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Rigid and flexible contracts, both of which have advantages and disadvantages, are widely used in public–private partnership (PPP) projects. How to choose an appropriate contract type to improve the performance of PPP projects is an important issue that governments need to address. The literature has focused mainly on the strategy evolution of governments and private investors under rigid contracts but has not considered the influence of contract type (rigid versus flexible) on their strategy evolution. In this study, by incorporating an other-regarding preference, evolutionary game models under rigid and flexible contracts in PPP projects are established. We compare the government's supervision strategy and the private investor's cooperation strategy under these two types of contracts and summarize the applicable situations. Our research results show that the type of contract (rigid or flexible) will not affect the government's supervision strategy but will affect the cooperative strategy of the private investor. The applicable conditions of these two types of contracts are determined by profit sharing, the government's expectation of the project performance, and the discount rate as well as other factors. There is no cross-influence between the government and private investor's other-regarding preferences. The private investor's other-regarding preference is conducive to reducing some opportunistic behaviors that cause damage to social welfare and in promoting cooperative behavior. This paper contributes to the literature on PPP project contract design by providing the applicable conditions for rigid and flexible contracts as well as contract choice suggestions for project managers in PPP projects. Choosing a proper contract type is important for the success of PPP projects. This study compares the strategy choices of government and private investors under rigid and flexible contracts, presents the applicability of those two contracts, and provides managerial insights and suggestions for the government to choose a suitable contract type and enhance project performance. First, for projects with small-scale or easy tasks for which private investors need to expend only a low level of effort, the government can pay less attention to the contract type. Second, for projects that have high prospects, i.e., will have high performance in the future (for example, infrastructure PPP projects in cities' core areas), a flexible contract outperforms a rigid contract. Otherwise, a rigid contract outperforms a flexible one. Third, governments should pay more attention to the preliminary feasibility study of a project to avoid either over- or underconfidence and ensure a proper contract choice. Fourth, the government should focus on examining private investors' personal abilities and behavioral preferences and choose private investors with high-capacity endowments and other-regarding preferences. Finally, increasing penalties for opportunistic behavior is not an efficient strategy for the government when a private investor has high cooperation motivation. [ABSTRACT FROM AUTHOR]

We consider the situation where multiple transportation service providers cooperate to offer an integrated multi-modal platform to enhance the convenience to the passengers through ease in multi-modal journey planning, payment, and first and last mile connectivity. This market structure allows the multi-modal platform to coordinate profits across modes and also provide incentives to the passengers. Accordingly, in this paper, we use cooperative game theory coupled with the hyperpath-based stochastic user equilibrium framework to study such a market. We assume that the platform sets incentives (price discount or excess charge on passengers) along every edge in the transportation network. We derive the continuity and monotonicity properties of the equilibrium flow with respect to the incentives along every edge. The optimal incentives that maximize the profit of the platform are obtained through a two time-scale stochastic approximation algorithm. We use the asymmetric Nash bargaining solution to design a fair profit sharing scheme among the service providers. We show that the profit for each service provider increases after cooperation on such a platform. Finally, we complement the theoretical results through two numerical simulations. [ABSTRACT FROM AUTHOR]

• A game theory approach in the reverse supply chain of ELVs collection is defined. • An ELV take-back center, an inspection center, and a repair center are considered. • The equilibrium values in the centralized and decentralized scenarios are obtained. • The impact of subsidy of the government on the supply chain centers is analyzed. • The best contract to increase the level of repair is the revenue-sharing contract. The presence of end-of-life vehicles (ELV) in the cities creates irreparable damage in environmental and economic terms. Thus, governments have been searching for ways to collect ELVs. An effective way to address ELVs is subsidies' policy. In this study, a supply chain including an ELV take-back center, an inspection center, and a repair center are considered. The decision variables are the purchase price of the ELVs, the sale price of the repaired vehicle, and the level of vehicle repair. In this supply chain, the government pays a subsidy to take-back centers that deliver their used vehicles. A Stackelberg game structure is considered with the government as the leader, the inspection center as the primary follower, and the collection and repair centers as the second followers. Using the game theory approach, the effects of government subsidies on equilibrium values of the decision-making variables of the centers in the ELV supply chain have been investigated in three scenarios. The scenarios comprise profit sharing, revenue sharing, and a centralized (cooperative) scenario. The results indicate that the centralized scenario has the most significant advantage compared to the two contracts of profit sharing and cost sharing. For example, the repair level of the ELVs, the amount of repaired vehicles demand, consumer surplus, and the whole supply chain's profit are at their maximum. The most significant impact of subsidy payment is related to the take-back center's profit and the ELV supply. On the other hand, the subsidy does not affect the profit of the repair center. [ABSTRACT FROM AUTHOR]

