However, the implementation of PC requires corresponding costs [ 8 ], which leads to the fact that both parties are not necessarily willing to perform PC. Does the improvement of project performance offset the cost of fulfilling PC? And why construction participants choose to fulfill PC, and why not?
However, there is a lack of description and analysis on the psychological contract and its complex process and formation between buyer and supplier of construction projects. In order to solve this problem, this paper first reviews the basic concepts of PC. Through literature review, we illustrate how PC affects project performance.
Then, based on the basic assumptions obtained from literature review, this paper proposes a model of the impact of PC on construction performance between buyer and supplier of construction projects. The model analysis uses game theory, including evolutionary game theory and repeated game theory. We believe that this study will contribute to maintain PC and improve project performance in construction projects.
The major innovations and contributions of this paper are as follows: 1 Based on the basic assumptions obtained from literature review, a model about the influence of PC on construction project is proposed.
However, Argyris proposed the concept without discussing the specific definition. Rousseau described the PC as the unwritten expectations distinct from the formal contract between the employee and the employer and regarded PC as a kind of unidirectional belief of employees, which is highly subjective and can be particular to each employee [ 10 ].
The basis of PC is the reciprocal relationship between enterprises and employees, that is, mutual perceived obligations and expectations between organizations and employees [ 13 ]. Essentially, PC is an unwritten agreement between organization and its employees based on mutually accepted commitments and obligations [ 14 ].
Many scholars believe that PC used between employees and employers can also be used for relationship between organizations [ 15 — 18 ]. The organizational PC, also known as the interorganizational PC, is a perception of mutuality, which is the belief of one party in the transactional exchange about the obligations that other parties should have [ 19 ]. It is worth noting that interorganizational PC may or may not differ from the expectations understood by other parties [ 16 ].
Thus, it may suffer from incongruences between parties [ 16 ]. No matter the PC between individuals and organizations, or the PC between organizations and organizations, the contents of the PC are so complicated that we could not list them all [ 20 ].
Although the specific contents cannot be listed one by one, the PC can be divided into transactional type and relational type, which has been accepted by many scholars [ 12 , 21 ]. The transactional PC is based on the exchange of economic interests, while the relational PC is based on the exchange of emotions [ 12 ].
For construction projects, the previous researches are shown in Table 1. Some scholars have studied the PC of both sides of project procurement and found that PC had a significant impact on fairness, trust, satisfaction, and project performance [ 5 — 7 ]. As a special form of procurement, the PC between important stakeholders public sector and supplier will affect sustainable project management and sustainability of project development.
However, unwritten psychological contracts are often ignored by stakeholders [ 5 , 6 ]. In previous study, some scholars thought the PC of construction procurement including unwritten perception and unwritten behaviors.
The unwritten perception mainly includes trust, commitment, good faith, and fair dealing, and the unwritten behaviors mainly include initiating behaviors, signaling behaviors, and disclosing behaviors [ 5 , 6 ].
These unwritten perceptions and unwritten behaviors can affect satisfaction of both parties [ 5 , 6 ]. In addition, the satisfaction of both parties can affect the performance of construction projects [ 34 ]. The influence of PC on project performance was also confirmed by Han [ 7 ].
Mutual trust has been proved by many scholars to have a significant impact on project performance [ 35 , 36 ]. In addition, commitment [ 36 , 37 ] and fairness [ 38 ] also have a significant impact on project performance. As a part of psychological contract, trust, commitment, and fairness have an impact on project performance, which also proves that PC has an impact on project performance.
This paper summarizes previous studies and obtains the impact of PC on construction project performance, as shown in Figure 1. Game theory is a branch of applied mathematics that deals with interactions between rational players [ 39 ]. Many classic problems of game theory are familiar, such as the prisoner's dilemma [ 40 ] and asymmetric games [ 41 ].
Human reason is limited [ 42 ], so humans lack foresight in individual or group decision-making [ 43 ]. Nash, based on the finite rationality of human beings, has made great progress in evolutionary game [ 43 ]. Evolutionary games, also known as finite rational games, mean that players are unable to find the optimal strategy from the start and try to improve their behavior choices through trial and error [ 44 ].
