Simulation of Technology Sourcing Overseas Post-MergerBehaviors inaGlobalGameModel

The abilities to e iciently identify potential innovation profits and formanoptimal post-merger strategy are important in evaluating overseasmerger and acquisition (M&A) performances. The paper uses a global game with asymmetric payo structure and multi-agent simulation method to analyze the optimal overseas post-merger strategy. We model three stages of the M&A processes: merger decision stage, post-merger integration stage, and technology innovation a er M&A, to analyze how di erent resource similarity and resource complementarity of the two companies influence the degree of optimal post-merger integration and target autonomy as well as technology innovation profit a er M&A. The agent-based simulation shows that in overseas M&As, resource similarity has a positive relationwith integration and a negative relationwith target autonomy; however, resource complementarity has the opposite e ect. The negative interaction e ect between resource similarity and complementarity will decrease the degree of integration. In high resource similarity and low resource complementarity M&As, a high integration degree and low target autonomy will maximize innovation profit, while for high resource similarity and high resource complementarity M&As, a medium integration degree and target autonomy is best for innovation profit. For low resource similarity and high resource complementarity M&As, a low integration degree and high target autonomy will be the best post-merger strategy. Model outputs are robust to variations of the parameters.


Introduction
. The use of overseas M&As is a feasible way of seeking external resources to upgrade a company's global competitiveness and technology innovation ability.However, due to cultural di erences, di erent management patterns and technology gaps, acquiring companies may face huge di iculties in transforming core technology, such as patents.Without a powerful post-merger strategy, acquiring companies are more likely to miss the opportunities to make technology innovation, leading to merger failures.
. The post-merger process involves resource deployment of the two companies and characteristic identification of the resource backgrounds.By positioning of the competitive resources and analyzing the cooperation in post-merger process, the positioning school (Mintzberg et al. ) of strategic management suggested that we could evaluate the post-merger process or M&A performances based on firms' resource backgrounds, which are resource similarity and resource complementarity (Cartwright ; Chatterjee ; Haspeslagh & Jemison ; Larsson & Finkelstein ).For resource similarity, Homburg & Bucerius ( ) suggested that resource similarity means that the two companies have a high degree of overlap in technology and the product market.In contrast, resource complementarity is a relationship in which upgrading a resource improves another resource's performance (Milgrom & Roberts ).It is worth noting that a very prominent research stream in strategic management literature presumes the strategic fit on the perspective of resource backgrounds as decisive for M&A success (Bauer & Matzler ).M&A benefits acquirers and targets through synergy from related resource backgrounds (Barney ; Singh & Montgomery ).Additionally, the resources of the two companies can have a synergistic e ect only under the proper degree of integration (Zaheer et al. ).Studying post-merger strategy based on the perspective of resource similarity and complementarity plays a key role in identifying important resources, promoting post-merger synergistic performances and realizing the goal of improving technology innovation in overseas technology sourcing M&A.

