Claus-Jochen Haake

The Shapley value of phylogenetic trees

Every weighted tree corresponds naturally to a cooperative game that we call a tree game; it assigns to each subset of leaves the sum of the weights of the minimal subtree spanned by those leaves. In the context of phylogenetic trees, the leaves are species and this assignment captures the diversity present in the coalition of species considered. We consider the Shapley value of tree games and suggest a biological interpretation. We determine the linear transformation M that shows the dependence of the Shapley value on the edge weights of the tree, and we also compute a null space basis of M. Both depend on the split counts of the tree. Finally, we characterize the Shapley value on tree games by four axioms, a counterpart to Shapley’s original theorem on the larger class of cooperative games. We also include a brief discussion of the core of tree games.

On the Institutional Design of Burden Sharing When Financing External Border Enforcement in the EU

Illegal immigration affects not only EU member states at the Mediterranean Sea but also more Northern states due to open internal borders and onward migration. Northern member states may free-ride on border countries’ enforcement efforts, leading to a sub-optimal level of border control. While neither a centralized nor a coordinated policy appears to be feasible, we show that employing an expected externality mechanism leads to voluntary preference revelation with respect to immigration policy under several (but not all) scenarios. This policy measure requires, however, the EU Commission to take on a very active role as moderator between member states, which at the same time must accept the Commission to play this role.

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.

DIVIDING BY DEMANDING: OBJECT DIVISION THROUGH MARKET PROCEDURES

We discuss a model, in which two agents may distribute finitely many objects among themselves. The conflict is resolved by means of a market procedure. Depending on the specifications, this procedure serves to achieve bargaining solutions such as the discrete Raiffa solution, the Kalai-Smorodinsky solution and the Perles-Maschler solution. The latter is axiomatized using the superadditivity axiom, which in the present context is readily interpreted as resolving a specific source of conflict potential.

Contract Design for Composed Services in a Cloud Computing Environment

In this paper, we study markets in which sellers and buyers interact with each other via an intermediary. Our motivating example is a market with a cloud infrastructure where single services are flexibly combined to composed services. We address the contract design problem of an intermediary to purchase complementary single services. By using a non-cooperative game-theoretic model, we analyze the incentives for high- and low-quality composed services to be an equilibrium outcome of the market. It turns out that equilibria with low quality can be obtained in the short run and in the long run, whereas those with high quality can only be achieved in the long run. In our analysis we explicitly determine the according discount factors needed in an infinitely repeated game. Furthermore, we derive optimal contracts for the supply of high- and low-quality composed services.

Provider Competition in Infrastructure-as-a-Service

This paper explores how cloud provider competition influences instance pricing in an IaaS (Infrastructure-as-a-Service) market. When reserved instance pricing includes an on-demand price component in addition to a reservation fee (two-part tariffs), different providers might offer different price combinations, where the clients choice depends on its load profile. We investigate a duopoly of providers and analyze stable market prices in two-part tariffs. Further, we study offers that allow a specified amount of included usage (three-part tariffs). Neither two-part nor three-part tariffs produce an equilibrium market outcome other than a service pricing that equals production cost, i.e., complex price structures do not significantly affect the results from ordinary Bertrand competition.

Two support results for the Kalai-Smorodinsky solution in small object division markets

We discuss two support results for the Kalai-Smorodinsky bargaining solution in the context of an object division problem involving two agents. Allocations of objects resulting from strategic interaction are obtained as a demand vector in a specific market. For the first support result games in strategic form are derived that exhibit a unique Nash equilibrium. The second result uses subgame perfect equlibria of a game in extensive form. Although there may be multiple equilibria, coordination problems can be removed.