In virtual communities of practice, many participants use their knowledge to achieve a common goal based on cooperation, and the key to such cooperation is knowledge collaboration. Knowledge collaboration is the primary method of increasing the virtual community of practice's knowledge ability and achieving the core competency advantage of sustainable growth. Knowledge collaboration inevitably involves the psychological elements of the collaborators. This study focuses on the elements of the psychological contract of the members of the virtual community of practice when participating in knowledge collaboration; the psychological contract summarizes the members’ collaboration via seven psychological factors spread across two dimensions. Based on these factors, this study uses the game theory to create a cost game model and profit-sharing game model in the virtual community of practice knowledge collaboration. The cost game model is built upon Stackelberg equilibrium, the model is solved using backward induction, and its effectiveness is established. The profit-sharing model is based upon a modified Nash bargaining solution; the model is applied to the Python software development team in the Github community of practice and yields positive results. Finally, the research outcomes are summarized, and directions for future research are provided. [ABSTRACT FROM AUTHOR]

Purpose: The aim of the paper is to pick up the result of a previously published paper in order to deepen the discussion. We analyze the solution against the background of some well-known concepts and we introduce a newer one. In doing so we would like to inspire the further discussion of supply chain collaboration. Design/methodology/approach: Based on game theoretical knowledge we present and compare seven properties of fair profit sharing. Findings: We show that the nucleolus is a core-solution, which does not fulfil aggregate monotonicity. In contrast the Shapley value is an aggregate monotonic solution but does not belong to the core of every cooperative game. Moreover, we present the Lorenz dominance as an additional fairness criteria. Originality/value: We discuss the very involved procedure of establishing lexicographic orders of excess vectors for games with many players. [ABSTRACT FROM AUTHOR]

We study profit sharing games in which players select projects to participate in and share the reward resulting from that project equally. Unlike most existing work, in which it is assumed that the player utility is monotone in the number of participants working on their project, we consider non-monotone player utilities. Such utilities could result, for example, from 'threshold' or 'phase transition' effects, when the total benefit from a project improves slowly until the number of participants reaches some critical mass, then improves rapidly, and then slows again due to diminishing returns.Non-monotone player utilities result in a lot of instability: strong Nash equilibrium may no longer exist, and the quality of Nash equilibria may be far away from the centralized optimum. We show, however, that by adding additional requirements such as players needing permission to leave a project from the players currently on this project, or instead players needing permission to join a project from players on that project, we ensure that strong Nash equilibrium always exists. Moreover, just the addition of permission to leave already guarantees the existence of strong Nash equilibrium within a factor of 2 of the social optimum. In this paper, we provide results on the existence and quality of several different coalitional solution concepts, focusing especially on permission to leave and join projects, and show that such requirements result in the existence of good stable solutions even for the case when player utilities are non-monotone. [ABSTRACT FROM AUTHOR]

- The primary purpose of this paper is to perform optimal energy management in a distribution network (DN) consisting of several microgrids (MG). A cooperative game method has been used to achieve the best coalitions to diminish the total system costs. A fair profit-sharing procedure is defined as the individual contribution value (ICV) to share profits between players. In addition to ICV, as an economic indicator, the DN's maximum voltage deviation (MVD) in each game has been used to allocate rewards to each game's players (MGs). Studies have been executed on a modified 33-bus DN consisting of three distinct MGs. In the system under study, there is no direct connection among MGs. The case study also deliberates the uncertainties of RESs and technical real power losses in the DN considering demand response program. The paper results concede that despite the reduction in the costs of MMGs due to the application of DRP, it is still possible to reduce the total costs of an MMG system by forming coalitions and adopting proper procedures to profit allocation. In addition, the proposed profit-sharing method based on ICVs and MVDs is simple, consistent, and clear, thus facilitating calculations. Examining the games one by one also identifies the inappropriate games/players to form a coalition and helps reduce problem size in the upcoming scheduling. Solutions obtained through the combined use of ICV and MVD indicators are more profitable, have better technical characteristics, and lead to larger alliances with more MGs participation, increasing network flexibility. [Display omitted] • Proposing a novel criterion for profit-sharing in multi-microgrid energy management based on cooperative game theory. • Considering renewable energy sources uncertainties via scenario generation-reduction process. • Including price-based demand response programs in microgrids integrated into the distribution network. • Solving optimal energy management problem where cost-technical performance are considered. [ABSTRACT FROM AUTHOR]