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Post-merger integration is the foundation of realizing synergy e ect of the M&A (Seth ).In previous studies, existing literature focuses on two dimensions, the integration level and target autonomy in the post-merger process.Integration means degree of structural unity (Pablo ) while target autonomy is whether the target company can retain the ability to operate as before or not (Datta & Grant ).The relationship between integration degree and target autonomy are neither opposite nor isolate.One should consider integration and target autonomy together as suggested by Haspeslagh & Jemison ( ).
. With respect to the degree of integration, technology resource similarity can reduce integration risk and increase predictability of potential technology performance(Lubatkin et al. ) which when combined with a high integration degree will improve the e iciency of resource deployment and gain synergy e ect (Puranam et al. ).High integration degree of similar resource gain synergy e ect in that the similar knowledge backgrounds, technology, language and cognitive structure will promote knowledge di usion or sharing (Makri et al. ) and technological overlap contributes the most in gaining synergy e ect (Bena & Li ).In contrast, resource complementarity has di erent e ect on integration degree.Colombo & Rabbiosi ( ) showed that a low degree of integration stimulates innovation when the product market is complementary.On the one hand, complementary resources gain synergy e ect in the integration process by boosting sales output, reducing average R& D costs and promoting technology innovation (Puranam et al. ).Makri et al. ( ) empirically showed that technology complementarity promotes innovation output through new product development in particular.On the other hand, the di erences brought by resource complementarity, if not e iciently integrated, will prevent synergy in value creation (Kim & Finkelstein ).
. As for target autonomy, existing literature suggests a low level of target autonomy when resource similarity is high (Datta & Grant ) because when two companies have a high level of resource similarity, a high level of target autonomy is not likely to result in good potential performance (Zaheer et al. ).Target autonomy is crucial to complementary resource because lacking a certain level of autonomy, technical personnel will not work as hard as before, which results in ine icient innovation performance (Paruchuri et al. ; Kapoor & Lim ).
. Post-merger gains depend on whether the agents make post-merger e orts.If both sides make the post-merger e ort, they both get synergy benefits; otherwise, they can only gain non-synergy benefits (Banal-Estañol & Seldeslachts ).Due to information asymmetry, either company can overvalue its private information of potential innovation output a er M&A and wait for the other side to make the integration e ort.The previous literature on resource backgrounds has two shortcomings.First, these studies mainly focused on either resource similarity or resource complementarity without considering their potential interaction.Second, financial-level theoretical and empirical studies cannot simulate agents' complex interactions and dynamic resource deployments.Here, multi-agent simulation can somehow overcome the problem.
. Multi-agent simulation is a loosely coupled network problem-solver.Interactions between solvers can resolve the problems that no single solver has the ability or knowledge to solve.It can simulate heterogeneous agents' actions and predict the steady state of the equilibrium considering the interactions of the agents.Agent-based modeling has been a powerful simulation technique which has wide real-world applications such as flow simulation, organizational simulation, market simulation and di usion simulation (Bonabeau ) and its repetitive competitive interactions between agents make us possible to explore dynamics out of the reach of pure mathematical methods and provide an emergent phenomenon of how the resources of the acquirer and the target company lead to di erent integration behaviors dynamically.Therefore, using multi-agent simulation to involve agent-level information exchange and interaction behaviors will provide a new perspective for us to figure out what matters in technology-sourcing overseas M&A integration and innovation output.With multiagent simulation, we can study how companies make merger decisions and post-merger decisions when facing huge cultural di erence and information asymmetry.Also, during the simulation we can provide a whole picture about what individual agents' information acquisition process can bring to the new innovation endowment combinations and increase innovation profits dynamically.

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Based on global game analysis (Carlsson & van Damme ), one company's payo is influenced by the other company's signal regarding action and information uncertainty.A company gathers its private information signal and the public signal to forecast the other side's actions.Furthermore, we try to link multi-agent simulation with global game under NetLogo . .(Wilensky ).By building the merger strategy (whether to engage in a M&A or not) and post-merger strategy (whether to make post-merger integration e ort or not) for the acquiring firm and the target firm, we introduce an innovation information signal based on resource background into the multi-agent simulation process for the first time according to our knowledge, which e ectively improves the static perspective in post-merger studies.
. The paper is as follows: Section is the basic global game model.It models firms' behaviors in merger decision period, post-merger period and technology innovation period.With equilibrium analysis we show how resource similarity and resource complementarity can influence the integration degree and target autonomy.Section is the simulation test.We first give the numerical simulation to ascertain the real cuto points in the switching strategies.Furthermore, we test the optimal integration degree and target autonomy under di erent resource backgrounds to maximize innovation profits.Section is the robustness checks.We first show whether changes to the key parameters -resource similarity and resource complementarity -can influence the model outputs.
Then we analyze sensitivity for the parameters, considering single-factor and global changes as part of Latin Hypercube Sampling uncertainty test.Section presents the discussion and conclusion, including limitations of the study and future work.

Basic Model
. Merger activity contains three stages: the merger decision period, post-merger integration period and technology innovation a er M&A.During a merger decision, there is public information about the potential innovation profit signal, and the two firms decide whether to merge.During post-merger integration period, the firms get their own private information about the innovation profit signal and choose whether to make the post-merger e ort.

