Solutions in multi-actor projects with collaboration and strategic incentives

This dissertation focuses on the mathematical analysis of projects involving decisions by multiple players. These players all have their own capabilities, requirements, and incentives, but their (monetary) outcome is dependent on the decisions of other players as well. Game theory is a mathematical tool to analyze the interactive decision-making process, generally paired with a method to ‘resolve’ the conflict situation. The way in which players interact in such a situation is commonly divided in two categories, distinguishing between cooperative and competitive (non-cooperative) behavior. This dissertation first studies two models within a cooperative framework, starting with the definition and analysis of a new influence measure for general, collaborative projects. The second model applies to situations where players cooperate on the construction of a new joint infrastructure, with a specific focus on cost allocation for CO2 transport infrastructure. Next, two-stage models are considered, in which a noncooperative first stage is followed by a cooperative second stage. Subsequently, social welfare loss in auctions with a corrupt auctioneer is studied. Finally, a new solution concept is presented that refines the notion of Nash equilibria for a general class of non-cooperative games

A Complete Characterization of the Gap between Convexity and SOS-Convexity

Our first contribution in this paper is to prove that three natural sum of squares (sos) based sufficient conditions for convexity of polynomials, via the definition of convexity, its first order characterization, and its second order characterization, are equivalent. These three equivalent algebraic conditions, henceforth referred to as sos-convexity, can be checked by semidefinite programming whereas deciding convexity is NP-hard. If we denote the set of convex and sos-convex polynomials in $n$ variables of degree $d$ with $\tilde{C}_{n,d}$ and $\tilde{\Sigma C}_{n,d}$ respectively, then our main contribution is to prove that $\tilde{C}_{n,d}=\tilde{\Sigma C}_{n,d}$ if and only if $n=1$ or $d=2$ or $(n,d)=(2,4)$. We also present a complete characterization for forms (homogeneous polynomials) except for the case $(n,d)=(3,4)$ which is joint work with G. Blekherman and is to be published elsewhere. Our result states that the set $C_{n,d}$ of convex forms in $n$ variables of degree $d$ equals the set $\Sigma C_{n,d}$ of sos-convex forms if and only if $n=2$ or $d=2$ or $(n,d)=(3,4)$. To prove these results, we present in particular explicit examples of polynomials in $\tilde{C}_{2,6}\setminus\tilde{\Sigma C}_{2,6}$ and $\tilde{C}_{3,4}\setminus\tilde{\Sigma C}_{3,4}$ and forms in $C_{3,6}\setminus\Sigma C_{3,6}$ and $C_{4,4}\setminus\Sigma C_{4,4}$, and a general procedure for constructing forms in $C_{n,d+2}\setminus\Sigma C_{n,d+2}$ from nonnegative but not sos forms in $n$ variables and degree $d$. Although for disparate reasons, the remarkable outcome is that convex polynomials (resp. forms) are sos-convex exactly in cases where nonnegative polynomials (resp. forms) are sums of squares, as characterized by Hilbert.Comment: 25 pages; minor editorial revisions made; formal certificates for computer assisted proofs of the paper added to arXi

Estimating Value Creation From Revealed Preferences: Application to Value-Based Strategies

Research summary: We develop and apply a new set of empirical tools consistent with the tenets of value-based business strategies, leveraging the principle that “no good deal comes undone” and the methods of revealed preferences, to empirically estimate drivers of value creation. We demonstrate how to use these tools in an analysis of value creation in buyer–supplier relationships in the UK corporate legal market. We show that our approach can uncover evidence of subtle mechanisms that traditional methods cannot easily distinguish from each other. Furthermore, we show how the estimates can be used as parameters of biform games for out-of-sample analyses of strategic decisions. With readily available data on relationships between firms, this approach can be applied to many other contexts of interest to strategy researchers. Managerial summary: Managers need to understand the drivers of value creation for customers in order to make competitive positioning decisions and understand when they can capture value under competition. However, estimates of the relative importance of each driver are typically difficult to obtain. In this article, we help remedy this problem by demonstrating a novel method that obtains estimates of the contribution of various drivers of value creation from commonly available data of buyer–supplier relationships. These estimates can then be used to inform the strategy-making process

Patent licensing, bargaining, and product positioning

Innovators who have developed advanced technologies, along with launching new products by themselves, often license these technologies to their rivals. When a firm launches a new product, product positioning is also an important matter. We consider a standard linear city model with two firms in which the licenser and the licensee negotiate on licensing and engage in Nash bargaining after they determine their product positions. We investigate how the bargaining power of the licenser affects the product positions of the firms. We find that the licenser more likely chooses the central position when its bargaining power is weak whereas the product position of the licenser accelerates price competition between the firms. We also discuss the welfare implication. We find that the inverse U shape relationship between the bargaining power of the licenser and total social surplus, i.e., neither too strong nor too weak bargaining power of the licensor is optimal.