We develop a (noncooperative) game theoretic model for a decentralized setting wherein fringe farmers compete with a two-tier cooperative network involving network farmers and a coordinator. We examine the roles of the coordinator and profit sharing in allocating costs/benefits of externalities in enhancing network efficiency and stability. Our main finding is that using profit sharing based mechanism the coordinator can overcome inherent inefficiency and instability of decentralization and noncooperative behavior of the network farmers. The roles of the coordinator and profit sharing are particularly important when it is economical for both network and fringe farmers to supply the product. [ABSTRACT FROM AUTHOR]

In real life, the vendor managed inventory (VMI) model is not always a stable supply chain partnership. This paper proposes a cooperative game based profit-sharing method to stabilize the VMI partnership. Specifically, in a B2C setting, we consider a VMI program including a manufacturer and multiple online retailers. The manufacturer provides the finished product at the equal wholesale price to multiple online retailers. The online retailers face the same customer demand information. We offer the model to compute the increased profits generated by information sharing for total possible VMI coalitions. Using the solution concept of Shapley value, the profit-sharing scheme is produced to fairly divide the total increased profits among the VMI members. We find that under a fair allocation scheme, the higher inventory cost of one VMI member increases the surplus of the other members. Furthermore, the manufacturer is glad to increase the size of VMI coalition, whereas, the retailers are delighted to limit the size of the alliance. Finally, the manufacturer can select the appropriate retailer to boost its surplus, which has no effect on the surplus of the other retailers. The numerical examples indicate that the grand coalition is stable under the proposed allocation scheme. [ABSTRACT FROM PUBLISHER]

In this paper we study the possibilities of sharing profit in combinatorial procurement auctions and exchanges. Bundles of heterogeneous items are offered by the sellers, and the buyers can then place bundle bids on sets of these items. That way, both sellers and buyers can express synergies between items and avoid the well-known risk of exposure (see, e.g., Cramton, Shoham, & Steinberg, Combinatorial Auctions, ). The reassignment of items to participants is known as the Winner Determination Problem (WDP). We propose solving the WDP by using a Set Covering formulation, because profits are potentially higher than with the usual Set Partitioning formulation, and subsidies are unnecessary. The achieved benefit is then to be distributed amongst the participants of the auction, a process which is known as profit sharing. The literature on profit sharing provides various desirable criteria. We focus on three main properties we would like to guarantee: Budget balance, meaning that no more money is distributed than profit was generated, no negative transfers, which guarantees to each player that participation does not lead to a loss, and the core property, which provides every subcoalition with enough money to keep them from separating. We characterize all profit distributions that satisfy these three conditions by a monetary flow network and establish a connection to the famous VCG payment scheme (Clarke in Public Choice 18:19ff, ; Groves in Econometrica 41:617-631, ; Vickrey in J. Finance 16:8-37, ) and the Shapley Value (Shapley in Kuhn & Tucker (Eds.), Contributions to the Theory of Games, vol. II, pp. 307-317, ). Finally, we introduce a novel profit sharing scheme based on scaling down VCG discounts using max-min fairness principles to achieve budget balance. It approximates the Shapley Value linearly in the number of bundles and can be computed efficiently. [ABSTRACT FROM AUTHOR]

A number of factors, including environmental legislations and increasing global uncertainties, have led many companies to consider engaging in remanufacturing. In this paper, we mainly address a topical issue of choosing the appropriate reverse channel format for collecting used products from customers. We suppose a manufacturer who has three reverse hybrid collection channel structures to choose: (1) manufacturer and retailer collecting used products at the same time, (2) manufacturer contracting the collection of used products to a retailer and a third party, and (3) manufacturer and third party collecting used products at the same time. To generate managerial insights into this important issue, we develop a structural model to explore the appropriate reverse channel structure for the manufacturer. Numerical examples are presented to demonstrate the applicability of the presented model. The results show that, ceteris paribus, the manufacturer and the retailer hybrid collection channel is the most effective reverse channel structure for the manufacturer. We also find that, under the same conditions, the manufacturer and the retailer hybrid collection approach is obviously superior to the single channel collection approach. Finally, we explore the channel coordination mechanism to implement channel cooperation for the manufacturer and the retailer. Our results indicate that the strategic alliance between the manufacturer and the retailer can effectively achieve the desired channel coordination. Furthermore, the Nash bargaining model is utilized to implement profit sharing for the manufacturer and the retailer in the channel coordination of strategic alliance. [ABSTRACT FROM AUTHOR]