Merger decision period .
In the M&A decision stage, there is a uncertain information, θ, indicating the post-merger innovation payo in the market.In particular, θ is based on the resource backgrounds (resource similarity and complementarity) of the two sides.Neither the acquirer nor the target knows the true value of θ, but a public information signal of the value is available.We set the public information using the uniform distribution: θ ∼ U (y + l, y − l) , where y is the public signal and l stands for signal noise.Acquirer A makes a proposal to target company B, and B chooses whether to take it or not.
. We set the resource level of the firms, which is expressed as R i , i = A, B. If the merger takes place, the merger gain is a combination of innovation gain, post-merger gain, and the merger cost, K i .If no merger takes place, the firms hold their own resource level without any change.
. We set acquiring firm's gain as θ A + (R A + R B )λ(θ A ) − K A .Specifically, the merger payo comes from merger innovation payo θ A minus the fixed merger cost K A , which catches the conflicts in the integration process caused by giving the target firm some certain level of target autonomy.Post-merger payo comes from the integration of the two firms' resources in the form of (R A + R B )λ(θ A ), where λ(θ) stands for the probability of integration, which depends on θ A .
. For the target firm, its merger payo is given as θ B + R B w(θ B ) − K B , where the first part stands for potential innovation payo and the second stands for post-merger payo , the probability of obtaining a certain level of target autonomy in dealing with its own resource R B .Here, the autonomy is given as w(θ B ) and it is a function of θ B , where acquirer A chooses to give the target company B some autonomy based on A's expectation of the potential innovation profits that B can make.K B is the fixed merger cost.
Post-merger integration period .
If the two companies agree to make the deal, they come to the integration stage.In this stage, the acquirer knows the true value of the two companies' resource backgrounds, and target company B knows its own true value.They get a private signal x i = θ + i , where i ∼ U (−l, l) and i is i.i.d.
. Like Farrell & Shapiro ( ), we assumed that if the two sides both make an integration e ort, their integration payo s are V .Otherwise, if either side or both does not make an e ort, in these circumstances both sides can only gain non-synergy payo which is V d .Here, d stands for resource complementarity and is based on Banal-Estañol & Seldeslachts ( ).We set d > 2.
. The acquirer's integration payo is V + kr − dt1 if both make integration e orts.Here, k stands for resource similarity, and k > 1, r is a similar resource's scale payo .The target's integration payo is V − ke − dt2.Similar resource integration transforms the resource from the target to the acquirer.Here, r and e stand for the acquirer's gain and the target's loss from the integration of a similar resource, respectively.And t1 and t2 stand for each company's cost for integrating complementary resources.Since the target firm is more powerful and has a high level of technology, it integrates complementary resource more easily than the acquirer, and hence we set t1 > t2.Here we have V + kr − dt1 < 0 and V + kr − dt1 − dt2 < 0, V − ke − dt1 − dt2 > 0. Thinking about helping the other side make integration e ort with the complementary resource, the target has the ability to do so, but the acquirer does not have the incentive to do this because in technology sourcing overseas M&A the acquirer company has a comparative disadvantage over the target company in technology and production abilities.

