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...alid for both the BCG and UCG. The set of Nash equilibria and pairwise Nash equilibria coincide in the UCG, since ci(s+Λ(i,j)) ≥ ci(s) is true for any Nash equilibrium. Following Jackson and Wolinsky =-=[14]-=-, we also define the following network stability concept for the BCG: Definition 3 (Pairwise stable). A graph G(s) ∈ ζ is pairwise stable in the BCG if for all (i, j) ∈ A(s), ci(s − Λ(i,j)) ≥ ci(s), w...

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... we obtain UA − Ua = UA − Ua. (2) Condition (2) is called “balancedness”, which under our requirements must hold for all bilateral negotiations and for all contingencies. We are now in the position to argue that our requirements (i)-(iii) indeed generate the Shapley value. This follows in two steps. First, under (A.1)-(A.2) total payoffs generated for any contingency maximize industry profits, i.e., we obtain the characteristic function W(·). Second, under our requirements the distribution of payoffs is generated by the balancedness condition for all players and contingencies. By results in Jackson and Wolinsky (1996), which extend those in Myerson (1977), this implies that individual payoffs are determined by the Shapley value.12 Summing up, it is the joint assumption of (simultaneous) efficient negotiations and contingent contracting that generates the Shapley value.13 10Formally, L is an element of the power set of S0 ×R0. 11Observe that xsr are uniquely determined due to Assumption (A.1). 12Precisely, we can apply Theorem 4 in Jackson and Wolinsky (1996) after noting that our condition of non-interdependent demand is equivalent to their requirement that the “value function” (i.e., W(·)) is “component a...

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...ehavior”, in which currently deviating coalitions evaluate the future multiplicity of other deviations in hopeful or pessimistic ways (see also [11], [26], and [34], which all suffer from this selection problem). This Knightian approach to the treatment of multiplicity can be avoided by borrowing more freely from the language of repeated or dynamic games, which we do. Future paths (perhaps probabilistic in nature) are evaluated using common beliefs (as embodied in the transition probability) and expected payoffs are calculated using these beliefs. 1See, for example, [5], [6], [7], [10], [13], [20], [27], [28] and [35]. An early concern with the limitations imposed by characteristic functions is to be found in [29] and [33]. 2In contexts where binding agreements can be written, see, for example, [12]. [14], [17] and [26]. 3See, for instance, [2], [11], [23] and [34]. 4 KONISHI AND RAY Third, several solution concepts, especially those that concern themselves with farsighted agents, inevitably run into the problem of cycles (for an early discussion of this, see [31]). Chains of coalitions may appear and reappear in the blocking process.4 In the present approach, recurrent cycles of moves...