Peter Borm’s research while affiliated with Tilburg University and other places

Modeling Cooperative and Noncooperative Incentives in Investment Projects: A Novel Approach Using Cooperative Game Theory and Real Options Theory In “Dynamic Stability of Cooperative Investment under Uncertainty,” Ketelaars, Borm, and Kort study an investment project involving multiple stakeholders. The research was prompted by the fact that many infrastructure projects, such as Feyenoord City in Rotterdam, Netherlands, and the new Berlin airport, failed or were significantly delayed. Recognizing that the various stakeholders have outside options, the authors combine concepts from cooperative game theory and real options to analyze a coalitional and dynamic stability concept. They characterize the proportional investment scheme as the scheme that maximizes total project value and results in the earliest investment timing. They show that dynamic stability can be present when the market is stable and when the market is growing and volatile. However, the proportional investment scheme is more sensitive to dynamic instability in a market with high profit growth and low profit uncertainty, or vice versa.

We analyze clearing mechanisms in financial networks in which agents may have both monetary individual assets and mutual liabilities. A clearing mechanism prescribes mutual payments between agents in a financial network to settle their mutual liabilities. The corresponding payments, summarized in a payment matrix, are made in accordance with agent-specific claims rules that stem from the vast literature on claims situations. The bottom payment matrix is the payment matrix that contains the minimal amount of payments required to clear the network. We explicitly characterize the bottom payment matrix as the result of a recursive centralized mechanism. We subsequently show that several types of decentralized clearing mechanisms lead to the bottom payment matrix as well. In fact, we show that this unification of centralized and decentralized clearing mechanisms relies on the composition property of the underlying agent-specific claims rules that dictate the payment mechanism.

This paper analyzes bankruptcy problems from a strategic perspective using the parameterized TAL family of bankruptcy rules. We construct a strategic game where every player selects a parameter, and the rule from the TAL family that corresponds to the mean of the chosen parameters is used to divide the estate. We prove the existence of Nash equilibria for this strategic game. In particular, we provide the set of all Nash equilibria for two players, and for more players, we prove existence by constructing a Nash equilibrium of a particular form based on the notion of a pivotal player.

We consider a model of influence over a network with finite-horizon opinion dynamics. The network consists of agents that update their opinions via a trust structure as in the DeGroot dynamics. The model considers two potential external influencers that have fixed and opposite opinions. They aim to maximally impact the aggregate state of opinions at the end of the finite horizon by targeting with precision one agent in one specific time period. In the case of only one influencer, we characterize optimal targets on the basis of two features: shift and amplification. Also, conditions are provided under which a specific target is optimal: the maximum-amplification target. In the case of two influencers, we focus on the existence and characterization of pure strategy equilibria in the corresponding two-person strategic zero-sum game. Roughly speaking, if the initial opinions are not too much in favour of either influencer, the influencers’ equilibrium behaviour is also driven by the amplification of targets.

This paper analyzes capacity restricted cooperative purchasing (CRCP) situations in which a group of cooperating purchasers face two suppliers with limited supply capacity. To minimize the total purchasing costs, we show that two extreme policies have to be compared: order everything at one supplier and the possible remainder at the other. Interestingly, as order quantities increase, various policy switches can occur. To find suitable cost allocations of the total purchasing costs, we model a CRCP-situation as a cost sharing problem. As increasing order quantities also imply concavity breaks due to a forced change in supplier, the corresponding cost function is piecewise concave. For cost sharing problems with concave cost functions, we show that the serial cost sharing mechanism satisfies two desirable properties, unit cost monotonicity (UCM) and monotonic vulnerability for the absence of the smallest player (MOVASP). However, these properties are lost in the setting of piecewise concave cost functions. We develop a new context specific class of piecewise serial rules based on claims rules. We show that the proportional rule is the only claims rule for which the corresponding piecewise serial rule satisfies UCM. Moreover, the piecewise serial rule corresponding to the constrained equal losses rule satisfies MOVASP.

We define and axiomatically characterize a new proportional influence measure for sequential projects with imperfect reliability. We consider a model in which a finite set of players aims to complete a project, consisting of a finite number of tasks, which can only be carried out by certain specific players. Moreover, we assume the players to be imperfectly reliable, i.e., players are not guaranteed to carry out a task successfully. To determine which players are most important for the completion of a project, we use a proportional influence measure. This paper provides two characterizations of this influence measure. The most prominent property in the first characterization is task decomposability. This property describes the relationship between the influence measure of a project and the measures of influence one would obtain if one divides the tasks of the project over multiple independent smaller projects. Invariance under replacement is the most prominent property of the second characterization. If, in a certain task group, a specific player is replaced by a new player who was not in the original player set, this property states that this should have no effect on the allocated measure of influence of any other original player.