Equilibrium analysis
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We build a binary variable m and set m = 1 if the merger happens and m = 0 otherwise.The expected gain in the merger decision period π i for a company is as follows: .
The company chooses whether to engage in a merger according to m = argmaxπ.We then build a binary variable s; if an agent makes an integration e ort, s = 1, and otherwise, s = 0.The expected gain in the post-merger decision period for a company is as follows: .
Company i has an integration strategy cuto point xi : if In the postmerger integration process, company i makes integration e ort only when Similarly, company i decides to engage in a merger only when θ i ≥ θi .
. Given private signal x i and public signal y, for company A, θ i |x i , y ∼ U (x i − l, x i + l).Firm A will engage in the merger process only if its potential innovation payo signal is higher than the merger switching strategy cuto point (which is θ A ≥ θA ).So the probability of firm A to engage in a merger is as follows: .
When the private signal satisfies x i = xA , the payo s of whether an integration e ort is made or not are of the same level : .
From Equation and Equation , we get: .
When θ A = θA , the payo s of whether engaging in a merger or not are of the same level: .
Equation is the same as: In the integration stage, both sides know their true private signal θ and they decide whether to make integration e orts or not in the post-merger integration period.If the acquirer company chooses to engage in a post-merger integration process which means x A ≥ xA , then the probability of making the integration e ort by the acquirer company is as follows: .
Equation suggests that when xA − θ A is larger, the post-merger integration probability is lower.In other words, compared to merger decision strategy θ A , when post-merger integration cuto point xA is high, the acquirer company does not prefer to make a post-merger integration e ort, which lowers the probability of integration.Equations , , show that: .
Firm B thinks the merger will happen according to a probability based on knowledge of the innovation signal.
. When private signal satisfies x i = xB , the payo s of whether an integration is made or not are of the same level, that is: .
Combine equations and , we obtain equation : .
When θ B = θB , the payo s of whether a company engages in a merger are of the same level: .
Equation is the same as: For company B, the concept of autonomy makes sense only when the M&A comes into the integration period.
That gives the target a certain level of autonomy with a probability: .
Equation suggests that when xB − θ B is larger, the target autonomy is lower.In other words, compared to merger decision strategy θ B , when post-merger integration cuto point xB is high, the acquired company does not prefer to make post-merger integration e ort.In this circumstance, the acquirer company would lower target autonomy by taking more controls over the production or sale process to compensate for the risks induced by target company's e ortless behaviors.With equations , , and we get the following equation:
We conducted comparative statics analyses (Appendix A provides the maths and economic salience of the analysis) of Equations and .Then, we determine some hypothesis about the integration and autonomy.
As the resource similarity level between an overseas M&A target and acquirer increases, the probability that the acquirer makes an integration e ort increases.When resource complementarity is high, the probability is lower.
In overseas M&As, when the resource similarity level increases, the probability that the target gets a certain level of autonomy decreases.With an increase in resource complementarity, the probability that a target receives autonomy increases.

H . δλ(θ A )
δkδd < 0. The interaction between resource similarity and complementarity will decrease the degrees of integration.
H . δ xA δk < 0, δ xA δd > 0. The post-merger integration cuto point is lower when resource similarity increases and is higher when resource complementarity increases.

Technology innovation output a er M&A .
Let T represent the number of new innovation combination a er the integration.The innovation output comes from the redeployment of the resources of the two firms.The integration process is built up on a search and matching process according to the firms' resource backgrounds.Given the theoretical and application literature of the search and matching model setups, we choose the constant return Cobb-Douglas function: Here, n is the elasticity of search and matching behaviors to innovation combinations and n ∈ (0, 1).Here, s stands for searching intensity, the degree of how intensive the searching behaviors are, and s > 0. N b, N s is the proportion of total resource of the acquirer and the target.
Post-merger integration is a process of the redeployment of the resources of the two firms and can be described as the change rate of the resources in acquirer and target firms.Ib, Is represents the change of the resources during the post-merger period, and they also stand for their abilities to integrate: Is, Ib ∈ (0, 1).We set the integration degree of the M&A to be the weighted average of Is and Ib in the form of I = IbN b + IsN s, I ∈ (0, 1).We set the integration ability of the M&A to be IA = Ib + Is, which is the sum of the two firm's integration abilities.
. We set the integration costs during the technology innovation process to be a simple version of what was used by Kaul & Wu ( ) in the form of C(IA) = td(IA) 2 .It satisfies C > 0 and C > 0. t is the average integration cost for complementary resources .We set the technology innovation profit R as: .
The first part is the multiplication of new innovation combination by the innovation output profit signal of the acquirer.As a whole, it stands for the innovation output revenue.
. So far, we have provided an innovation-signal-based global game analysis of merger and post-merger switching strategy, considering both the acquirer's and the target's resource backgrounds, especially resource similarity and resource complementarity.A flow diagram is given in Appendix B to better understand the model.In the next section, we will use the global game model as the foundation of our multi-agent simulation and in return use the simulation result to validate our findings in this section.

