Core Allocations in Co-investment Problems
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Core Allocations in Co‑investment Problems Josep Maria Izquierdo1 · Carlos Rafels1
© Springer Nature B.V. 2020
Abstract In a theoretical co-investment problem, a set of agents face a surplus-sharing situation with a single input and a single output exhibiting increasing average returns. All agents contribute their respective inputs and expect part of the collective output. Focusing on the core of the problem, we analyze whether a core allocation of the output is acceptable or compatible with a variation of input contributions, where larger payoffs are expected by those agents whose contribution has increased. We state a necessary and sufficient condition for a core allocation to be acceptable. We also introduce and study the acceptable core, that is, those core allocations acceptable for any possible increase of inputs. Finally, we axiomatically characterize when a set-solution that contains acceptable core allocations shrinks into the proportional allocation. Keywords Co-investment · Increasing average returns · Proportional solution · Incentive monotonicity · Acceptable core allocations
1 Introduction In many economic and social situations agents cooperate exerting some level of effort in order to obtain a common profit. The implication of each participant in the joint project depends on the payoff agents expect to receive. The negotiation process determines the level of effort and the allocation of the total gain. In this paper, we focus on specific resource-pooling situations that we name co-investment problems.
* Josep Maria Izquierdo [email protected] Carlos Rafels [email protected] 1
University of Barcelona, Av. Diagonal 690, 08034 Barcelona, Spain
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J. M. Izquierdo, C. Rafels
1.1 Co‑investment Problems General co-investment problems are situations where a set of agents pool their resources to obtain a surplus. In these problems, the effort of an agent is represented by the corresponding resource contribution and the common profit is the surplus obtained. Examples of these situations are the joint investment in infrastructures by the operators in the telecommunication sector (see Bourreau et al. 2012 and Bourreau et al. 2018), cooperation at the supply chain level between firms (see Kogan and Tapiero 2012), or the situation where agents pool their money to make a joint investment. In corporate finance, it is remarkable the fast and quite recent development of private equities firms (PE) that collect capital from investors who act as limited partners (LPs). On behalf of their LPs, the fund manager of the private equity firm (the general partner or GP) selects portfolio companies in which they invest capital and retain them with the aim to increase their value during a limited period, after which they exit. The literature on this topic is reviewed in Tykvová (2018). Recently, we can find more sophisticated funding figures that require the co-investment between private equities and other external limited partners that enable qualified investors to invest alongside a private
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