An Axiomatization of the Banzhaf Index to Measure Influence in Qualitative Comparative Analysis - Haake, Claus-Jochen; Schneider, Martin (International Journal of Game Theory)
The Banzhaf power index can be used to quantify the explanatory power of single conditions in a configurational analysis that aims at identifying whether combinations of conditions are sufficient for an outcome. The latter method is an integral part of the Qualitative Comparative Analysis (QCA) approach. It is widely used in the literature, e.g., in the field of International Management. Haake and Schneider (2023) give a rigorous description of the connection between the empirical and game theoretic modeling. To justify that the Banzhaf index is an appropriate tool to measure the influence of a condition, this paper discusses a novel axiomatization of the Banzhaf index that uses axioms that are directly linked to the QCA methodology. As a side result, we demonstrate that in our model the Banzhaf index can be reinterpreted as an average of Shapley-Shubik indices.
Keywords: Banzhaf index; axiomatization; QCA; explanatory power

A Note on the Size Reduction Reform in the German Parliament: A Game Theoretic Analysis of Power Indices - Duman, Papatya; Haake, Claus-Jochen (Review of Economics)
Abstract We investigate whether the recently approved reforms of the apportionment of parliamentary seats to parties in the German Bundestag affects the parties’ political influence measured by power indices. We find that under neither reform the underlying simple game, which describes the possibilities to form governments, remains unchanged and as a result the Shapley-Shubik and the Banzhaf index are unaltered. As a consequence, the major change resulting from the reforms is the reduction of the Bundestag’s size to 630 seats.
Keywords: Bundestag reform; Banzhaf power index; Shapley-Shubik power index

Playing games with QCA: Measuring the explanatory power of single conditions with the Banzhaf index - Haake, Claus-Jochen; Schneider, Martin (Journal of International Management)
Qualitative comparative analysis (QCA) enables researchers in international management to better understand how the impact of a single explanatory factor depends on the context of other factors. But the analytical toolbox of QCA does not include a parameter for the explanatory power of a single explanatory factor or “condition”. In this paper, we therefore reinterpret the Banzhaf power index, originally developed in cooperative game theory, to establish a goodness-of-fit parameter in QCA. The relative Banzhaf index we suggest measures the explanatory power of one condition averaged across all sufficient combinations of conditions. The paper argues that the index is especially informative in three situations that are all salient in international management and call for a context-sensitive analysis of single conditions, namely substantial limited diversity in the data, the emergence of strong INUS conditions in the analysis, and theorizing with contingency factors. The paper derives the properties of the relative Banzhaf index in QCA, demonstrates how the index can be computed easily from a rudimentary truth table, and explores its insights by revisiting selected papers in international management that apply fuzzy-set QCA. It finally suggests a three-step procedure for utilizing the relative Banzhaf index when the causal structure involves both contingency effects and configurational causation.
Keywords: Qualitative comparative analysis; Banzhaf power index; causality; explanatory power

On-The-Fly Computing -- Individualized IT-services in dynamic markets - Haake, Claus-Jochen; Meyer auf der Heide, Friedhelm; Platzner, Marco; Wachsmuth, Henning; Wehrheim, Heike
In the proposal for our CRC in 2011, we formulated a vision of markets for IT services that describes an approach to the provision of such services that was novel at that time and, to a large extent, remains so today: „Our vision of on-the-fly computing is that of IT services individually and automatically configured and brought to execution from flexibly combinable services traded on markets. At the same time, we aim at organizing markets whose participants maintain a lively market of services through appropriate entrepreneurial actions.“ Over the last 12 years, we have developed methods and techniques to address problems critical to the convenient, efficient, and secure use of on-the-fly computing. Among other things, we have made the description of services more convenient by allowing natural language input, increased the quality of configured services through (natural language) interaction and more efficient configuration processes and analysis procedures, made the quality of (the products of) providers in the marketplace transparent through reputation systems, and increased the resource efficiency of execution through reconfigurable heterogeneous computing nodes and an integrated treatment of service description and configuration. We have also developed network infrastructures that have a high degree of adaptivity, scalability, efficiency, and reliability, and provide cryptographic guarantees of anonymity and security for market participants and their products and services. To demonstrate the pervasiveness of the OTF computing approach, we have implemented a proof-of-concept for OTF computing that can run typical scenarios of an OTF market. We illustrated the approach using a cutting-edge application scenario – automated machine learning (AutoML). Finally, we have been pushing our work for the perpetuation of On-The-Fly Computing beyond the SFB and sharing the expertise gained in the SFB in events with industry partners as well as transfer projects. This work required a broad spectrum of expertise. Computer scientists and economists with research interests such as computer networks and distributed algorithms, security and cryptography, software engineering and verification, configuration and machine learning, computer engineering and HPC, microeconomics and game theory, business informatics and management have successfully collaborated here.