Furthermore, bounded rationality means that, in general, at least some of the players will not use the strategy of a perfectly rational game. Any resulting equilibrium will be upset by these deviations. Therefore, the core of evolutionary game is not the optimal choice of strategy, but the process, trend, and stability of strategic adjustment [ 40 ].
Generally speaking, game theory can be divided into two main types, namely, static game and dynamic game [ 45 ]. When the player takes only one action, it is called a static game; conversely, while the player takes many actions, it is called a dynamic game. Repeated game is a dynamic game [ 46 ], which can be divided into two types, namely, whether the time range is limited or infinite [ 47 ].
An experiment showed that repeated games are helpful to the evolution of cooperation between two parties [ 48 ].
In recent years, evolutionary game and repeated game have been widely used in construction projects. Some scholars have used evolutionary game theory to discuss construction projects, including behavioral strategies of buyer and investor [ 49 ], opportunistic behavior of investors in the operation stage [ 50 ], selection of buyer regulation mode in operation phase [ 51 ], public participation in buyer regulation [ 52 ], government incentive strategies of prefabricated construction [ 53 ], and how to enhance stakeholder cooperation [ 54 ].
For repeated games, Tserng et al. These above results have important contributions. However, these games only consider the game within the scope of the contract, without considering the factors outside the contract, that is, the impact of PC on construction projects.
In addition, the joint analysis of evolutionary game and repeated game is applied to construction projects for the first time. In order to construct the game model, the following assumptions are made based on the above analysis.
H1: The two participants in the evolution game are the buyer and the supplier, both of which have valued their reputations as much as their economic interests [ 56 ]. H2: The fulfillment of the buyer or the supplier needs to pay cost [ 8 ]. H3: If one side fulfills PC, and another fails to do it, the commercial reputation of breaching party will be destroyed, and vice versa [ 57 ].
H4: As long as either participant chooses nonfulfillment, PC of the other participant will be broken, the relationship will be damaged, and the project performance will decline [ 7 ]. H5: When both participants fulfill PC, the project performance will increase [ 7 ]. According to the basic assumptions above, set the following parameters all greater than zero : 1 In case the supplier fulfills PC, the benefits of the buyer are R.
In case the buyer fulfills PC, the benefits of the supplier are W. If the buyer fulfills PC, and the supplier fails to fulfill PC, the cost of the supplier's damaged commercial reputation is T 2.
The model is the result of simplification choices made by the modeler, which selects only the parameters that seem to be the most relevant and may not have absolute faith in their values [ 59 ].
So, this model might be a little bit different from reality, but it could reflect the main status. From the above analysis, the following can be concluded: 1 As long as the buyer or supplier perceives that the other party does not fulfill PC, neither party will fulfill PC, because PC, as a kind of implicitness, without legal constraints, is extremely easy to break.
When one party perceives that the other party does not fulfill PC, PC will be broken. In other words, if one party fulfills PC, the other party may not fulfill PC. Then, as long as the buyer fulfills PC, the supplier can often fulfill PC. However, the performance of construction project is often not linked to the buyer or has little impact on the buyer; that is, P 1 and D 1 are relatively small.
Second, delays occur. All these tactics are designed to rattle the advantaged player and get it to reduce the price. She had a good relationship with the CEO of a medium-sized chemical company and had done a lot of work with the customer over the years. Martha held firm. You can ask tough qualifying questions to try to become a serious contender for the business, or you can walk away and not waste your time.
The only question is whether you want to bluff hard, as Martha did, and stick to your price. The alternative is soft bluffing. You have 1 free article s left this month. How do we explain the growth in spending on out-of-home activities and cell phone-related entertainment? The first is a likely barometer of improving overall consumer confidence while the second may reflect a broader shift toward mobile in how consumers invest their media and entertainment dollars.