Multi Agent Simulation
Simulation environment setups and agent behaviors .The paper is based on NetLogo . ., and Figure provided a so ware graph.In the simulation environment, there is one target firm and one acquirer firm randomly distributed on * areas with their resource agents (i = 1, 2, . . .H, H > 15).We use a purple circle to represent acquirer agents and a red square for target agents.According to NetLogo so ware, there are color di erences between these two kinds of agents at the beginning.

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At the initialization, we give every agent a random number from uniform distribution U (0, 10) to represent their signals about the innovation profit.We use the parameters about integration revenue, resource backgrounds and integration costs to obtain a set of numerical simulations of θ A , θ B , xa and xb.Every time the agent randomly moved one step.Every simulation run lasts for time ticks, which is able to lead the model outputs into a stable state.Each time, all agents searched for the other firm's agents with one step distance and made merger or post-merger decisions with them.For all agents, if they were close within one step, we noted one encounter. .
During an encounter, the agents compared their own signals with the numerical θ.If their signal was larger than the numerical one, they started to merge, and we counted one positive encounter; otherwise, we counted one negative encounter.For every agent, we totaled the positive encounters and the negative encounters.These encounters could provide private information about the signal for the agents when they made post-merger decisions.In the post-merger decisions, if the encounter number was larger than the numerical one, the agents started to make an integration e ort and changed their color number by units ; otherwise, they did not make the e ort.A er making one integration e ort, they reset their encounter to .
. Integration is measured by agents' color-change proportion.A er each simulation, we calculated the acquirer's color-change proportion to be Ib and the target to be Is.Every time, we used and calculated Equation to get the integration degree I and Equation to get target autonomy level w as follows.Equation gives the search intensity s:

Simulation parameters setup .
As for the acquirer's gain r and the target's loss e from the integration of a similar resource, Banal-Estañol & Seldeslachts ( ) set the cost to be uniformly distributed in [ . , . ].In post-merger integration period, the integration of similar resource can be seen as a transformation of the resource from the target to the acquirer.Thus, the acquirer's gain r equals the target's loss e from the integration of similar resource.We set e = r ∈ U (0.25, 0.75).For the post-merger cost of complementary resource t1 and t2, as target company has comparative advantages in technology sourcing overseas M&A, in the process of integration complementary resources, the target company faced a small cost compared with the acquirer company and it was lower than its loss of integration of the similar resources.We set t2 < e by t2 ∈ U (0.01, 0.25).

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As for the integration cost of resource complementarity for the acquirer company t1 and the integration payo V , we consider the setups of the theoretical models: V + kr − dt1 < 0, V + kr − dt1 − dt2 < 0, V − ke − dt1 − dt2 < 0 and t1 > t2 with all the resource similarity [ , ] and resource complementarity [ , ] satisfied.In the equilibrium, the payo of integrating similar resources should be equal to integrating complementary resource.Taking k, d = 10, 2 for example, we have t1 > (V +7.5)/4 and 10 * (0.5+0.5) = 2 * (t1+0.12).We get t1 ≈ 5, < 12.We make post-merger integration costs have the same range.We set t1 ∈ U (4.75, 5.25).Furthermore with a report of BCG , the success ratio of overseas M&A in China is only % and post-merger integration is the main problems resulting in merger failures.The profits of those successful integrations should be higher or equal to the costs of the failed integration, which is V = 100/23Costs > 4 * Costs = 4(0.5 + 0.5 + 5 + 0.12)/4.That is V > 6.In short we set V ∈ U (7.5, 8.5).In the basic model of simulation, we set the calibration parameters to be the mean of the distribution: r = 0.5, e = 0.5, t1 = 5, t2 = 0.12 and V = 8.For the signal noise, we let l = 1.
. As for the initial resource of the two companies, recalling that in technology sourcing overseas M&A, target company has comparative advantages over acquirer company.We let H A ∈ U (18, 22) and H B ∈ U (23, 27).As for the merger costs, the acquirer company has a higher cost than the target company, so we let K A ∈ U (7, 9) and K B ∈ U (3, 5).
. In the basic model of simulation, we set the calibration parameters to be the mean of the distribution and we test the sensitivity of the parameters in the robustness check section, as part of Latin hypercube sampling analysis.
In Appendix C we provide a complete list of the value, distribution, and calibration in the basic simulation model of all parameters.
. We set the elasticity of innovation search and matching to be a function of the length of steps, f i, from one move in the simulation as f a 2 +f b 2 (f a+f b+1) 2 .In the simulation process we set the length of one move in one time tick to be ; hence, the elasticity parameter is equal to n = 2 9 .We let the parameter of searching intensity be a function of the post-merger integration cuto points as s = xa 2 +xb 2 (xa+xb+1) 2 .The more contacts and encounters the agents make, the larger the searching intensity would be.

