PROFIT DISTRIBUTION IN IPD PROJECTS BASED ON WEIGHT FUZZY COOPERATIVE GAMES

Integrated Project Delivery (IPD) is regarded as an effective project delivery method that can deal with the challenge of the rapid development of the architecture, engineering, and construction (AEC) industry. In the IPD team, the alliance profit is not distributed fairly and effectively due to uncertainty, preventing the achievement of the IPD project goals. This study focuses on optimizing the profit distribution among stakeholders in IPD projects and uses quadratic programming models to solve fuzzy cooperative games in the IPD. A payoff function is used in the fuzzy alliance to determine the characteristics of the interval-valued fuzzy numbers, and different weights of the alliance and the efficiency of the player’s participation in the IPD are considered in the profit distribution. A case study is conducted, and the results of the proposed method are compared with those of crisp cooperative games. The results show that the fuzzy cooperative game increases the profit of participants in IPD projects. It is more practical to use weight fuzzy cooperative games than crisp games to express imputation. Moreover, the quadratic programming models and methods result in a fair and efficient profit distribution scheme in IPD projects.

Using Shapley Values and Genetic Algorithms to Solve Multiobjective Optimization Problems

This paper proposes a new methodology to solve multiobjective optimization problems by invoking genetic algorithms and the concept of the Shapley values of cooperative games. It is well known that the Pareto-optimal solutions of multiobjective optimization problems can be obtained by solving the corresponding weighting problems that are formulated by assigning some suitable weights to the objective functions. In this paper, we formulated a cooperative game from the original multiobjective optimization problem by regarding the objective functions as the corresponding players. The payoff function of this formulated cooperative game involves the symmetric concept, which means that the payoff function only depends on the number of players in a coalition and is independent of the role of players in this coalition. In this case, we can reasonably set up the weights as the corresponding Shapley values of this formulated cooperative game. Under these settings, we can obtain the so-called Shapley–Pareto-optimal solution. In order to choose the best Shapley–Pareto-optimal solution, we used genetic algorithms by setting a reasonable fitness function.

Sufficient condition for nondominated maximin strategy of arbitrary player with terminal payoff function in two-step positional game of n persons with strategies-syntheses and finite sets of controlling actions of players

Two-step positional game of $n$ persons with strategies-syntheses, $n\geqslant 2$, and finite sets of controlling actions of players is investigated. Sufficient condition for nondominated maximin strategy of arbitrary player, whose payoff function is terminal, has been obtained.

The characteristics of average abundance function with mutation of multi-player threshold public goods evolutionary game model under redistribution mechanism

Background In recent years, the average abundance function has attracted much attention as it reflects the degree of cooperation in the population. Then it is significant to analyse how average abundance functions can be increased to promote the proliferation of cooperative behaviour. However, further theoretical analysis for average abundance function with mutation under redistribution mechanism is still lacking. Furthermore, the theoretical basis for the corresponding numerical simulation is not sufficiently understood. Results We have deduced the approximate expressions of average abundance function with mutation under redistribution mechanism on the basis of different levels of selection intensity $$\omega$$ ω (sufficiently small and large enough). In addition, we have analysed the influence of the size of group d, multiplication factor r, cost c, aspiration level $$\alpha$$ α on average abundance function from both quantitative and qualitative aspects. Conclusions (1) The approximate expression will become the linear equation related to selection intensity when $$\omega$$ ω is sufficiently small. (2) On one hand, approximation expression when $$\omega$$ ω is large enough is not available when r is small and m is large. On the other hand, this approximation expression will become more reliable when $$\omega$$ ω is larger. (3) On the basis of the expected payoff function $$\pi \left( \centerdot \right)$$ π ⋅ and function $$h(i,\omega )$$ h ( i , ω ) , the corresponding results for the effects of parameters (d,r,c,$$\alpha$$ α ) on average abundance function $$X_{A}(\omega )$$ X A ( ω ) have been explained.

Time-Consistency of an Imputation in a Cooperative Hybrid Differential Game

This work is aimed at studying the problem of maintaining the sustainability of a cooperative solution in an n-person hybrid differential game. Specifically, we consider a differential game whose payoff function is discounted with a discounting function that changes its structure with time. We solve the problem of time-inconsistency of the cooperative solution using a so-called imputation distribution procedure, which was adjusted for this general class of differential games. The obtained results are illustrated with a specific example of a differential game with random duration and a hybrid cumulative distribution function (CDF). We completely solved the presented example to demonstrate the application of the developed scheme in detail. All results were obtained in analytical form and illustrated by numerical simulations.