Given the popularity of games as a paid form of content on mobile devices Angry Birds, etc. The same logic may apply to the other categories that experienced slight declines in share. The screen is shifting but the content may be the same. Video game buyer households account for 26 percent of U. The G reputation does not change in one time step if the paired buyer decides to buy with probability and correctly assign G to with probability or, decides not to buy with probability.
Otherwise, 's reputation turns into B. When has reputation B, it is unchanged if decides to buy with probability and commit assignment error with probability , or decides not to buy with probability. Otherwise, 's reputation turns into G. Therefore, the transition matrix of the Markov chain is represented as 16 where represents the transition probability from state to state , and we associate G and B with states 1 and 2, respectively.
Because is a nondegenerate right stochastic matrix, we can decompose using the left and right eigenvectors corresponding to eigenvalue 1 as 17 where is the other eigenvalue of , and and are the left and right eigenvectors corresponding to , respectively. We do not calculate , , and because their values are immaterial in the following arguments.
Note that the eigenvectors are normalized such that 18 Assume that the C seller initially has reputation G and B with probability and , respectively, where. Then, the probability that 's reputation is G and B after playing games is given by the first and second columns of , respectively. The expected payoff for in a single game is equal to multiplied by the probability that decides to buy.
Therefore, the expected payoff for per single game, averaged over , converges in the limit to 20 21 22 which reproduces Eq. The expected payoff for the D seller, given by Eq.
Next, we calculate the payoff for a Buy buyer. In each time step, the expected number of C seller with reputation G and B with whom is paired is equal to the first and second columns of , respectively. When the C seller has reputation G B , the expected payoff for in a single game is equal to. Therefore, the contribution of the C seller to the expected payoff for per single game, averaged over games, converges to 23 This quantity is equal to the first term on the right-hand side of Eq.
Analogous calculations for the case of D seller yields the second term on the right-hand side of Eq. Here is the end of the proof. Based on the expected payoff determined by Proposition 1, we identify the equilibria of the game.
In the analysis, we exploit the fact that is linear in and. There are three types of Nash equilibria. The so-called uncooperative equilibrium is composed of NoBuy and the D seller.
In the so-called cooperative equilibrium, Buy and Disc are mixed in the buyer's strategy and the probability of C is large in the seller's strategy. The cooperative equilibrium corresponds to the situation in which buyers and sellers do not repeatedly interact but trust each other on the basis of the reputation mechanism.
When it exists, it coexists with the uncooperative equilibrium. The other equilibrium appears only for a singular parameter set. Therefore, we are not concerned with it in the later analysis. The asymmetric trust game with a reputation mechanism whose expected payoffs are defined by Eqs. We remark that the cooperative equilibrium is called so because. We prove Proposition 2 in the next section. It should be noted that extending the concept of the evolutionary stability to the asymmetric game is not straightforward.
In the matrix game, a strictly i. Nevertheless, Proposition 2 dictates that the cooperative equilibrium is an asymptotically stable strictly mixed strategy. This is possible because the payoff values are density-dependent in our model; it is not a matrix game. Therefore, we directly prove that the cooperative equilibrium is asymptotically stable in the replicator dynamics.
We identify all the mixed-strategy Nash equilibria of the asymmetric game whose payoffs are given by Eqs. Consider a possible equilibrium composed of a single buyer's strategy. Therefore, must be satisfied in a possible Nash equilibrium.
When , Eq. Therefore, the combination of NoBuy and D seller is the only strict Nash equilibrium allowed in this regime. We call this equilibrium the uncooperative equilibrium. Suppose instead that there is only Disc. If 33 where and , we obtain for any. Substituting Eq. Therefore, the combination of Disc and Eq.
If Eq. If , substituting and in Eqs. When Eq. In conclusion, the only pure strict Nash equilibrium is the uncooperative equilibrium composed of NoBuy and D seller. Consider the mixed strategies i. If we select two strategies out of Buy, AntiDisc, and NoBuy, we can show in a manner similar to the case of the one buyer's strategy.