A review of non-cooperative newsvendor games with horizontal inventory interactions

There are numerous applications of game theory in the analysis of supply chains where multiple actors interact with each other in order to reach their own objectives. In this paper we review the use of non-cooperative game theory in inventory management within the newsvendor framework describing a single period inventory control model with the focus on horizontal interactions among multiple independent newsvendors. We develop a framework for identifying these types of horizontal interactions including, for example, the models with the possibility of inventory sharing via transshipments, and situations with substitutable products sold by multiple newsvendors. Based on this framework, we discuss and relate the results of prior research and identify future research opportunities

Value Creation and Value Capture With Frictions

We use a formal value-based model to study how frictions—incomplete linkages in the industry value chain that keep some parties from meeting and transacting—affect value creation and value capture. Frictions arise from search and switching costs and moderate the intensity of industry rivalry and the efficiency of the market. We find that firms with a competitive advantage prefer industries with less, but not zero, frictions. We show that rivalry interacts nontrivially with other competitive forces to affect industry attractiveness. Firm heterogeneity emerges naturally when we introduce resource development. Heterogeneity falls with frictions, but the sustainability of competitive advantage increases. Overall, we show that introducing frictions makes value-based models very effective at integrating analyses at the industry, firm, and resource levels

On benefits of cooperation under strategic power

We introduce a new model involving TU-games and exogenous structures. Specifically, we consider that each player in a population can choose an element in a strategy set and that, for every possible strategy profile, a TU-game is associated with the population. This is what we call a TU-game with strategies. We propose and characterize the maxmin procedure to map every game with strategies to a TU-game. We also study whether or not the relevant properties of TU-games are transmitted by applying the maxmin procedure. Finally, we examine two relevant classes of TU-games with strategies: airport and simple games with strategies.Ministerio de Economía y Competitividad | Ref. PGC2018-097965-B-100Ministerio de Economía y Competitividad | Ref. MTM2017-87197-C3-1-PMinisterio de Economía y Competitividad | Ref. MTM2017-87197-C3-2-PMinisterio de Economía y Competitividad | Ref. MTM2014-53395-C3-1-PMinisterio de Economía y Competitividad | Ref. MTM2014-53395-C3-3-PMinisterio de Economía y Competitividad | Ref. MTM2014-54199-PXunta de Galicia | Ref. ED431C-2016-015Xunta de Galicia | Ref. ED431C-2016-040Xunta de Galicia | Ref. ED431G/0

Increasing the penetration of renewable energy through community energy projects. An economic approach based on biform games

In 2014, the Chilean government promulgated the Law 20,571. This law gives to regulated clients, mainly residential electricity customers, the right to produce energy/electricity for self-consumption and sell any surplus to the grid. After five years of implementation, including an update in 2018, the installed capacity of these projects is still very low. In contrast, in Scotland it is possible to find a much higher citizen participation in energy production through more collective initiatives, specifically community energy projects. This situation begs important questions about the effectiveness of net billing schemes in promoting citizen participation in energy production. In this doctoral thesis, a variety of tools inspired by game theory, social science, and mathematical programming are used and adapted to answer these questions. This leads to the following findings. Firstly, the current Chilean net billing scheme may not be the best support mechanism for citizen-led energy production developments. Secondly, some residential electricity customers would be willing to participate in local energy initiatives by devoting money and/or time, even when their main concern is the lack of financial resources necessary to fund such projects, and project ownership can influence this willingness. Thirdly, community energy projects can be the best strategy to follow for residential electricity customers in Scotland and Chile, although cost subsidisation can further improve community energy incentives. Even when the incumbents do not know their share of the benefits at the time of choosing a particular energy production scheme or mechanism, community energy projects present more opportunities to be implemented in comparison with net billing schemes in both countries. Finally, under specific circumstances, community energy deployment can have positive effects on variables like social welfare, consumer surplus, nodal prices, and carbon dioxide emissions. Based on these findings, we then draw conclusions and recommendations, which can help further development in the community energy sector, particularly in Chile