Solving Multiobjective Game in Multiconflict Situation Based on Adaptive Differential Evolution Algorithm with Simulated Annealing

In this paper, we study the multiobjective game in a multiconflict situation. First, the feasible strategy set and synthetic strategy space are constructed in the multiconflict situation. Meanwhile, the value of payoff function under multiobjective is determined, and an integrated multiobjective game model is established in a multiconflict situation. Second, the multiobjective game model is transformed into the single-objective game model by the Entropy Weight Method. Then, in order to solve this multiobjective game, an adaptive differential evolution algorithm based on simulated annealing (ADESA) is proposed to solve this game, which is to improve the mutation factor and crossover operator of the differential evolution (DE) algorithm adaptively, and the Metropolis rule with probability mutation ability of the simulated annealing (SA) algorithm is used. Finally, the practicability and effectiveness of the algorithm are illustrated by a military example.

Understanding climate and non-climate decision triggers to minimize Spring rainfall risks in vineyards

<p>Climate services have travelled a long way, however, the last mile still has to be covered until climate information can be appropriately integrated in the users’ decision making processes. When is the signal offered by a seasonal forecast useful? How and when can forecasts influence users’ choices? How does the use of the forecasts compare with the methods currently in place? The answer can vary across users and even across decisions that the same user may take.</p><p>This work analyses these questions through the decision making process of a wine producer aiming at reducing its exposure to spring rain variability. Spring rain drives risks of fungal disease causing crop loss and increased costs related to plant protection and canopy management. A transdisciplinary approach, including experts from various disciplines and the end user, is used to understand how and when a particular wine producer needs to trigger a decision linked to total Spring rainfall in order to reduce the risk entailed for plant protection and canopy management. Based on close collaboration, we construct a payoff function and simulate the decision driven by the choice of different forecasted probability thresholds and the business-as-usual decision, and we finally compare them to the observation. This exercise is repeated over 23 years to try eliciting the optimal threshold.</p><p>The results show that the optimal decision to avoid climate risks is not always a feasible solution, demonstrating that climate is only one of the variables taken into account in the complex decision making context of a business. This highlights the importance of interpreting seasonal forecasts appropriately according to each user's context and understanding how this information will be integrated in the decision processes.  Finally, it calls attention to the importance of co-creation in climate services and the need for extending the collaboration process up to the delivery phase, the so-called last mile.</p><p> </p>

Guaranteed Deterministic Approach to Superhedging: Case of Binary European Option

For the superreplication problem with discrete time, a guaranteed deterministic formulation is considered: the problem is to guarantee coverage of the contingent liability on sold option under all admissible scenarios. These scenarios are defined by means of a priori defined compacts dependent on price prehistory: the price increments at each point in time must lie in the corresponding compacts. In a general case, we consider a market with trading constraints and assume the absence of transaction costs. The formulation of the problem is game theoretic and leads to the Bellman–Isaacs equations. This paper analyses the solution to these equations for a specific pricing problem, i.e., for a binary option of the European type, within a multiplicative market model, with no trading constraints. A number of solution properties and an algorithm for the numerical solution of the Bellman equations are derived. The interest in this problem, from a mathematical prospective, is related to the discontinuity of the option payoff function.

Legitimate equilibrium

We present a general existence result for a type of equilibrium in normal-form games, which extends the concept of Nash equilibrium. We consider nonzero-sum normal-form games with an arbitrary number of players and arbitrary action spaces. We impose merely one condition: the payoff function of each player is bounded. We allow players to use finitely additive probability measures as mixed strategies. Since we do not assume any measurability conditions, for a given strategy profile the expected payoff is generally not uniquely defined, and integration theory only provides an upper bound, the upper integral, and a lower bound, the lower integral. A strategy profile is called a legitimate equilibrium if each player evaluates this profile by the upper integral, and each player evaluates all his possible deviations by the lower integral. We show that a legitimate equilibrium always exists. Our equilibrium concept and existence result are motivated by Vasquez (2017), who defines a conceptually related equilibrium notion, and shows its existence under the conditions of finitely many players, separable metric action spaces and bounded Borel measurable payoff functions. Our proof borrows several ideas from (Vasquez (2017)), but is more direct as it does not make use of countably additive representations of finitely additive measures by (Yosida and Hewitt (1952)).

Synthesis of equilibria in infinite-duration

In this survey, we propose a comprehensive introduction to game theory applied to computer-aided synthesis. We study multi-player turn-based infinite-duration games played on a finite directed graph such that each player aims at maximizing a payoff function. We present the well-known notions of Nash equilibrium and subgame perfect equilibrium, as well as interesting strategy profiles of players as response to the strategy announced by a specific player. We provide classical and recent results about the related threshold synthesis problem.