The Generalized Nash Bargaining Solution for Transfer Price Negotiations Under Incomplete Information

In our model two divisions negotiate over type-dependent contracts to determine an intrafirm transfer price for an intermediate product. Since the upstream division’s (seller’s) costs and downstream division’s (buyer’s) revenues are supposed to be private information, we formally consider cooperative bargaining problems under incomplete information. This means that the two divisions consider allocations of expected utility generated by mechanisms that satisfy (interim) individual rationality, incentive compatibility and/or ex post efficiency. Assuming two possible types for buyer and seller each, we first establish that the bargaining problem is regular, regardless whether or not incentive and/or efficiency constraints are imposed. This allows us to apply the generalized Nash bargaining solution to determine fair transfer payments and transfer quantities. In particular, the generalized Nash bargaining solution tries to balance divisional profits, while incentive constraints are still in place. In that sense a fair profit division is generated. Furthermore, by means of illustrative examples we derive general properties of this solution for the transfer pricing problem and compare the model developed here with the models existing in the literature. We demonstrate that there is a tradeoff between ex post efficiency and fairness.     

Proportionality and the power of unequal parties

In this paper we introduce the concept of an overall power function that is meant to combine two sources of a party's power in a parliament. The first source is based on the possibilities for the party to be part of a majority coalition and it is typically modeled using a cooperative simple game. The second source takes into account parties' asymmetries outside the cooperative game and it is displayed by a vector of exogenously given weights. We adopt a normative point of view and provide an axiomatic characterization of a specific overall power function, in which the weights enter in a proportional fashion.     

On the institutional design of burden sharing when financing external border enforcement in the EU

Illegal immigration affects not only EU member states adjacent, but also those distant from the Mediterranean Sea due to open internal borders and intra-EU onward migration. Member states without a direct influx of illegal immigrants may therefore free-ride on border countries’ enforcement efforts, leading to a sub-optimal level of border control when immigration policy remains uncoordinated. By applying a numerical example, we show that an expected externality mechanism leads to voluntary preference revelation with respect to immigration policy under several (but not all) scenarios, thereby avoiding strategic behavior in the regular negotiation process. This policy measure requires, however, the EU Commission to take on a very active role as moderator between member states (rather than as legislator).     

On Maskin monotonicity of solution based social choice rules

Howard (J Econ Theory 56:142–159, 1992) argues that the Nash bargaining solution is not Nash implementable, as it does not satisfy Maskin monotonicity. His arguments can be extended to other bargaining solutions as well. However, by defining a social choice correspondence that is based on the solution rather than on its realizations, one can overcome this shortcoming. We even show that such correspondences satisfy a stronger version of monotonicity that is even sufficient for Nash implementability.     

Monotonicity and Nash implementation in matching markets with contracts

We consider general two-sided matching markets, so-called matching with contracts markets as introduced by Hatfield and Milgrom (in A Econ Rev, 95(4), 913–935, 2005), and analyze (Maskin) monotonic and Nash implementable solutions. We show that for matching with contracts markets the stable correspondence is monotonic and implementable. Furthermore, any solution that is Pareto efficient, individually rational, and monotonic is a supersolution of the stable correspondence. In other words, the stable correspondence is the minimal solution that is Pareto efficient, individually rational, and implementable.     

Stable governments and the semistrict core

We consider the class of proper monotonic simple games and study coalition formation when an exogenous weight vector and a solution concept are combined to guide the distribution of power within winning coalitions. These distributions induce players' preferences over coalitions in a hedonic game. We formalize the notion of semistrict core stability, which is stronger than the standard core concept but weaker than the strict core notion and derive two characterization results for the semistrict core, depending on conditions we impose on the solution concept. A bounded power condition, which connects exogenous weights and the solution, turns out to be crucial. It generalizes a condition termed “absence of the paradox of smaller coalitions” that was previously used to derive core existence results.     

Negotiating Transfer Prices

We consider a team-investment setting in which transfer prices between two divisions are negotiable. Investments are made independently and simultaneously after the bargaining stage, i.e. with a given transfer price ‘on the table’. Both divisions’ investments jointly affect the sales price of the final product and total revenue. We analyze two transfer-pricing schemes and their corresponding bargaining problems. Both bargaining settings exhibit non-transferable utility because the transfer price not only allocates corporate profit but also affects corporate profit through the incentives it creates for the divisions’ investment and quantity decisions. In particular, we discuss how concepts from bargaining theory can be use used to determine a ‘fair’ agreement concerning the transfer price.     

Trading bargaining weights

We consider a model, in which two agents are engaged in two separate bargaining problems. We introduce a notion of bargaining weights (bargaining power), which is basically given by asymmetric versions of the Perles–Maschler bargaining solution. Thereby, we view bargaining power as ordinary goods that can be traded in an exchange economy. With equal initial endowment of bargaining power there exists a Walrasian equilibrium in this exchange economy such that the utility allocation in equilibrium coincides with the Perles–Maschler bargaining solution of the aggregate bargaining problem. Equilibrium prices are given by the primitives of the two bargaining problems.     

Wage bargaining and employment revisited: separability and efficiency in collective bargaining*

We analyse the two-dimensional Nash bargaining solution (NBS) by deploying the standard labour market negotiations model of McDonald and Solow. We show that the two-dimensional bargaining problem can be decomposed into two one-dimensional problems, such that the two solutions together replicate the solution of the two-dimensional problem if the NBS is applied. The axiom of “independence of irrelevant alternatives” is shown to be crucial for this type of decomposability. This result has significant implications for actual negotiations because it allows for the decomposition of a multi-dimensional bargaining problem into one-dimensional problems – and thus helps to facilitate real-world negotiations.     

Government versus Opposition: Who Should be Who in the 16th German Bundestag?

We model the process of coalition formation in the 16th German Bundestag as a hedonic coalition formation game. In order to induce players' preferences in the game we apply the Shapley value of the simple game describing all winning coalitions in the Bundestag. Using different stability notions for hedonic games we prove that the ``most' stable government is formed by the Union Parties together with the Social Democratic Party.