The Market for Services: Incentives, Algorithms, Implementation - Haake, Claus-Jochen; Hehenkamp, Burkhard; Polevoy, Gleb (On-The-Fly Computing -- Individualized IT-services in dynamic markets)

Distortion through modeling asymmetric bargaining power - Haake, Claus-Jochen; Streck, Thomas
We study the consequences of modeling asymmetric bargaining power in two-person bargaining problems. Comparing application of an asymmetric version of a bargaining solution to an upfront modification of the disagreement point, the resulting distortion crucially depends on the bargaining solution concept. While for the Kalai-Smorodinsky solution weaker players benefit from modifying the disagreement point, the situation is reversed for the Nash bargaining solution. There, weaker players are better off in the asymmetric bargaining solution. When comparing application of the asymmetric versions of the Nash and the Kalai-Smorodinsky solutions, we demonstrate that there is an upper bound for the weight of a player, so that she is better off with the Nash bargaining solution. This threshold is ultimately determined by the relative utilitarian bargaining solution. From a mechanism design perspective, our results provide valuable information for a social planner, when implementing a bargaining solution for unequally powerful players.
Keywords: Asymmetric bargaining power; Nash bargaining solution; Kalai-Smorodinsky bargaining solution

Wage Bargaining and Employment Revisited: Separability and Efficiency in Collective Bargaining - Haake, Claus-Jochen; Upmann, Thorsten; Duman, Papatya (Scandinavian Journal of Economics)
We analyse the two-dimensional Nash bargaining solution (NBS) by deploying the standard labour market negotiations model of McDonald and Solow (1981). 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.
Keywords: Labour market negotiations; efficient bargains; Nash bargaining solution; sequential bargaining; restricted bargaining games

Socio-legal systems and implementation of the Nash solution in Debreu–Hurwicz equilibrium - Haake, Claus-Jochen; Trockel, Walter (Review of Economic Design)
Abstract In this article we combine Debreu’s (Proc Natl Acad Sci 38(10):886–893, 1952) social system with Hurwicz’s (Econ Design 1(1):1–14, 1994; Am Econ Rev 98(3):577–585, 2008) ideas of embedding a “desired” game form into a “natural” game form that includes all feasible behavior, even if it is “illegal” according to the desired form. For the resulting socio-legal system we extend Debreu’s concepts of a social system and its social equilibria to a socio-legal system with its Debreu–Hurwicz equilibria. We build on a more general version of social equilibrium due to Shafer and Sonnenschein (J Math Econ 2(3):345–348, 1975) that also generalizes the dc-mechanism of Koray and Yildiz (J Econ Theory 176:479–502, 2018) which relates implementation via mechanisms with implementation via rights structures as introduced by Sertel (Designing rights: invisible hand theorems, covering and membership. Tech. rep. Mimeo, Bogazici University, 2001). In the second part we apply and illustrate these new concepts via an application in the narrow welfarist framework of two person cooperative bargaining. There we provide in a socio-legal system based on Nash’s demand game an implementation of the Nash bargaining solution in Debreu–Hurwicz equilibrium.