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Figure provides the numerical simulation results of θ A , θ B , xa, xb, λ, and w in D form .As for λ, it moves in the same direction as resource similarity and is opposite of resource complementarity.From the graph, we can say the probability to integrate is the highest when resource similarity is high and resource complementarity is low.What is more, around those areas the curvature of the surface is the largest, and the surface is downward concave.The contour line of λ is upward sloping and divergent when resource similarity is high and resource complementarity is low, which means by increasing resource similarity and resource complementarity for one same unit the changes of λ becomes smaller.This suggests that resource similarity and resource complementarity have negative interaction e ects on integration probability.Similarly to w, it moves in the opposite direction of resource similarity and in the same direction as resource complementarity.The post-merger integration cuto point is lower when resource similarity increases and is higher when resource complementarity increases.So far, the simulation results match the comparative static in the theoretical model.

Multi-agent simulation results
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Once the parameters are set, we focus on analyzing how resource similarity and resource complementarity influence post-merger integration, target autonomy, and innovation profit.We run the model times using each set of parameters discussed below to account for stochastic variation and the output characteristics (such as mean and standard error).For each simulation, the run lasts for ticks.

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We give three di erent resource combinations to analyze agents' behaviors, as seen in Table .Figures -report the simulation results, the full line is mean of the runs and the dotted line is the range of one standard error.
. Figure reports innovation profit of the series.We can see the high-resource-similarity/low-resource-complementarity group has the lowest innovation profit level.The other two groups have rather high levels of innovation profit.
. Figure and report integration degree and target autonomy results.For integration degree, high-resourcesimilarity/low-resource-complementarity has a higher integration degree than the other two groups.Consid- ering target autonomy, there is no apparent di erence in the whole simulation period of the three groups since the ranges of plus/minus one standard error of the three groups have some degrees of overlaps.But considering the mean of the simulations, the low-resource-similarity high-resource-complementarity group has the highest target autonomy and the high-resource-similarity low-resource-complementarity group has the lowest target autonomy while high-resource-similarity high-resource-complementarity group has the medium autonomy level.

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We move on to find the optimal post-merger strategy under di erent resource backgrounds that maximize the innovation profit.Figures and report how innovation profit changes with integration degree and target autonomy.
. Now, we study the integration degree with the highest innovation profit in Figure .The high-resource-similarity low-resource-complementarity group reaches the highest innovation profit the fastest.Its optimal integration degree is around % with a highest innovation profit around . .The integration degree for high-resourcesimilarity / high-resource-complementarity is around % and low-resource-similarity / high-resource-complementarity is around % which matches the comparative static results and shows resource similarity and complementarity has negative interaction e ect on integration degree.
. As in Figure , for high-resource-similarity/low-resource-complementarity , as target autonomy increases the innovation profit decreases.But for the other two groups, as target autonomy increases, innovation profit first increases and later decreases.So the optimal target autonomy of the two groups are higher than high-resourcesimilarity/ low-resource-complementarity group.
. In sum, the simulation sections validate the comparative static results: In high-resource-similarity and lowresource-complementarity M&As, a high integration degree and low target autonomy will maximize innovation profit, while for the high-resource-similarity and high-resource-complementarity M&As, a medium-integration degree is best for innovation profit which shows the negative interaction e ect on integration degree.For lowresource-similarity and high-resource-complementarity M&As, a low integration degree and high target autonomy will be the best post-merger strategy.In addition, the high-resource-similarity / low-resource-complementarity group has the lowest innovation profit level.The other two groups have a rather high level of innovation profit.

