is expected to be volatile (as characterized by the breakdown probability), intermediated trade will be desirable. Conversely, when either the supplier or the buyer is in a strong bargaining position, or when direct trade is expected to be stable, disintermediation is likely to occur. 

In this section, we consider the case when players are subject to asymmetric information, i.e., each player may hold private information on her valuation of the object, her outside options, or her quality level/expectation, which directly influence the bargaining process. Specifically, we are interested in the case where the supplier holds private information on her opportunity cost 5, and the buyer holds private information on her willingness to pay level v. Acting on this information, the supply chain intermediary establishes intermediated trade via a mechanism. We introduce the analytic framework established by Myer-son (1982), and Myerson and Satterthwaite (1983) that lays out the foundation for intermediated trades under incomplete information. We then introduce potential research topics using this perspective. 

We consider a one-buyer, one-supplier basic model where the players could either trade through an intermediary, or via a direct matching market (their outside option). The players hold private information on their costs, established based on their respective outside options. The supplier holds private information on her opportunity cost 5, which takes values on the interval [51,52] with a prior probability density function /(5), and cumulative distribution function F s). Similarly, the buyer holds private information on her willingness to pay level V, taking on the interval [v, V2 y with cumulative distribution G, and den-... 

By the revelation principle (Section 3.2), it is sufficient to consider an incentive compatible direct mechanism. In other words, regardless of the mechanism constructed by the intermediary, given the equilibrium of the mechanism, we can construct an equivalent incentive compatible direct mechanism, where the buyer and the supplier report their respective valuations to the intermediary, and the intermediary determines if the trade is to take place. If so, she determines the buyer s payment and the suppliers revenue. Otherwise, the players take their outside options in a direct matching market. Let T(/3,p, w) represents the direct revelation mechanism, where /3(s, v) is the probability that the trade will take place, p(s, v) is the expected payment to be made by the buyer to the intermediary (the asked price), and w(s, v) is the expected payment from the intermediary to the supplier (the bid price), where s and v are the valuations given by the supplier and buyer, respectively. As mentioned above, the intermediary is aware of the buyer and the supplier s outside options as random variables characterized by distributions G and F, respectively. Based on this information the intermediary establishes the buyer s virtual willingness to pay follows ... 

Step 1. To the intermediary, the buyer reveals her valuation, her outside options, and her quality requirements, characterized by v. The supplier reveals her valuation, her outside options, and her quality type, characterized by s. 

If the trade is not to take place (/3(s, v) = 0), the players take their outside options. 

Ponsati, C. and Sakovics, J. (1998). Rubinstein bargaining with two-sided outside options. Econom. Theory, ll(3) 667-672. 

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