Introduction to the Special Issue “Bargaining” - Haake, Claus-Jochen; Trockel, Walter (Homo Oeconomicus)
Keywords: Industrial and Manufacturing Engineering; Environmental Engineering

The Decomposability of the Nash Bargaining Solution in Labor Markets - Haake, Claus-Jochen; Upmann, Thorsten; Duman, Papatya
In this paper, we analyze the two-dimensional Nash bargaining solution (NBS) deploying a standard labor market negotiations model (see McDonald and Solow, 1981; Creedy and McDonald, 1991). We show that the two-dimensional bargaining problem can be decomposed into two one-dimensional problems such that the (Cartesian) product of the solutions of these problems replicates the solution of the two-dimensional problem, if the NBS is applied. However, this decomposition fails for any solution concept that does not satisfy the axiom of Independence of Irrelevant Alternatives (IIA axiom). Our decomposition result has significant implications for actual negotiations, as it allows for the decomposition of a multi-issue bargaining problem into a set of simpler problems, in particular a set of single-issue bargaining problems. In this way, the decomposition may help facilitate negotiations in labor markets and also in other environments.
Keywords: Labor market negotiations; Efficient bargains; Nash bargaining solution; Sequential bargaining; Restricted bargaining games

Disaggregating User Evaluations Using the Shapley Value - Feldotto, Matthias; Haake, Claus-Jochen; Skopalik, Alexander; Stroh-Maraun, Nadja (Proceedings of the 13th Workshop on Economics of Networks, Systems and Computation (NetEcon 2018))
We consider a market where final products or services are compositions of a number of basic services. Users are asked to evaluate the quality of the composed product after purchase. The quality of the basic service influences the performance of the composed services but cannot be observed directly. The question we pose is whether it is possible to use user evaluations on composed services to assess the quality of basic services. We discuss how to combine aggregation of evaluations across users and disaggregation of information on composed services to derive valuations for the single components. As a solution we propose to use the (weighted) average as aggregation device in connection with the Shapley value as disaggregation method, since this combination fulfills natural requirements in our context. In addition, we address some occurring computational issues: We give an approximate solution concept using only a limited number of evaluations which guarantees nearly optimal results with reduced running time. Lastly, we show that a slightly modified Shapley value and the weighted average are still applicable if the evaluation profiles are incomplete.

Outcome Equivalence in School Choice with Reciprocal Preferences - Haake, Claus-Jochen; Stroh-Maraun, Nadja (Economics Letters)
We show that the Boston school choice mechanism (BM), the student proposing deferred acceptance algorithm (DA) and the top trading cycles algorithm (TTC) generate the same outcome when the colleges’ priorities are modified according to students’ preferences in a “first preferences first” manner. This outcome coincides with the BM outcome under original priorities. As a result, the DA and TTC mechanism that are non-manipulable under original priorities become vulnerable to strategic behavior.

On unification of solutions to the bargaining problem - Haake, Claus-Jochen; Qin, Cheng-Zhong
We establish axioms under which a bargaining solution can be found by the maximization of the CES function and is unique up to specification of the distribution and elasticity parameters. This solution is referred to as the CES solution which includes the NASH and egalitarian solutions as special cases. Next, we consider a normalization of the CES function and establish axioms, under which a bargaining solution can be found by the maximization of the normalized CES and is unique up to the specifications of the distribution and its substitution parameters. We refer to this solution as the normalized CES solution, which includes the Nash and Kalai-Smorodinsky solutions as special cases. Our paper contributes to bargaining theory by establishing unified characterizations of existing as well as a great variety of new bargaining solutions.
Keywords: Bargaining problem; CES Function; Normalized CES Function; Nash solution; Kalai-Smorodinsky Solution; Egalitarian Solution.

Thoughts on Social Design - Trockel, Walter; Haake, Claus-Jochen (Studies in Economic Design)
One of the fundamental problems in applications of methods and results from mechanism design and implementation theory is the effective enforcement of theoretically established equilibria by which social choice rules are implemented. Hurwicz (2008) and Myerson (2009) introduce different concepts of formalizing enforcement of institutional rules via the introduction of legal and illegal games. In this note the relation of their concepts with that of a social system defined inDebreu (1952) is analyzed and its potential of being instrumental for modelling institution design is discussed. The existence proof for such a system, also known as generalized game or abstract economy had been the basis for the existence proof of a competitive equilibrium of an economy.

The Generalized Nash Bargaining Solution for Transfer Price Negotiations under Incomplete Information - Haake, Claus-Jochen; Recker, Sonja (Group Decision and Negotiation)
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.