Robustness Checks
. We consider the robustness of the model.We check in the following ways: First for the key parameters resource similarity and resource complementarity, we test whether the relationships of model outputs integration degree, target autonomy, innovation profit and resource backgrounds still remains when we change the resource background in their ranges with single factor variation.Second, as part of the parameters setups tests, we give the single parameter sensitivity test and global parameter sensitivity test as part of the Latin Hypercube Sampling uncertainty analysis.All the robustness checks are done with Behavior Space in NetLogo.
Robustness for key parameters: Resource similarity .
We set resource complementarity d = 4 and change resource similarity from k = 1 to k = 10.Figuresreport the integration degree, target autonomy, and innovation profits of the simulations.For every set of parameters, the model runs for times and we report the mean of the results.For each simulation, the run lasts for ticks. .
Figure shows that the contour line of integration degree leans toward high-resource-similarity side which means that the higher the resource similarity, the higher the integration degree.  .
Figure shows that the contour line of integration degree leans toward low resource complementarity, which means that the lower the resource complementarity, the higher the integration degree.Figure shows that as resource complementarity increases the contour line of target autonomy leans toward high resource complementarity which means when resource complementarity increases, the target autonomy increases.
. Table : Simulation key parameters setup target autonomy and innovation profit are small with the greatest variations in response to the following: Series to innovation profit: a higher initial resource of the target company increases innovation profit and a lower initial resource of the target decreases innovation profit.
Series to innovation profit: a higher merger cost of the acquirer company decreases innovation profit and a lower merging cost increases it.Series to target autonomy: a higher merger cost of the target company will increase the target autonomy level.

Latin hypercube sampling uncertainty test
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In this section we test how global changes of the parameters a ect model output.Latin hypercube sampling (Iman ) is suitable for testing the e ects of jointly variations of the parameters.Continuous parameters are supposed to be uniformly distributed and divided into same intervals to get sample points.For each hyper sample points we run the model for times and report the mean of the results.Considering there are parameters in our model and this will lead to 11 1 0 hypercube sample points which is too large for simulation runs so we divide the parameters into five groups: Group Initial resources: acquirer's resource HA, target's resource HB.Model runs , times.
Group Merger costs: acquirer's merger costs KA and target's merger costs KB.Model runs , times.
Group Post-merger costs: cost of integration complementary resource of acquirer t1 and complementary resource of target t2, loss of integration similar resource of target e.Model runs , times.
Group Post-merger benefits: payo s V , unit benefits of integration similar resource of the acquirer r.Model runs , times.
Group key parameters: resource similarity k and complementarity d.Model runs , times.
. Figure reports the results of Latin hypercube sampling tests.Group and Group have a large influence on integration degree.Merger costs and resource backgrounds also strongly influence output variations.Group merger cost has a large influence on target autonomy.Group initial resource, group merger cost, and group resource backgrounds have large influence on innovation profit.This indicates that merging cost, resource similarity, resource complementarity and initial resources should be well treated when making M&A and postmerger integration decisions.

Discussion and Conclusions
. Post-merger plays a key role in technology-sourcing overseas M&As.We tried a multi-agent simulation based on an innovation signal global game model.Through analyzing di erent resource groups, we obtain the optimal integration strategy that maximizes the innovation profits.
. We improve Banal-Estañol & Seldeslachts ( ) global model of M&A by introducing firm heterogeneity.We consider di erent payo s of the acquirer and the target companies.Compared with existing studies of M&A simulation with perspectives of cultural integration (Zhu et al. ) and organizational complexity (Frantz & Carley ), we combine global game model with multi-agent simulation to show repetitive emergent dynamics of merger and post-merger integration processes on the perspective of resource similarity and resource complementarity and furthermore study post-merger integration's e ect on innovation performance.