In Kleinberg and Weiss, Math Soc Sci 12:21-30 (), the authors used the representation theory of the symmetric groups to characterize the space of linear and symmetric values. We call such values 'membership' values, as a player's payoff depends on the worths of the coalitions to which he belongs and not necessarily on his marginal contributions. This could mean that the player would get some share of $$v(N)$$ regardless of whether or not he makes a marginal contribution to the welfare of society. In this paper it is demonstrated that the set of (non-marginal) membership values include those that embody numerous widely held notions of fairness, such as partial 'benefit equalization', individual rationality and 'greater rewards follow from greater contributions', where one's contributions are not measured marginally. We also present a very simple and revealing way of interpreting all values, including those having a marginal interpretation. Finally, we obtain a mapping which effectively embeds the space of marginal values in the space of all membership values. [ABSTRACT FROM AUTHOR]

In the framework of cooperative games with coalition structure, it studied the problem of profit allocation by introducing lattice structure based on the situation that all the coalitions are not feasible. First, it generalized five properties which Owen value satisfies and then gave the definition of restricted Owen value by two step allocation. It proves that Owen value satisfies some properties, such as additivity, efficiency, symmetric with coalitions, dummy player property and so on. Finally, it gave an example to verify the allocation method in the paper. [ABSTRACT FROM AUTHOR]

Along with globalization of the construction market, international construction firms often choose to cooperate with local construction firms in the form of Joint Ventures (JV) when they enter into the domestic markets of different countries. In this way, they cannot only reduce investment risks, but also enhance production efficiency, reduce costs and generate more profits. The conventional method of profit-sharing between JV firms is based on ratio of investment. However, as the firms make different contributions to the project, the rationality of such a profit-sharing method is often doubtful and thus is difficult to maintain a stable cooperative relationship for a JV team. Based on the concept of the cooperative game theory, this paper proposes a contribution-based profit-sharing model using Shapley Value. A case study is used to describe how firms can use this model to reach decisions of participation, and determine a fair profit-sharing rule after cooperation to enhance mutual trust and create the advantages of cooperation. [ABSTRACT FROM AUTHOR]

The highly distributed and frequently changing resources, as well as the rising costs and uncertainties of developing and launching new products necessitate that firms continuously collaborate in R&D projects. However, management of new product development, especially the leadership assignment of the sustainable collaboration between firms, presents a new set of challenges in sharing the benefits of innovation. This paper conceptualizes and formulates a sustainable collaborative R&D project involving two firms with diverse R&D and leadership technologies. Based on game theory, it examines the optimal mechanism of profit allocation and leadership distribution from a sustainability perspective that outweighs investigating them alone. The analysis shows that when leadership is technically impossible, the optimal profit allocation to each firm should be positively related to its comparative importance in the collaborative innovation project. However, when the two firms are much dependent on each other to complete the project, the focal firm, which is usually more important in the project, needs to give up more its profit shares to the partner firm to lighten the bottleneck R&D effects and induce a sustainable collaboration with partner firm. In contrast, when leadership is technically possible, the optimal leadership distribution for sustainable and effective collaboration depends on the interplay relationships between each firm's comparative importance in the collaborative R&D project, leadership ability, and the R&D and leadership efforts and costs. Furthermore, it is also found that distributing leadership to a firm with absolute dominances is always preferred to distributing to a firm with absolute weaknesses in both R&D and leadership technologies. • A higher degree of teamwork tends to result in a more equal profit allocation scheme. • One firm with lower R&D costs will not only increase the value of its own efforts but also its partner firm's efforts at a slightly lower rate. • The optimal sustainable profit allocation held by each firm should be positively related to its relative importance in the collaborative R&D project. • The less important firm should be allocated more profits than proportional to its relative importance in the project. • It is optimal to let the firm with both advantages in R&D and leading technologies to be the leader of the sustainable collaborative R&D project. [ABSTRACT FROM AUTHOR]