In this case, must hold true in the equilibrium. Equation 12 with indicates that the payoff for NoBuy is larger than that for AntiDisc, which is larger than that for Buy. Therefore, such a mixed-strategy Nash equilibrium, in which the payoff for the two strategies of buyers must be the same, does not exist. This implies that Disc must be selected as one of the two buyer's strategies in a possible Nash equilibrium.
Mixture of Buy and Disc: cooperative equilibrium : Consider a mixture of Buy and Disc, which we call the cooperative equilibrium. Note that 40 41 Because must be satisfied in the Nash equilibrium, the coefficient of in Eq. This condition combined with yields 42 and 43 Equation 43 replicates Eq.
The mixture of Buy and Disc is equivalent to. The inequality is always satisfied if note that the denominator of Eq. The inequality is equivalent to Eq. Given Eq. NoBuy gains a smaller payoff than Buy and Disc if the coefficient of in Eq. The substitution of Eqs. Therefore, NoBuy gains a smaller payoff than Buy and Disc. Because implies , AntiDisc also gains a smaller payoff than Buy and Disc in the cooperative equilibrium.
Consider the invariant subspace of the strategy space where only Buy and Disc buyers and C and D sellers exist. The mixed strategy specified by is a Nash equilibrium when the buyer's strategies are restricted to either Buy and Disc because and.
Because , is a Nash equilibrium when all the four types of buyer's strategies are allowed. The inequality also assures that, under the replicator dynamics, the cooperative equilibrium is asymptotically stable against the introduction of an infinitesimal fraction of AntiDisc or NoBuy. Therefore, we are left to show the asymptotic stability of the cooperative equilibrium within the abovementioned two-dimensional subspace parametrized by and.
For the sake of the linear stability analysis, we take and as the independent variables and linearize Eqs. The Jacobian in the equilibrium is given by 46 where all the derivatives are evaluated at , and 47 48 49 50 The necessary and sufficient condition for the cooperative equilibrium to be stable under the replicator dynamics is given by and.
By substituting Eqs. Therefore, the cooperative equilibrium is asymptotically stable under the replicator dynamics. Because is linear in and , the coefficient of and that of must be the same for Eq. If both coefficients are positive, the payoff for Buy is larger than that for Disc and AntiDisc in this equilibrium. If both coefficients are negative, the payoff for NoBuy is larger than that for Disc and AntiDisc in the equilibrium. In either case, the mixture of Disc and AntiDisc cannot be Nash.
Therefore, the coefficient of in Eq. From and , we obtain 57 and 58 If in the equilibrium, Disc NoBuy in a mixed strategy in which there are slightly more less probability of Disc than in the equilibrium obtains a larger payoff than NoBuy Disc. In this case, is not Nash because such a slightly modified mixed strategy of the buyer obtains a larger payoff than.
On the basis of the relationship , which is derived from Eq. Using the fact that the right-hand side of Eq. Therefore, the mixture of Disc and NoBuy is not Nash. If three or four buyer's strategies are mixed in an equilibrium, their payoffs must be identical. Therefore, the coefficient of and that of in Eq. Because , this relationship is not satisfied when the image scorer exists i. When , we obtain by substituting and derived from Eqs.
Therefore, must hold in the equilibrium. In this situation, Eq. Consequently, three or four buyers' strategies cannot be mixed in an equilibrium. In a case with only indifferent scorers i. Therefore, the uncooperative equilibrium is the only Nash equilibrium. This outcome is expected because, under indifferent scoring, the players perform the usual trust game [28] — [31]. When there are only image scorers i.
In the limit , the equilibrium probability of Buy i. In the parameter region in which black region in Fig. In the cooperative equilibrium, the fraction of Buy is large for a large or a small. In particular, irrespective of the value of. In the limit , the trust game is a weak social dilemma such that the D seller's payoff is only infinitesimally larger than the C seller's payoff.
The advantage of the D seller is offset by the B reputation that the D seller receives from just a small fraction of Disc buyers i.
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