Maintaining vs. Milking Good Reputation when Customer Feedback is Inaccurate - Mir Djawadi, Behnud; Fahr, Rene; Haake, Claus-Jochen; Recker, Sonja (PLoS ONE)
In Internet transactions, customers and service providers often interact once and anonymously. To prevent deceptive behavior a reputation system is particularly important to reduce information asymmetries about the quality of the offered product or service. In this study we examine the effectiveness of a reputation system to reduce information asymmetries when customers may make mistakes in judging the provided service quality. In our model, a service provider makes strategic quality choices and short-lived customers are asked to evaluate the observed quality by providing ratings to a reputation system. The customer is not able to always evaluate the service quality correctly and possibly submits an erroneous rating according to a predefined probability. Considering reputation profiles of the last three sales, within the theoretical model we derive that the service provider’s dichotomous quality decisions are independent of the reputation profile and depend only on the probabilities of receiving positive and negative ratings when providing low or high quality. Thus, a service provider optimally either maintains a good reputation or completely refrains from any reputation building process. However, when mapping our theoretical model to an experimental design we find that a significant share of subjects in the role of the service provider deviates from optimal behavior and chooses actions which are conditional on the current reputation profile. With respect to these individual quality choices we see that subjects use milking strategies which means that they exploit a good reputation. In particular, if the sales price is high, low quality is delivered until the price drops below a certain threshold, and then high quality is chosen until the price increases again.

Towards an Economic Theory of Destabilization War - Gries, Thomas; Haake, Claus-Jochen (Peace Economics, Peace Science and Public Policy)

An Economic Theory of 'Destabilization War' - Gries, Thomas; Haake, Claus-Jochen
While Islamic State is the most present example, it is a fact that in many places around the globe, throughout history initially small groups have tried to challenge and destabilize or even overthrow governments by means of terrorist and guerrilla strategies. Therefore, we answer two questions. Why does a small group of insurgents believe it can overthrow the government by turning violent, even if the government is clearly superior? And how does a conflict develop into terrorism, a guerilla war, or a major conventional civil war, or is resolved peacefully? We develop a formal model for rebels and government and derive optimal choices. Further, we focus on three elements as important ingredients of a "destabilization war". All three of these - large random events, time preference (which we relate to ideology), and choice of duration of fight - are rarely considered in formal conflict theory. We can answer the above two questions using game theory analysis. First, insurgents rise up because they hope to destabilize through permanent challenging attacks. In this context, large randomness is an important ally of rebels. While each individual attack may have a low impact, at some point a large random event could lead to success. Hence, the duration of activities is a constitutive element of this kind of armed conflict. Patience (low time preference), which may reflect rebels' degree of ideological motivation, is crucial. Second, the mode of warfare or the conflict resolutions that develop are generally path-dependent and conditioned on the full set of options (including compromise). Various conditions (level of funding, ease of recruitment, access to weapons) influence different modes of warfare or a peaceful compromise in a complex way.
Keywords: terrorism; civil war; conflict duration; game theory; stochastic process; ideology

Strategic Formation of Customer Relationship Networks - Brangewitz, Sonja; Haake, Claus-Jochen; Möhlmeier, Philipp
We analyze the stability of networks when two intermediaries strategically form costly links to customers. We interpret these links as customer relationships that enable trade to sell a product. Equilibrium prices and equilibrium quantities on the output as well as on the input market are determined endogenously for a given network of customer relationships. We investigate in how far the substitutability of the intermediaries' products and the costs of link formation influence the intermediaries' equilibrium profits and thus have an impact on the incentives to strategically form relationships to customers. For networks with three customers we characterize locally stable networks, in particular existence is guaranteed for any degree of substitutability. Moreover for the special cases of perfect complements, independent products and perfect substitutes, local stability coincides with the stronger concept of Nash stability. Additionally, for networks with n customers we analyze stability regions for selected networks and determine their limits when n goes to infinity. It turns out that the shape of the stability regions for those networks does not significantly change compared to a setting with a small number of customers.

Provider Competition in Infrastructure-as-a-Service - Künsemöller, Jörn; Brangewitz, Sonja; Karl, Holger; Haake, Claus-Jochen (Proceedings of the 2014 IEEE International Conference on Services Computing (SCC))
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 client’s 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.