Limitations .
Due to lack of data of overseas post-merger integration, the model has the following limitations: First, most of the parameters are set according to existing literature and model setups together with sensitivity analysis.To overcome the complexity of the model and the limitation of data on real M&A cases, future analysis would benefit from more micro-data of the M&A surveys.Second, since the overseas M&As are heterogeneous, the merger costs or post-merger integration costs of di erent M&A cases would be very di erent, which makes the setting of parameter distribution a problem.Third, in our model, we set the parameter to be independently distributed, but in real cases some parameters may have correlations with each other and studying those parameters' joint distribution would further improve the study.

Future works .
In dealing with the theoretical model and multi-agent simulation, the paper may have some extensions as follows: First, we set the potential innovation signal to be exogenously decided between public information and private information.In fact, there are multiple chances that agents can obtain acquisition of information, and how they admire or evaluate that information is actually an endogenous process.Myatt & Wallace ( ) provided an innovative way to make the private or public level of the information endogenously decided by the agents instead of mechanically set via a binary choice.In future studies, we could take further steps to subdivide the resource in a similar or complementary way, which can provide di erent information channels that let the agents endogenously decide what kinds of resource similarity or resource complementarity he or she values the most.Moreover, we can relax the parameter constraints to allow more variable parameters in the simulation process instead of fixed ones.

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Second, more data based on actual M&A cases would improve the simulation model in this study.Our model only focuses on one kind of agent's behavior preference, contact with di erent resource agents.Other contacting or communication mechanisms could be added in future simulation frameworks, to make the e ect of resource similarity and resource complementarity on post-merger integration endogenously set in agents' behavior preference.
. Third, other research methods of M&A simulation such as a social network could be used in future analysis of post-merger integration study.Frantz ( ) suggest that post-merger integration rebuilds the social networks of the companies.A combination of social network analysis and agent-based modeling in future simulation study would provide a new insight for M&A studies.

Conclusions
. The paper draws the following conclusions: In technology sourcing overseas M&As, resource similarity has a positive relation with integration and a negative relation with target autonomy; however, resource complementarity and resource similarity have opposite e ects.The negative interaction between resource similarity and complementarity will decrease integration degree.In high-resource-similarity and low-resource-complementarity M&As, strong integration and low target autonomy will maximize innovation profit; meanwhile, for high-resourcesimilarity, high-resource-complementarity M&A, a medium integration degree and target autonomy is best for innovation profit.For low-resource-similarity, high-resource-complementarity M&As, a low integration degree and high target autonomy will be the best post-merger strategy.
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Notice that coordinate axis with -stands for resource similarity and that coordinate axis with -stands for resource complementarity.Axis of ordinates in the first graphs stands for innovation signal value, and axis of ordinates in the last two stands for probability.
We use Equations , , , in numerical simulation.Resource R i 's unit is agents which means R i = Hi 10 .The NetLogo code of our simulation can be found at http://mqs1991.lofter.com/

Figure :
Figure : The Agent-based Post-merger Global Game: The Netlogo Demonstration: The upper-le panel shows the user-supplied control parameters.The core parameters of our model is resource similarity k and resource complementarity named com in the sliders.The right panel is the parameters for sensitivity analysis.The middle upper panel gives the results of two companies' merger decision cuto points and post-merger integration cuto points, probability of integration and target autonomy.The middle lower panel give the monitors of four time series which are changes of resource Ib and Is, innovation profit, integration degree and target autonomy.

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Figure : Numerical simulation results in D form.

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Figure : Innovation profits simulation

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Figure : Innovation output's change with integration

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Figure : Robustness of resource similarity with Integration degree Figure shows that as resource similarity increases the contour line of target autonomy leans toward low resource similarity, which means when resource similarity increases, the target autonomy decreases.Figure shows that when resource similarity increases, innovation profits decrease.

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Figure : Robustness of resource similarity with Innovation profit

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Figure : Robustness of resource complementarity with target autonomy

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Figure : Sensitivity of integration degree, target autonomy and innovation profit: box plot show the mean, inter-quartile range and lower (blue)/ upper (green) bounds from simulation runs.

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Figure : Latin Hypercube sampling uncertainty analysis: box plot show the mean, inter-quartile range and lower(blue)/upper(green) bounds.